[Yufeng]

Shen Kuo or Shen Kua (Chinese: 沈括; Pinyin: Shěn Kuò) (1031–1095 AD) was a polymath Chinese scientist and statesman of the Song Dynasty (960–1279 AD). Excelling in many fields of study and statecraft, he was a mathematician, astronomer, meteorologist, geologist, zoologist, botanist, pharmacologist, agronomist, ethnographer, encyclopedist, poet, general, diplomat, hydraulic engineer, inventor, academy chancellor, finance minister, and governmental state inspector. He was the head official for the Bureau of Astronomy in the Song court, as well as an Assistant Minister of Imperial Hospitality.[1] At court his political allegiance was to the Reformist party of the New Policies Group, headed by Chancellor Wang Anshi (王安石; 1021-1086).

In his Dream Pool Essays (梦溪笔谈; 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).[2][3] Kuo also discovered the concept of true north in terms of magnetic declination towards the north pole,[3] with experimentation of suspended magnetic needles and “the improved meridian determined by Shen’s [astronomical] measurement of the distance between the polestar and true north”.[4] This was the decisive step in human history to make compasses more useful for navigation, and was a concept unknown in Europe for another four hundred years.[5] Alongside his colleague Wei Pu (衛朴), Shen accurately mapped the orbital paths of the moon and the planets, in an intensive five-year project that rivaled the later work of the Danish astronomer Tycho Brahe (1546–1601).[6] To aid his work in astronomy, Shen Kuo made improved designs of the armillary sphere, gnomon, sighting tube, and invented a new type of inflow clepsydra clock. Shen Kuo devised a geological theory of land formation, or geomorphology, based upon findings of inland marine fossils, knowledge of soil erosion, and the deposition of silt.[7] He also advocated a theory for gradual climate change, after observing ancient petrified bamboos that were preserved underground in a dry northern habitat that did not support their growth in his time. He was the first literary figure in China to mention the use of the drydock to repair boats suspended out of water, and also wrote of the effectiveness of the relatively new invention of the canal pound lock. Shen Kuo wrote extensively about movable type printing invented by Bi Sheng (畢昇; 990–1051), and because of his written works the legacy of Bi Sheng and the modern understanding of the earliest movable type has been handed down to later generations

Birth and youth
Shen Kuo was born in Qiantang (modern-day Hangzhou) in the year 1031. His father Shen Zhou (沈周; 978–1052) was a somewhat lower-class gentry figure serving in minor posts on the provincial level; his mother was from a family of equal status in Suzhou, with her maiden name being Xu (許).[9] Kuo received his initial childhood education from his mother, which was a common practice in China during this period.[9]a[›] She was very educated herself, teaching Kuo and his brother Pi (披) the military doctrines of her own elder brother Xu Tang (許洞; 975–1016).[9] Since Shen was unable to boast of prominent familial clan history like many of his elite peers born in the north, he was forced to rely on his wit and stern determination of achievement in his studies to enter the challenging and sophisticated life of an exam-drafted state bureaucrat.[9]

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 territory.[10] Shen Zhou also served several years in the prestigious capital judiciary, the equivalent of a federal supreme court.[9] Shen Kuo took notice of the various towns and rural features of China as his family traveled, while Kuo became interested during his youth in the diverse topography of the land.[10] He also observed the intriguing aspects of his father's engagement in administrative governance and the managerial problems involved in governance; experiences which would have a deep impact upon Kuo as he later became a government official.[10] Since he often became ill as a child, Shen Kuo also developed a natural curiosity for medicine and pharmaceutical knowledge.[10]

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 Confucian ethics, remained inactive in a state of mourning for three years until 1054 (or early 1055).[11] As of 1054, Shen began serving in minor, local governmental posts. However, his natural abilities to plan, organize, and design were proven early in life; one example is his design and supervision of the hydraulic drainage of an embankment system, which converted some one hundred thousand acres of swampland into prime farmland.[11] Shen Kuo noted in his writing that the success of the silt fertilization method relied upon the effective operation of sluice gates of irrigation canals.[12]


Career and later life
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.[11] He not only passed the exam, however, but placed into the higher category of the best and brightest students.[11] 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.[11] Shen would also eventually marry Zhang's daughter, who became his second wife.

In his career as a scholar-official for the central government, Shen Kuo was also an ambassador to the Western Xia Dynasty and Liao Dynasty,[13] a military commander, a director of hydraulic works, and the leading chancellor of the Hanlin Academy.[14] By 1072, Shen was appointed as the head official of the Bureau of Astronomy.[11] With his leadership position in the bureau, Shen was responsible for projects in improving calendrical science,[8] and proposed many reforms to the Chinese calendar alongside the work of his colleague Wei Pu (衛朴).[6] With his impressive skills and aptitude for matters of economy and finance, Shen was appointed as the Finance Commissioner at the central court.[15] 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 collections, negligence, ineffective disaster relief, and inadequate water-conservancy projects.[16] Shen Kuo was also awarded the honorary title of a State Foundation Viscount by Emperor Shenzong of Song (神宗; r. 1067–1085), who placed a great amount of trust in Shen Kuo.[15]

At court Shen was a political favorite of the Chancellor Wang Anshi (王安石; 1021–1086), who was the leader of the political faction of Reformers, also known as the New Policies Group (新法, Xin Fa).[17]b[›] Shen Kuo had a previous history with Wang Anshi, since it was Wang who had composed the funerary epitaph for Kuo's father.[18] Shen Kuo soon impressed Wang Anshi with his skills and abilities as an administrator and government agent. In 1072, Shen was sent to supervise Wang's program of surveying the building of silt deposits in the Bian Canal outside the capital city. Using an original technique, Shen successfuly dredged the canal and demonstrated the formidable value of the silt gathered as a fertilizer.[18] He gained further reputation at court once he was dispatched as an envoy to the Khitan Liao Dynasty in the summer of 1075.[18] The Khitans had made several aggressive negotiations of pushing their borders south, while manipulating several incompetent Chinese ambassadors who conceded to the Liao Kingdom's demands.[18] In a brilliant display of diplomacy, Shen Kuo came to the camp of the Khitan monarch at Mt. Yongan (near modern Pingquan, Hebei), armed with copies of previously archived diplomatic negotiations between the Song and Liao dynasties.[18] Shen Kuo refuted the Khitan ruler's bluffs point for point, while the Song reestablished their rightful border line.[18] With these reputable achievements, Shen became a trusted member of Wang Anshi's elite circle of eighteen unofficial core political loyalists to the New Policies Group.[18]

Although much of Wang Anshi's reforms outlined in the New Policies centered around state finance, land tax reform, and the Imperial examinations, there were also military concerns. This included policies of raising militias to lessen the expense of upholding a million soldiers,[19] putting government monopolies on saltpetre and sulphur production and distribution in 1076 AD (to ensure that gunpowder solutions would not fall into the hands of enemies),[20][21] and aggressive military policy towards China's northern rivals of the Western Xia and Liao dynasties.[22] A few years after Song Dynasty military forces had made victorious territorial gains against the Tanguts of the Western Xia, in 1080 Shen Kuo was entrusted as a military officer in defense of Yanzhou (modern-day Yan'an, Shaanxi province).[23] During the autumn months of 1081, Shen was successful in defending Song Dynasty territory while capturing several fortified towns of the Western Xia.[15] The Emperor Shenzong of Song rewarded Shen with numerous titles for his merit in these battles, and in the sixteen months of Shen's military campaign, he received 273 letters from the Emperor.[15] However, Emperor Shenzong trusted an arrogant military officer that 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.[15] The result of this was nearly catastrophic, as the forces of the arrogant officer were decimated. Nonetheless, Shen was successful in defending his fortifications and the only possible Tangut invasion-route to Yanzhou.[15]

However, the new Chancellor Cai Que (蔡確; 1036–1093) held Shen responsible for the disaster and loss of life.[15] Along with abandoning the territory which Shen Kuo had fought for, Cai ousted Shen from his seat of office.[15] Shen's life was now forever changed, as he lost his once reputable and fruitful career in state governance and the military.[15] Shen was then put under probation in a fixed residence for the next six years. However, as he was isolated from governance, he decided to pick up the quill and dedicate himself to intensive scholarly studies. After completing two 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.[15] Shen was also pardoned by the court for any previous faults or crimes claimed against him.[15]

According to Zhu Yu's book Pingzhou Table Talks (萍洲可談; Pingzhou Ketan) of 1119 AD, Shen Kuo had two marriages; the second wife was the daughter of Zhang Chu (張蒭), who came from Huainan. Lady Zhang was said to be overbearing and fierce, often abusive to Shen Kuo, even attempting at one time to pull off his beard. Shen Kuo's children were often upset over this, and prostrated to Lady Zhang to quit this behavior. Despite this, Lady Zhang went as far as to drive out Shen Kuo's son from his first marriage, expelling him from the household. However, after Lady Zhang died, Shen Kuo fell into a deep depression and even attempted to jump into the Yangtze River to drown himself. Although this suicide attempt failed, he would die a year later.

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.[15] 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 Mengxi Bitan (梦溪笔谈; Dream Pool Essays), naming the book after his garden-estate property. This book was Shen's ultimate attempt to comprehend and describe a multitude of various aspects of nature, science, and reality, and all the practical and profound curiosities found in the world. The literal translation of Mengxi Bitan is Dream Brook Brush Talks. For this, Shen Kuo is quoted as saying:

Because I had only my writing brush and ink slab to converse with, I call it Brush Talks.c[›]
It was there at his peaceful garden estate that Shen Kuo spent the last several years of his life in leisure, isolation, and illness, until his death in 1095.[15]

Scholarly achievements
Shen Kuo wrote extensively on a wide range of different subjects. His written work included two geographical atlases, a treatise on music with mathematical harmonics, governmental administration, mathematical astronomy, astronomical instruments, martial defensive tactics and fortifications, painting, tea, medicine, and was a profuse writer of poetry.[24] Shen's largest atlas included twenty three maps of China and foreign regions that were drawn at a uniform scale of 1:900,000.[4] Shen also created a three dimensional raised-relief map using sawdust, wood, beeswax, and wheat paste.[4] In terms of meteorology, Shen wrote vivid descriptions of tornadoes, and gave reasoning (earlier proposed by Sun Sikong) that rainbows were formed by the shadow of the sun in rain, occurring when the sun would shine upon it.[25] Shen believed that, although trees were a growing scarcity due to the needs of the iron industry, "petroleum is produced inexhaustibly within the earth".[25]g[›] For pharmacology, Shen wrote of the difficulties of adequate diagnosis and therapy, as well as the proper selection, preparation, and administration of drugs.[26] In the realm of botany and zoology, Shen Kuo documented and systematically described hundreds of different plants, agricultural crops, rare vegitation, and animals found in China.[27][28][29] Furthermore, Shen Kuo described the phenomena of natural predator insects controlling the population of pest infestations, the latter of which had the potential to wreak havoc upon the agricultural base of China.[30]

Without the writing of Shen Kuo, the date which the drydock was first used in China would have remained unknown and uncertain. Shen Kuo wrote that in the Xi-Ning reign period (1068–1077 AD) the court official Huang Huaixin devised a plan on how to repair 200 ft. long, lavish, palatial boats that were a century old and in need of repair; essentially, Huang Huaixin devised the first use of the drydock in China, and afterwards these boats were placed in a roof-covered dock warehouse to protect them from weathering.[31] Shen Kuo also wrote about the effectiveness of a relatively new invention (i.e. by the 10th century engineer Qiao Weiyo) of the pound lock to replace the old flash lock design used in canals. He wrote that it saved the work of five hundred annual labors, annual costs of up to 1,250,000 strings of cash, and instead of hauling boats of smaller size (hence lighter cargo of only 21 tons/21337 kg), the pound lock allowed canal traffic of large government-owned ships holding cargo weight of up to 700 tan (49½ tons/50294 kg) and large privately-owned ships holding cargo weight of up to 1600 tan (113 tons/114813 kg).[32]

Along with the introduction of the drydock, if it were not for Shen Kuo's extensive analysis and quoting of the written work of the 10th century architect Yu Hao, the latter's work would have been lost to history.[33]d[›] The preserved writing of Yu Hao in Shen Kuo's Dream Pool Essays is even more valuable considering the fact that Yu Hao's famed wooden Chinese pagoda was burnt down by lightning in 1044 AD, replaced by a brick-built pagoda tower of similar height, the Iron Pagoda of 1049 AD.

Shen Kuo's scientific literature has often been compared to that of his equally brilliant contemporary Su Song (1020–1101), the mechanical genius who incorporated a waterwheel, clepsydra, escapement mechanism, and chain drive to operate the orrery and armillary sphere of his astronomical clock tower. Shen Kuo has also been compared to many Western intellectual achievers and polymaths, such as Gottfried Leibniz and Mikhail Lomonosov.[34]


Mathematics
In the broad field of mathematics, Shen Kuo mastered many practical mathematical problems, including many complex formulas for geometry,[35] 'packing' equations for calculus,[36] and chords and arcs problems employing trigonometry.[37] He 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.[38] Shen once computed the amount of terrain space required for battle formations in military strategy,[39] 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.[40] Shen Kuo experimented with the pinhole camera and burning mirror as the ancient Chinese Mohists had done in the 4th century BC. Although the Iraqi Muslim scientist Ibn al-Haitham (965-1039 AD) was the first to experiment with camera obscura, Shen Kuo was the first to apply geometrical and quantitative attributes to the camera obscura, just several decades after Ibn al-Haitham's death.[41] Shen wrote about the earlier Yi Xing (一行; 672–717 AD), a Buddhist monk who applied an early escapement mechanism to a water-powered celestial globe. 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.[42][43] However, some of his most impressive written work in mathematics would be applied to his work in astronomy.

Magnetic needle compass

A Han Dynasty (202 BC–220 AD) ladle-and-basin lodestone south-pointing compass, used by ancient Chinese geomancers, but not for navigation.Since the time of the engineer and inventor Ma Jun (馬鈞, c. 200–265 AD), the Chinese had used a mechanical device known as the South Pointing Chariot in order to navigate on land (and possibly at sea, as the Song Shu text of c. 500 AD alludes). This device was especially impressive, since it featured the use of a differential gear, an essential component used in the correct steering and application of equal amount of torque for the wheels of all modern automobiles. In 1044 AD the famous Wujing Zongyao (武经总要; "Collection of the Most Important Military Techniques") 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.[44][45]

However, it was not until the time of Shen Kuo that the earliest magnetic compasses would be used for navigation. In his written work, Shen Kuo made one of the first references in human history to the magnetic compass-needle, the concept of true north, and its use for navigation at sea.[14] He wrote that needles were magnetized once they were rubbed with lodestone, were put in floating position or in mountings, described the suspended compass as the best form to be used, and noted that the magnetic needle of compasses pointed either south or north.[44] Shen Kuo asserted that:

"[The magnetic needles] are always displaced slightly east rather than pointing due south".[44]

Shen Kuo wrote that it was preferable to use the twenty-four-point rose instead of the old eight compass cardinal points, as the former was recorded in use for navigation shortly after Shen's death.[4] The preference of use for the twenty-four-point-rose compass was under the stimulus of Shen's finding of a more accurate astronomical meridian, determined by his measurement between the polestar and true north.[4] However, it could also have been inspired by geomantic beliefs and practices.[4] The book of the Chinese author Zhu Yu, the Pingzhou Table Talks (萍洲可談, Pingzhou Ketan) published in 1119 AD (written from 1111 to 1117 AD), was the first actual recorded use of a compass for seafaring navigation. However, the accounts of Zhu Yu's book went back to events in 1086 AD, when Shen Kuo was writing the Dream Pool Essays; this meant that in Shen's time the compass could have already been used for actual navigation.[46] In any case, Shen Kuo's writing on magnetic compasses proved invaluable for the understanding of China's earliest seafaring navigation by use of the compass.


Geological theory
Long before Shen Kuo, the ancient Greek Aristotle (384 BC–322 BC) wrote of how the earth had the potential for physical change. The Greek writer Xenophanes (570 BC–480 BC) wrote of how inland marine fossils were evidence that massive periodic flooding had wiped out mankind several times in the past, but never wrote of land formation or shifting seashores.[47] The later Persian Muslim scholar Abū al-Rayhān al-Bīrūnī (973–1048 AD) hypothesized that India was once covered by the Indian Ocean while observing rock formations at the mouths of rivers.[48] However, it was Shen Kuo who formulated a hypothesis for the process of land formation (geomorphology). This was based on his observation of fossil shells in a geological stratum of a mountain hundreds of miles from the ocean. He inferred that the land was reshaped and formed by soil erosion of the mountains, uplift, and the deposition of silt, after observing strange natural erosions of the Taihang Mountains and the Yandang Mountain near Wenzhou.[49] He hypothesized that, with the inundation of silt, the land of the continent must have been formed over an enormous span of time.[50] While visiting the Taihang Mountains in 1074 AD, Shen Kuo noticed strata of bivalve shells and ovoid rocks in a horizontal-running span through a cliff like a large belt.[50] Shen proposed that the cliff was once the location of an ancient seashore that by his time had shifted hundreds of miles east.[50] Shen wrote that in the Zhi-Ping reign period (1064–1067 AD) a man of Zezhou unearthed an object in his garden that looked like a serpent or dragon, and after examining it, the dead animal had apparently turned to "stone".[51][52] The magistrate of Jincheng, Zheng Boshun, examined the creature as well, and noted the exact scale-like markings that were seen on other marine animals.[51][52] Shen Kuo likened this account with the 'stone crabs' found in China.[51][52]

Shen also wrote that since petrified bamboos were found underground in a climate area where they were never known to be grown, geographical climates naturally shifted over time.[52][53] Around the year 1080, Shen Kuo noted that a landslide on the bank of a large river near Yanzhou (modern Yan'an) had revealed an open space of several dozens of feet under the ground once the bank collapsed.[52][53] This underground space revealed hundreds of petrified bamboos still intact with roots and trunks, "all turned to stone" as Shen Kuo wrote.[52][53] Shen Kuo noted that bamboos do not grow in Yanzhou, located in northern China, and he was puzzled as to which previous dynasty the bamboos could have grown.[52][53] Considering that low places of damp and gloomy attributes provide suitable conditions for the growth of bamboos, Shen believed that the climate of Yanzhou must have fit that description in very ancient times.[52][53]

The philosopher Zhu Xi (朱熹; 1130-1200 AD) wrote of this curious natural phenomena of fossils as well, and was known to have read the works of Shen Kuo.[52] Shen's description of soil erosion and weathering predated that of Georgius Agricola's work of 1546, De veteribus et novis metallis.[54] Furthermore, Shen's theory of sedimentary deposition predated that of James Hutton, who wrote his groundbreaking work in 1802 (considered the foundation of modern geology).[54] The historian Joseph Needham likened Shen's account in Yanzhou with the Scottish scientist Roderick Murchison (1792–1871), who was inspired to become a geologist after observing a providential landslide.

Astronomy
Being the head official for the Bureau of Astronomy, Shen Kuo was an avid scholar of medieval astronomy, and improved the designs of several astronomical instruments. Shen is credited with making improved designs of the gnomon, armillary sphere, and clepsydra clock.[55] For the clepsydra he designed a new overflow-tank type, and argued for a more efficient higher-order interpolation instead of linear interpolation in calibrating the measure of time.[55] Improving the 5th century model of the astronomical sighting tube, Shen Kuo widened its diameter so that the new calibration could observe the polestar indefinitely.[55] This came about due to the position of the polestar shifting in position since the time of Zu Geng in the 5th century, hence Shen Kuo diligently observed the course of the polestar for three months, plotting the data of its course and coming to the conclusion that it had shifted slightly over three degrees.[55] Apparently this astronomical finding had an impact upon the intellectual community in China at the time. Even Shen's political rival and contemporary astronomer Su Song featured Shen's corrected position of the polestar (halfway between Tian shu, at -350 degrees, and the current Polaris) in the fourth star map of his celestial atlas.[56] Along with his colleague Wei Pu in the Bureau of Astronomy, Shen Kuo plotted out exact coordinates of planetary and lunar movements by recording their astronomical observations three times a night for a continuum of five years.[6] Although star maps were created then and in previous times, an extensively long and time-consuming method of astronomical observation on the scale of Shen Kuo and Wei Pu's project was not proposed in Europe until the time of the astronomer Tycho Brahe (1546–1601 AD).[6]

The astronomical phenomena of the solar eclipse and lunar eclipse had been known in China since at least the time of the astronomers Gan De (甘德; fl. 4th century BC) and Shi Shen (石申; fl. 4th century BC)[57] The philosopher Wang Chong (王充; 27–97 AD) and astronomer Zhang Heng (張衡; 78–139 AD) both wrote of 'radiation influence' theories for solar and lunar eclipse, as Zhang Heng correctly hypothesized that the brightness of the moon was merely light reflected from the sun.[58] Shen Kuo also wrote of solar and lunar eclipses, yet expanded upon this to explain why the celestial bodies were spherical, going against the flat earth theory for celestial bodies.[59] When Zhao Wen, the Director of the Astronomical Observatory, asked Shen Kuo if the shapes of the sun and moon were round like balls or flat like fans, Shen Kuo explained that celestial bodies were spherical because of knowledge of waxing and waning of the moon.[59] Much like what Zhang Heng had said, Shen Kuo likened the moon to a ball of silver, which does not produce light, but simply reflects light if provided from another source (the sun).[59] He explained that when the sun's light is slanting, the moon appears full.[59] He then explained if one were to cover any sort of sphere with white powder, and then viewed from the side it would appear to be a crescent, hence he reasoned that celestial bodies were spherical.[59] He also wrote that, although the sun and moon were in conjunction and opposition with each other once a day, this did not mean the sun would be eclipsed every time their paths met, because of the obliquity by a small degree of their orbital paths.[59]

Shen Kuo is also known for his cosmological hypotheses in explaining the variations of planetary motions, including retrogradation.[60] His colleague Wei Pu realized that the old calculation technique for the mean sun was inaccurate compared to the apparent sun, since the latter was ahead of it in the accelerated phase of motion, and behind it in the retarded phase.[61] Shen's hypotheses were similar to the concept of the epicycle in the Greco-Roman tradition,[60] only Shen compared the side-section of orbital paths of planets to the shape of a willow leaf.[62] Shen's work and theory of planetary motion can also be compared to the Persian astronomer Nasir al-Din al-Tusi (1201–1274 AD), who wrote the Zij-i Ilkhani.

The Song Dynasty astronomers of Shen's day still retained the lunar theory and coordinates of the earlier Yi Xing, which after 350 years had devolved into a state of considerable error.[6] To fix this, Shen and Wei kept similar astronomical records for the moon as they did the planets, plotting its course down three times a night for five successive years.[6] Wei and Shen's work was deeply opposed by the officials and fellow astronomers at court, who were offended by their insistence that the coordinates of the renowned Yi Xing were inaccurate.[63] When Wei and Shen made a public demonstration using the gnomon to prove the doubtful wrong, the other ministers reluctantly agreed to correct the lunar error.[63] Although correcting the lunar error was a success, the other ministers and officials eventually dismissed Wei and Shen's recorded course plotting of planetary motions, while the court relied upon the inefficient and older model for them.[18]

Movable type printing
Shen Kuo wrote that during the Qing-li reign period (1041–1048 AD), under Emperor Renzong of Song (仁宗; 1022–1063), an obscure commoner and artisan known as Bi Sheng (毕升; 990–1051) invented ceramic movable type printing.[64] Although the use of assembling individual characters to compose a piece of text had its origins in antiquity, Bi Sheng's methodical innovation was something completely revolutionary for his time. Shen Kuo noted that the process was tedious if one only wanted to print a few copies of a book, but if one desired to make hundreds or thousands of copies, the process was incredibly fast and efficient.[64] Beyond Shen Kuo's writing, however, nothing is known of Bi Sheng's life or the influence of movable type in his own day.[65] Although the details of his life were scarcely known, Shen Kuo wrote "When Bi Sheng died, his fount of type passed into the possession of my followers, among whom it has been kept as a precious possession until now."[1] With this statement, it becomes apparent that prominent Chinese scholars and elite men of letters such as Shen Kuo were capable of gathering a considerable entourage of aiding technicians.[1]

Use of movable type in China was extended into later periods. Yao Shu (1201–1278 AD), an advisor to Kublai Khan, once persuaded a disciple Yang Gu to print philological primers and Neo-Confucian texts by using what he termed the "movable type of Shen Kuo".[66] Wang Zhen (王禎; fl. 1290–1333 AD), who wrote the valuable agricultural, scientific, and technological treatise of the Nong Shu, mentioned an alternative method of baking earthenware type with earthenware frame in order to make whole blocks.[66] Wang Zhen also improved its use by inventing wooden movable type in the years 1297 or 1298, while he was a magistrate of Jingde, Anhui province.[67] The earlier Bi Sheng had experimented with wooden movable type,[68] but Wang's main contribution was improving the speed of typesetting with simple mechanical devices, along with the complex, systematic arrangement of wooden movable types involving the use of revolving tables.[69] Although later metal movable type would be used in China, Wang Zhen experimented with tin metal movable type, but found its use to be inefficient.[70]

By the 15th century, metal movable type printing was developed in Ming Dynasty China (and earlier in Joseon Korea, by the mid 13th century), and was widely applied in China by at least the 16th century.[71] In Jiangsu and Fujian, wealthy Ming era families sponsored the use of metal type printing (mostly using bronze). This included the printing works of Hua Sui (1439–1513), who pioneered the first Chinese bronze-type movable printing in 1490 AD.[72] In 1718, during the later Qing Dynasty (1644–1911), the scholar of Tai'an known as Xu Zhiding developed movable type with enamelware instead of earthenware.[66] There was also Zhai Jinsheng (b. 1784), a teacher of Jingxian, Anhui, who spent thirty years making a font of earthenware movable type, and by 1844 he had over 100,000 Chinese writing characters in five sizes.[66]

Despite these advances, movable type printing never gained the amount of widespread use in East Asia that woodblock printing had achieved since the Chinese Tang Dynasty in the 9th century. With written Chinese, the vast amount of written morpheme characters impeded movable type's acceptance and practical use, and was therefore seen as largely unsatisfactory.[64] Furthermore, the European printing press, first invented by Johannes Gutenberg (1398–1468), was eventually wholly adopted as the standard in China, yet the tradition of woodblock printing remains popular in East Asian countries still.

Personal beliefs and philosophy
Shen Kuo's writing was not all scientific or practical, however. Besides his writing on Chinese divination, magic, and folklore, Shen Kuo was also an art critic. For example, he criticized the work of the painter Li Cheng for failing to observe the principle of "seeing the small from the viewpoint of the large" in portraying buildings and the like.[73] Despite all of his scientific achievements, Shen Kuo was much in favor of philosophical Daoist notions which challenged the authority of empirical science in his day. Although much could be discerned through empirical observation and recorded study, Daoism asserted that the secrets of the universe were boundless, something that scientific investigation could merely express in fragments and partial understandings.[74] Shen Kuo referred to the ancient Daoist Book of Changes in explaining the spiritual processes and attainment of foreknowledge that cannot be attained through "crude traces", which he likens to mathematical astronomy.[74]

Dream Pool Essays
As the historian Chen Dengyuan points out, much of Shen Kuo's written work was probably purged under the leadership of minister Cai Jing (蔡京; 1046–1126), who revived the New Policies of Wang Anshi, although he set out on a campaign of attrition to destroy or radically alter the written work of his predecessors and especially Conservative enemies.[75] For example, only six of Shen's books remain, and four of these have been significantly altered since the time they were penned by the author.[76] The Dream Pool Essays was first quoted in a Chinese written work of 1095 AD, showing that even towards the end of Shen's life his final book was becoming widely printed.[77] Shen Kuo's Dream Pool Essays consists of some 507 separate essays exploring a wide range of subjects.[78] The book was originally 30 chapters long, yet an unknown Chinese author's edition of 1166 AD edited and reorganized the work into 26 chapters.[77] There is one surviving copy of this 1166 edition housed now in Japan, while a Chinese reprint was produced in 1305 as well.[77] In 1631 another edition was printed, but it was heavily reorganized into three broad chapter.[77] In the Chiwuming Shitukao (Illustrated Investigations of the Names and Natures of Plants) book of 1848, written material of Shen's Mengxi Bitan is mentioned often, such as classifications of plant species.[27]

In modern times, the best attempt at a complete list and summary of Shen's writing was an appendix written by Hu Daojing in his standard edition of Brush Talks, written in 1956.[75] Of the 1166 Chinese edition, it was accurately translated into Japanese by the History of Science Seminar, Institute for Research in Humanities (Jimbun Kagaku Kenkyusho) for Kyoto University, printed by the author Umehara Kaoru in his 3 volume edition of Bokei hitsudan (1978–1981).[79] Selected translations of the Dream Pool Essays from Middle Chinese into modern Vernacular Chinese was made by Zhang Jia Ju's biographical work Shen Kuo (1962). Zhang's biography on Shen is of great importantance as it contains, according to the historian Nathan Sivin, the fullest and most accurate account of Shen Kuo's life.[79] The largest amount of selected translations in English for the Dream Pool Essays are found in various volumes of Joseph Needham's Science and Civilization in China series, from 1954 onwards.[79] In French, quoted excerpts from the Dream Pool Essays were printed in the written work of J. Brenier e[›] as well as J. F. Billeter.f[›]

Other written works
Although the Dream Pool Essays is certainly his most extensive and important work, Shen Kuo wrote other books as well. In 1075, Shen Kuo wrote the Xining Fengyuan Li (熙寧奉元曆; The Oblatory Epoch astronomical system of the Splendid Peace reign period), which was lost, but listed in a 7th chapter of a Song Dynasty bibliography.[80] This was the official report of Shen Kuo on his reforms of the Chinese calendar, which were only partially adopted by the Song court's official calendar system.[80] Shen Kuo wrote a pharmaceutical treatise known as the Liang Fang (良方; Good medicinal formulas), compiled sometime during his years of retirement from governmental service.[81] Around the year 1126 AD it was combined into a written work of the famous Su Shi (苏轼; 1036–1101 AD), who was ironically a political opponent to Shen Kuo's faction of Reformers and New Policies supporters at court,[81] yet it was known that Shen Kuo and Su Shi were nonetheless friends and associates.[82] Shen wrote the Mengqi Wanghuai Lu (夢溪忘懷錄; Record of longings forgotten at Dream Brook), compiled during Shen's retirement as well. This book was a treatise in the working since his youth on rural life and ethnographic accounts of living conditions in the isolated mountain regions of China.[83] Only quotations of it survive in the Shuo Fu (說郛) collection, which mostly describe the agricultural implements and tools used by rural people in high mountain regions. Shen Kuo also wrote the Changxing Ji (長興集; Collected Literary Works of [the Viscount of] Changxing). However, this book was without much doubt a posthumous collection, including various poems, prose, and administrative documents written by Shen.[83] By the 15th century (during the Ming Dynasty), this book was reprinted, yet only the 19th chapter remained.[83] This chapter was reprinted in 1718, yet poorly edited.[83] Finally, in the 1950s the author Hu Daojing supplemented this small yet valuable work with additions of other scattered poems written by Shen, in the former's Collection of Shen Kua's Extant Poetry (Shanghai: Shang-hai Shu-tian, 1958).[83]

Legacy
Upon his death, Shen Kuo was interred at a tomb in Yuhang District of Hangzhou, at the foot of the Taiping Hill.[84] His tomb was eventually destroyed, yet Ming Dynasty records indicated and provided clue of his tomb's location, found in 1983 and protected as a governmental site in 1986.[84] The Hangzhou Municipal Committee completed a restoration of Shen's tomb in September of 2001, and although it had fallen into dilapidation, the remnants of the tomb's brick structure remained, along with discovery of Song Dynasty glasswares and coins.[84] In addition to his tomb, Shen Kuo's Mengxi garden estate, his former two-acre property in Zhenjiang, was restored by the government in 1985.[85] However, the renovated Mengxi Garden is only part of the original found in Shen Kuo's time.[86] A Qing Dynasty era hall built on the site is now used as the main gate of admissions for visitors and tourists.[85] In the Memorial Hall of the gardens, there is a large painting depicting the original garden of Shen Kuo's time, including wells, green bamboo groves, stone-paved paths, and decorated walls of the original halls.[86] At the garden estate there are marble banners on display, erected statues of Shen Kuo, along with a model of an armillary sphere and a small museum gallery displaying Shen's various achievements.[85] In this exhibition hall there stands a 1.4 m (4.6 ft) tall statue of Shen Kuo sitting on a platform, along with centuries-old published copies of his Dream Pool Essays viewable behind glass cabinets, which includes an old Japanese publication of his written work as well.[86]

The Chinese Mount Zijinshan Observatory had discovered a new planetoid in 1964, and in 1979 the Chinese Academy of Sciences decided to honor Shen by listing "Shen Kuo" as one of the planetoid's many names.


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[Yufeng]

Shen Kua

Shen Kua 沈括 was the most prominent of the polymathic statesmen who flourished in the Northern Sung. He was born in 1031, with registration at Ch’ien-t’ang 錢塘 [now Hangchow, Chekiang province], China, and died at Ching-k’ou 京口, Jun prefecture 潤州 (now Chinkiang, Kiangsu province) in 1095.

Shen was the son of Shen Chou 沈周 (ca. 978–1052) and his wife, whose maiden name was Hsu 許. Shen Chou came of a gentry family with neither large landholdings nor an unbroken tradition of civil service. He spent his life in minor provincial posts, with several years in the capital judiciary. Shen Kua apparently, like a number of other important southern intellectuals of his time, received his early education from his mother. A native of Soochow, known for its flourishing manufactures, commerce, and agriculture, she was forty-four or forty-five years old when he was born. Among other things, she taught him and his brother P’i 披 the military doctrines of her elder brother Hsu Tung 許洞 (ca. 976–ca. 1016).

Shen’s background made it possible for him to enter the imperial bureaucracy, the only conventional road to advancement for educated people of his time. Unlike colleagues who came from the ancient great clans, he could count on few advantages save those earned by his striving and the full use of his talents. Shortly after he was assigned to the court, he became a confidant of the emperor and played a brilliant part in resolving the crises of the time. Within slightly over a decade, his career in the capital was ended by impeachment. After exemplary service in a provincial appointment and five years of meritorious military accomplishment, he was doubly disgraced and politically burnt out. The extremes of Shen’s career and the shaping of his experience in science and technology become comprehensible only if the pivotal circumstances of his time are first considered.

Historical Setting

Shen’s time was the climax of a major transition in the Chinese polity, society, and economy.

Three centuries earlier the center of gravity in all these respects still lay in the north, the old center of civilization of the Han people. Wealth and power rested in the hands of the old aristocratic land-owning families. Governmental institutions could not resolve the tension between civil servants’ private interests and the emperor’s inevitable desire to concentrate authority. The civil service examination system was beginning to let the central government shape a uniform education for its future officials. Since birth or local recommendation determined who was tested, the mass of commoners were not involved. The social ideals prevalent among the elite were static; the ideal past was cited to discourage innovation; and the moral example of those who ruled, rather than responsive institutions or prescriptive law, was held to be the key to the healthy state. The classicist’s ideal of a two-class society—
self-sufficient agriculturalists ruled and civilized by humane generalists, with land as the only true wealth—did not encourage commerce, industry, or the exploitation of natural resources. The wants of the great families, whose civil servant members were becoming city dwellers by the middle of the eighth century, nonetheless gave momentum to all of these activities. The rural majority of the population still took no part in the rudimentary money economy.

The T’ang order began a long, slow collapse about 750, until in the first half of the tenth century the empire of "All under Heaven" was reduced to a jumble of ephemeral and competing kingdoms. When the Northern Sung rebuilt the universal state (960–1126), its foundations were in many important respects different from those of the early T’ang. A new dynasty was not only, as classical monarchic theory had it, a fresh dispensation of the cosmos; it was also the occasion for institutionalizing a new distribution of power in society. Changes in taxation made the old families accountable for their estates as they had not been earlier, and encouraged smaller landholdings. The cumulative result was a wider diffusion of wealth.

The center of vitality moved southeast to the lower Yangtze valley, which had long before emerged as the major rice-yielding region. By this time its fertility, combined with fewer social restrictions, had bred a new subculture that was more productive in industry than elsewhere. It encouraged the growth of commerce and stable markets, the beginnings of a uniform money economy, and the great broadening of education that printing had just made possible. The new southern elite was, on the whole, small gentry, and lacked the military traditions of the ancient northern clans and of power holders in the period of disunion. Their families were often too involved in trade for them to despise it. Although conservative, as all Chinese elites have been, they were prepared to think of change as a useful tool. The novelties of attitude and value were often slighter or subtler than such a brief account can convey, but within the established limits of Chinese social ideals their consequences were great.

In Shen Kua’s time the old families of the north and west still provided many of the very highest officials and thus wielded great influence, positive or obstructive, in discussions about the future of China. But they had become merely influential members of a new political constellation that brought a variety of convictions and interests to that perennial debate. An especially obvious new element was that many southern small gentry families like Shen’s established traditions of civil service, either as a main means of support or to protect and further their other concerns. Once a family’s social standing was achieved, one or more members could enter the bureaucracy freely because of experience as subordinates in local administration or because they were amply prepared by education for the examinations. Their sons could enter still more freely because offspring of officials were given special access to both direct appointment and examination.

Not sharing the old vision of a social order fixed by precedent, men of the new elite were willing to sponsor institutional renovation in order to cope directly with contemporary problems. Dependent on their own talents and often needing their salaries, they were dedicated to building a rational, systematic, and in most respects more centrally oriented administration. They were willing to make law an instrument of policy, and insisted that local officials be rated not only on the moral example they set but also quantitatively—on how effectively they made land arable and collected taxes. In the name of efficiency, they devoted themselves to removing customary curbs on imperial authority and (with only partial success in the Sung) to dismantling the structures of privilege that underlay regional autonomy. Only later would it become clear that they were completing the metamorphosis of the emperor from paramount aristocrat to autocrat. At the same time they were successfully demanding more policymaking authority as the emperor’s surrogates, although at the cost to themselves of greater conformity than officials of the old type had willingly accepted.

This irreversible transition did not lead to a modern state, but only to a new and ultimately stagnant pattern. The most accelerated phase of change was the activity of what is called the New Policies group (hsin fa 新法, actually a shifting coalition) between 1069 and 1085. In 1068 the young emperor Shen-tsung, who had just taken the throne, brought its leader, Wang An-shih 王安石 (1021–1086), to the capital. Within two years Wang had become paramount Grand Councillor. He resigned for nine months in 1074, when pressure from his antagonists persuaded the emperor to be less permissive, and returned to private life in 1076. The New Policies continued to be applied and extended, but with less and less attention to their founding principles, until Shen-tsung’s death in 1085. Under the regency of the Empress Dowager, enemies of the reform attempted for eight years to extirpate Wang’s influence and take revenge upon his adherents. When Emperor Che-tsung came of age in 1093, the New Policies were revived, but were so bent toward factional ends and administered so disastrously that the word "reform" is hardly applicable.

Wang An-shih’s opponents were many: the old aristocrats, career bureaucrats of the sort who would oppose any change as disruptive, officials whose individual or group interests ran in other directions—and men of high ideals who found his proposals ill-advised and his personal style too intolerant.

No institution had evolved through Chinese history to work out and resolve conflicts of political viewpoint. This lack was filled by cliques, intrigues, and appeals to imperial intervention. Division and corruption among active supporters of the New Policies had been a problem from the start. Wang’s program was so ambitious that he had to take competent support where he found it. The new access to power that he offered attracted enterprising men. Many had little sympathy for his convictions, and dedicated themselves to manipulation and graft. Once Wang was gone, the leadership of his group tended to become a battleground for aspirations of this kind. The internal and external enemies of the New Policies left the program a shambles by the time the Chin Tartars drove the Sung south in 1127.

A primary aim of the reforms was financial security of the state, which prompted initiatives in water control and land reclamation, encouragement of extractive industries and agriculture, intervention in commerce, and rationalization of taxes. Another goal, particularly at the emperor’s insistence, was military strength. There had been a long confrontation along the northern border between the Chinese and the powerful Khitan empire, pastoral masters of mounted combat (renamed Liao in 1066). Seventy years of fitful peace were punctuated by humiliating Chinese failures to recapture territory south of the Great Wall. The peace was maintained by large annual bribes. For three decades the Tangut people of the northwest had posed an almost equally unpalatable demand for appeasement. The wealth that the New Policies could generate from man’s exploitation of Nature, the emperor hoped, could buy victory, or détente through strength, on both fronts. Either goal demanded expertise in cartography, strategic theory and tactical doctrine (both of which contained cosmological elements), design and manufacture of war matériel, fortification, troop organization and training, and development of a stable economy in border regions.

Shen Kua contributed to nearly every field of New Policies activity, both civil and military. His social background and political commitments cannot be considered responsible for his scientific talent or curiosity; the antecedents and loyalties of other major contemporary scientific figures were very different from his. But a review of his career and of his work will show how regularly his involvement with particular technical themes and problems grew out of his activities in government.

Life

From about 1040 Shen traveled with his father to successive official posts from Szechwan in the west to the international seaport of Amoy. He was exposed not only to the geographical diversity of China but also to the broad range of technical and managerial problems in public works, finance, agriculture, and maintenance of waterways, that were among the universal responsibilities of local administrators. Because his physical constitution was weak, he became interested in medicine at an early age.

Late in 1051, when Shen was twenty, his father died. As soon as the customary inactivity of the mourning period ended in 1054, Shen received the first of a series of minor local posts. His father’s service exempted him from the prefectural examination. His planning ability became almost immediately apparent when he designed and superintended a drainage and embankment system that reclaimed some hundred thousand acres of swampland for agriculture. This was the first of a series of projects that established his reputation for skill in water control. This ability seems to have run in his family. Shen recorded a visit to his brother P’i, subprefect in Ning-kuo寧國 (now Fu-hu, Anhwei province), in 1061. After a cartographic survey and a historical study of previous earthworks in the region, Shen P’i applied the labor of fourteen thousand people to another massive land reclamation scheme that won the recognition of the emperor.

In 1063 Shen Kua passed the national examinations in the highest category. Posted to Yangchow, he impressed Chang Ch’u 張蒭 (1015–1080), the Fiscal Intendant (a post then equivalent to governor), who recommended him for a court appointment leading to a career in the professional financial administration.

Shen apparently used the time not occupied by his early metropolitan appointments, which were conventional and undemanding, to study astronomy. In reply to the informal questions of a superior he set down clear explanations, still extant, of the sphericity of the sun and moon as proved by lunar phases, of eclipse limits, and of the retrogradation of the lunar nodes. They demonstrate an exceptional ability to visualize motions in space, which were at best implicit in the numerical procedures of traditional astronomy and seldom were discussed in technical writing. In 1072 Shen was given an additional appointment as Supervisor of the Directorate of Astronomy. With the collaboration of his remarkable commoner protégé Wei P’u 衛朴 and the aid of other scholarly amateurs, using books gathered from all over the country, he undertook a major calendar reform. He planned an ambitious series of daily observations to extend over five years, using renovated and redesigned instruments.

The incompetent career officials who staffed the bureau stymied him. He forced the dismissal of six whom he caught falsifying records of phenomena. Those who remained doomed his program of observations and kept his new system of ephemeris computation from being among the two or three most securely founded before modern times. Shen’s personal involvement in later stages of the reform undoubtedly was limited by his gradual movement into the vortex of factional politics.

Shen was early known to Wang An-shih, who composed his father’s epitaph while a young provincial official. Shen eventually was publicly identified by enemies of the New Policies as among the eighteen members of Wang’s intimate clique. In late 1072, in support of Wang’s program, Shen used an original technique to survey the silting of the Pien Canal near the capital, dredged it, and demonstrated the value of the silt as fertilizer. Until mid-1075 he spent much time traveling as a troubleshooter of sorts, inspecting and reporting on water control projects, military preparations, and local administrations—and, it has been conjectured, providing encouragement to Wang’s provincial supporters. Shen was put in charge of arsenal activities and, in 1075, was sponsored by Wang (then head of government) to revise defensive military tactics, a task the throne had proposed for Wang himself.

In 1074 the Khitan were pressing negotiations to move their borders further south. Incompetent and timorous Chinese negotiators were conceding unfounded Liao claims about the language and substance of previous agreements. Shen built a solid Chinese case by going to the archives, as no one before him had bothered to do. His embassy in mid-1075 to the camp of the Khitan monarch on Mt. Yung-an 永安 (near modern P’ing-ch’üan, Hopei) was triumphant. He described himself, encircled by a thousand hostile onlookers, calling on his staff, who had memorized the old documents of the Khitan themselves, to cite without pause or flurry the exact reference to refute one historical bluff after another.

Shen returned to China (with biological specimens and maps of the territories he had passed through) to become a Han-lin Academician, to take charge of a large-scale water control survey in the Yangtze region, and then to become head of the Finance Commission. While in this very powerful position he untangled a variety of contradictory policies, producing in the process some of the most penetrating writings before modern times on how to affect and regulate supply and demand, how to forecast prices in order to intervene effectively in the market, and how hoarding, counterfeiting, and melting affect the supply of currency as the price of the metal in it fluctuates about its controlled monetary value. In the autumn of 1077, just as he had launched his revision of critical fiscal measures, the corrupt and vindictive censor Ts’ai Ch’ueh 蔡確 (1036–1093) impeached him. The charge was that Shen had opposed a New Policies taxation measure in an underhanded, inconsistent, and improper way. Historians credited it for centuries, but modern Chinese research has refuted it in every detail. His protector Wang An-shih had just left government. By threatening an established budget item in order to ease the burdens of the poor, it seems, Shen became an easy victim of factional maneuvering.

The emperor was not only the ritual synapse between the political and natural orders. He was a human being whose likes and dislikes courtiers indulged within broad limits that could be further widened by force of his charisma and will. The closer to him an official penetrated, the more achievement and even survival became subject to imperial whim and the intrigue of colleagues. Wang An-shih maneuvered Shen Kua into the proximity of the throne because of Shen’s brilliance, judgment, and effectiveness at complicated tasks. He was not adept at protecting himself. He attracted the most damaging animosity not from opponents of the New Policies but from designing members of the coalition to which he belonged. Once the emperor qualified his support of the New Policies in 1074, the risk of debacle remained imminent. Many officials who had risen with Wang fought furiously for the power that would keep them afloat even though the program sank. They did not wish to be deterred by a colleague who judged issues on their own merits. They probably also felt, as others did, that a man in his early forties and low in rank did not merit the emperor’s increasing confidence.

Ts’ai Ch’ueh was rising into the vacuum that Wang’s retirement had left. The emperor depended increasingly on Ts’ai’s monetary counsel and could not easily disregard what he insisted upon. For three years it was impossible to overcome his objections and those of another censor, and to rehabilitate Shen. In 1080 he was sent to Yen-chou 延州 (now Yenan, Shensi province), on the inevitable route for military operations by or against the Tanguts, as Commissioner for Prefectural Civil and Military Affairs. The Tanguts were then divided and weakened, minor Chinese conquests around 1070 had set the stage for a war, and the treasury had ample funds. Shen played an important part in organizing and fortifying for the victorious offensive of the autumn of 1081. In extending Sung control he showed a practical as well as a theoretical mastery of the art of warfare. He was cited for merit and given several honorary appointments. It was probably at the same time that he was ennobled as State Foundation Viscount. In his sixteen months at Yen-chou, Shen received 273 personal letters from the emperor. His standing at the court was in principle reestablished. Whether he had become shrewd enough to survive there was never tested.

Shen and a colleague followed up the victory by proposing fortifications to close another important region to the Tanguts. The emperor referred the matter to an ambitious and arrogant official who, ignoring the proposal, changed the plan to provide defenses for what Shen argued was an indefensible and strategically useless location. Shen was commanded to leave the vicinity of the new citadel so as not to share in the credit for the anticipated victory. When the Tangut attack came, the emissary’s force was decimated while Shen, with imperial permission, was successfully defending a key town on the enemy invasion route to Yen-chou. He denied the Tanguts an opening for advance.

Be that as it may, Ts’ai Ch’ueh was now a Grand Councillor. As titular military commander Shen was held responsible for the defeat and considerable loss of life. At the age of fifty-one he found his career was over. The anti-New Policies regime later, to no advantage, abandoned the towns he protected, just as another negotiator lost the lands he had saved from the Khitan through diplomacy.

Shen spent six years in fixed probationary residence, forbidden to engage in official matters. He used at least two of these years to complete a great imperially commissioned atlas of all territory then under Chinese control. He had been working on this atlas intermittently since, as Finance Commissioner a decade earlier, he had had access to court documents. His reward included the privilege of living where he chose.

Ten years earlier Shen had bought, sight unseen, a garden estate on the outskirts of Ching-k’ou. In 1086, visiting it for the first time, he recognized it as a landscape of poignant beauty that he had seen repeatedly in dreams, and named it Dream Brook (Meng ch’i 夢溪, also read Meng hsi). He moved there in 1088. With a pardon and sinecures to support him, he spent his last years in leisure, isolation, and illness.

Writings

Shen’s writings, of which only a few are extant even in part, included commentaries on Confucian classics, two atlases, reports on his diplomatic missions, a collection of literary works, and monographs on rituals, music, mathematical harmonics, administration, mathematical astronomy, astronomical instruments, defensive tactics and fortification, painting, tea, medicine, and poetry. Of three books compiled during his last years at Dream Brook, one, Good Medicinal Formulas (Liang fang 良方), was devoted to medical therapy, doctrine, and philology. The other two belong to particularly Chinese genres.

Records of Longings Forgotten at Dream Brook (Meng ch’i wang huai lu 夢溪忘懷錄), a collection of notes on the life of the gentleman farmer in the mountains, contains useful information on implements and agricultural technique and, unlike more conventional agricultural treatises up to that time, on the culture of medicinal plants.

Brush Talks From Dream Brook (Meng ch’i pi t’an 夢溪筆談) survives and has been well edited in modern times. It is by any reckoning one of the most remarkable documents of early science and technology, not to mention philosophy, art and literary criticism, diplomacy, occultism, linguistics, archaeology, and not a few other topics. It is a collection of about six hundred recollections and observations, ranging from one or two sentences to about a page of modern print. "Because I had only my writing brush and ink slab to chat with, I call it Brush Talks." The jottings are loosely grouped under topics (seventeen in all current versions), of which seven are most pertinent to Nature and man’s use of it: "Regularities Underlying the Phenomena" (mostly astronomy, astrology, cosmology, divination), "Technical Skills" (mathematics and its applications, technology, medicine), "Philology" (including etymology and meanings of technical terms), "Strange Occurrences" (incorporating various natural observations), "Artifacts and Implements" (techniques reflected in ancient objects), "Miscellaneous Notes" (greatly overlapping other sections), and "Deliberations on Materia Medica" (most of it devoted to untangling historic and regional confusions in identities of medical substances).

Under all these rubrics, notices of the highest originality stand cheek by jowl with trivial didacticisms, court anecdotes, and ephemeral curiosities. Other sections are given to topics conventional in collections of jottings—memorable people, wisdom in emergencies, and so on. Shen’s theoretical discussions of scientific topics employed the abstract concepts of his time—yin-yang, the Five Phases (wu-hsing 五行), ch’i 氣, and so on.

A large fraction of the book’s contents is devoted to fate, divination, and portents. Historians seeking in him the prototype of the modern scientist have ignored Shen’s belief in such things, normal among people of his time. The author of Brush Talks has been compared with Leibniz. In an era of happy relations between China and the Soviet Union, Hu Tao-ching 胡道靜, the foremost authority on Shen, called him the Lomonosov of his day. But Shen was writing for gentlemen of universal curiosity and humanistic temperament. Custom, wisdom, language, and spiritual anomaly were as important themes as nature and artifice.

Because Shen’s interests were multifarious, the record unsystematic, and its form too confining for anything but fragmentary insight, only accumulation can fairly convey why he is important. What follows is a mere sample of his attempts to deepen the contemporary understanding of Nature, his observations that directed the attention of his educated contemporaries to important phenomena or processes, and his own technical innovations. I have grouped them to bring out contiguity of subject matter without interposing the radically different, and quite irrelevant, disciplinary divisions of modern science. On the basis of these samples I discuss—tentatively, given the state of research—the epistemological underpinnings of Shen’s work, and the unity of his scientific thought with elements that today would be considered unscientific, primitive, or superstitious. That done, I evaluate Shen’s life as a case study in the reconcilability of Confucianism and science, which the conventional wisdom among Sinologues for over a generation has tended to place in opposition.

Quantity and Measure

Mathematics was not the queen of sciences in traditional China. Chinese natural philosophers, unlike most in the postclassical West, did not dismiss the possibility that terrestrial phenomena could conform to mathematical regularities. But given the strength of Chinese quantitative sciences in numerical rather than geometric approaches, the very late and partial development of mathematical generalization, and the complete absence of notions of rigor, it is only consistent that much of the effort to discover such regularities produced numerology (that is, the use of numbers to label qualities, mainly in order to establish associations, meanings, or hierarchies). This practice was firmly founded on the "Great Commentary" to the Book of Changes.

Mathematics was, at least until the seventeenth century, embodied in specific problems about the physical world. Abstract thought about numbers was always concerned with their qualities rather than their properties, and thus remained numerology. This art, although it blended into arithmetic, was only partly distinct from other symbolic means for exploring the inherent patterns of Nature and man’s relation to it. Computation, on the other hand, was applied in a coherent tradition of textbooks to a great variety of mensurational, accounting, and other everyday tasks of the administrator. They were categorized by the type of practical problem to be solved: surveying, computing land tax, estimating requirements, and so on. Occasionally curiosity and skill pushed beyond these pragmatic limits, but, in Shen’s time, never very far. Some of the problems that Shen presented in Brush Talks had no application, but his enthusiasm for them was undiminished.

In addition to this accumulation of individual problems, there were two exact sciences in which mathematics served to advance knowledge of the patterns underlying the phenomena. One was mathematical harmonics (lü lü 律呂), which explored the relations between musical intervals and the dimensions of instruments that produced them, in ways analogous to the Pythagorean art. Its appeal was much the same in both China and Greece: it demonstrated how deeply the power of number was rooted in Nature. For this reason in China mathematical harmonics was often put into the same category as mathematical astronomy, which also had foundations in cosmology. Astronomy, by far the more technically elaborate of the two exact sciences, was normally employed on behalf of the monarch. Successfully predicting a phenomenon fitted it into the dynamic cosmic and social order that the emperor maintained on behalf of his people. Unpredictable phenomena and failed predictions were either good or bad omens. Each challenged the established order, and each had a meaning. Bad omens warned that the emperor’s mediating virtue, which maintained concord between the cosmic and political orders, was deficient. Good portents generally signalled, and approved, a step in a new direction. Successfully predicting celestial events neutralized their ominousness, preserving the charisma of the ruling dynasty.

The annual calendar (or almanac) issued by the throne was thus important in the solemn ceremonies that asserted the emperor’s authority, as the ancient motto put it, to "grant the seasons." The calendar encompassed all predictable events, including planetary phenomena and eclipses. The utilitarian calendrical aspects—lunar months and solar years—had long since been refined past any practical demand for accuracy, but astronomical reinforcement of the Mandate of Heaven called forth endless attempts to improve constants. As it became conventional to institute a complete new system for computing these ephemerides when a new emperor was enthroned, technical novelty was at a premium. When new ideas were unavailable, the Directorate of Astronomy tended to trivially repackage old techniques.

Repeated failures of prediction were another motive to reform the astronomical system. In such cases too, the system was in principle replaced as a unit rather than repaired. Most systems survived or fell on their ability to predict eclipses, particularly solar eclipses. These were the least suited of all celestial phenomena to the algebraic, non-geometric style of mathematics. Prior to Shen’s time little effort had gone into predicting the apparent motions of the planets, which lacked the significance of solar and lunar phenomena. This was, in fact, an omission that Shen seems to have been the first to confront.

General mathematics. As wood-block printing became widespread, the government, eager to control the content of education, recognized its value. The court used it to propagate carefully chosen and edited collections of ancient textbooks. It was doing so for medicine at the time Shen entered the capital bureaucracy. In 1084 it printed a collection of ten mathematical manuals, made four centuries earlier and reconstituted as well as extant texts allowed. The authority of these projects served both to fix textual traditions, preserving selected treatises from further attrition, and to consign to oblivion the books that government committees decided not to include. Shen thus lived at a decisive period in the development of mathematical traditions. His judgments on lost techniques and disused technical terms (e.g., 300, 306) have played an important part in later attempts to interpret them. Brush Talks is also an essential source for the study of pre-Sung metrology, currency, and other subjects related to computation.

Shen used mathematics in formulating policy arguments more consistently than most of his colleagues. Examples are his critique of military tactics in terms of space required for battle formations (579) and his computation that a campaign of thirty-one days is the longest that can feasibly be provisioned by human carriers (205). But of the computational methods discussed in his "Technical Skills" chapter, those not related to astronomy are almost all abstractly oriented.

This original bent emerges most clearly in two problems. One is a new method for computing the frustum of a solid rectangular pyramid. Shen worked out the volume of the same figure if composed of stacked articles (he mentioned flat round chess pieces, bricks, and wine vats) that leave interstices (301). Since Shen intended this "volume with interstices" (hsi chi 隙積) method to be applicable regardless of the shape of the objects stacked, what he gave is a correct formula for the number of objects, which are thus to be considered of unit volume. His presentation has several interesting features. Needham has suggested (III, 142–143) that the concern with interstices (and, one would add, unit volumes) may have been a step in the direction of geometric exhaustion methods, although it was tentative and bore fruit only in seventeenth-century Japan. Second, instead of the worked-out problem with actual dimensions that is conventional in early textbooks, Shen simply gave a generalized formula: "double the lower length, add to the upper length, multiply by the lower width," and so on. Third, this was the earliest known case in China of a problem involving higher series. Built on earlier numerical approaches to arithmetical progressions, it provided a basis for more elaborate treatment by Yang Hui 楊輝 (1261) and Chu Shih-chieh 朱世傑 (1303).

The second problem of interest was said "in a story" to have been solved by one of China’s greatest astronomers, the Tantric Buddhist patriarch I-hsing 一行 (682–727). It sought the number of possible situations on a go board, with nineteen by nineteen intersections on which any number of black or white stones may be placed. Whether I-hsing actually solved this problem we do not know; Shen’s single paragraph was the first and last known discussion of permutations in early Chinese mathematics. It stated the order of magnitude of the answer—"approximately speaking one must write the character wan 萬 (10,000) fifty-two times in succession." This amounts to an order of magnitude of roughly 10208. Shen added to this solution exact answers for smaller arrays, three methods of solution, and a note on the limited traditional notation for very large numbers (304).

Mathematical harmonics. The Pythagoreans were fascinated by the relations of concordant intervals to the plucked strings that produced them, since the lengths between stops were proportionate to simple ratios of integers. By about 200 B.C., the Chinese built up a similar science on a gamut of standard pipes. Beginning with a pipe eight inches long and 0.9 inch in diameter, they generated the lengths of subsequent pipes by multiplying the previous length alternately by 2/3 and 4/3, making twelve pipes within an approximate octave. The dozen were then related to such categories as the twelve divisions of the tropical year, in order to provide a cosmic basis for the system of modes that the pipes determined. A pentatonic scale, which could be used in any of the twelve modes, provided similar associations with the Five Phases. This basis was extended to metrology by defining the lengths and capacities of the pipes in terms of millet grains of standard dimensions. Shen lucidly and concisely explained these fundamentals of mathematical harmonics, and corrected grotesque complications that had crept into a canonic source through miscopying of numbers (143, 549).

He also studied stringed instruments. By straddling strings with paper figures, he showed that strings tuned to the same notes on different instruments resonate, as do those tuned an octave apart on the same instrument (537; cf. IV.1, 130). His two chapters on music and harmonics are also a trove of information on composition and performance.

Astronomy. Shen’s major contributions in astronomy were his attempts to visualize celestial motions spatially, his arc-sagitta methods that for the first time moved algebraic techniques toward trigonometry, and his insistence on daily observational records as a basis for his calendar reform. The first had no direct application in computation of the ephemerides, although it may well have inspired (and at the same time have been inspired by) the second, which evolved from traditional mensuration. It has been suggested that the clarity of Shen’s cosmological explanations led to his appointment to the Directorate of Astronomy, which provided opportunity for his contributions in the second and third areas. But circumstances that arose from the bureaucratic character of mathematical astronomy made these contributions futile in his lifetime.

Shen’s discussions of solar, lunar, and eclipse phenomena (130–131; excerpts, III, 415–416) have been mentioned (p. 6). By far the most remarkable of his cosmological hypotheses attempted to account for variations in the apparent planetary motions, including retrogradation. This concern is not to be taken for granted, since traditional astronomers, in addition to their disinterest in planetary problems, preferred purely numerical approaches to prediction, unlike the spatial geometric models of Greek antiquity. Constructing explanatory models was not part of their work. Noting that the greatest planetary anomaly occurred near the stationary points, Shen proposed a model in which the planet traced out a figure like a willow leaf attached at one side to the periphery of a circle. The change in direction of the planet’s motion with respect to the stars was explained by its travel along the pointed ends of the leaf (148).

The willow leaf, in other words, served one of the same functions that the epicycle served in Europe. It is characteristic that, having taken a tack that in the West was prompted entirely by geometric reasoning, Shen’s first resort should have been a familiar natural object with rich poetic connotations. Use of a pointed figure would hardly have survived a mathematical analysis of observational data, but this simile remained an offhand suggestion.

Another early outcome of Shen’s service at the court was a series of proposals to redesign major astronomical instruments: the gnomon, which was still employed to measure the noon shadow and fix the solstices; the armillary sphere, with which angular measurements were made; and the clepsydra, used to determine the time of observations as well as to regulate court activities. Shen’s improved versions of the armillary and the clepsydra apparently were not built until late 1073, after he had taken charge of the Directorate of Astronomy. The armillary at least was discarded for a new one in 1082, a casualty of his personal disgrace.

Shen’s clepsydra proposals represent a new design of the overflow-tank type (Needham’s Type B; III, 315–319, 325), but the most significant outcome of his work on this instrument was a jotting on problems of calibration. Day and night were by custom separately divided into hours, the length of which varied with the season. The time was read off graduated float rods, day and night sets of which were changed twenty-four times a year. Shen pointed out that this crude and inadequate scheme amounted to linear interpolation, "treating the ecliptic as a polygon rather than a circle," and argued for the use of higher-order interpolation (128).

The best armillary sphere available in the central administration when Shen first worked there was based on a three-hundred-year-old design "and lacked ease of operation" (150). Shen’s most interesting improvement was in the diameter of the naked-eye sighting tube. At least from the first millennium B.C. a succession of stars had been designated the polestar until each strayed unacceptably far from the celestial pole, the still point in the sky about which the stars rotate in the course of a day and night. In the late fifth century A.D. Tsu Keng 祖暅 discovered that the current polestar, 4339 Camelopardi, rotated about a point slightly more than a degree away. This determination of the true pole was incorporated in subsequent instruments by making the radius of their sighting tubes 1.5 Chinese degrees (each of which is 360/365.25°). The nightly excursion of the polestar just inside the field of view thus provided a check on whether the instrument was pointing true north. Six hundred years later Shen found that the polestar could no longer be kept in view throughout the night. He gradually widened the tube, using plots of the polestar’s position made three times each night for three months to adjust aim, until his new calibration revealed that the distance of the star from "the unmoving place at the celestial pole" was now slightly over three degrees (127; III, 262). Shen’s successors followed him in treating the distance as variable. The relation of this secular change to what is now called the precession of the equinoxes remained unexplored. Aware of the periodic retrogradation of the lunar nodes, Shen also discarded the armillary ring representing the moon’s path, which did not reflect this motion. It was never used again.

Calendar reform. On the accession of Shen-tsung in 1068, a new computational system was expected. The inability of the incumbent specialists to produce one left Shen with a clear mandate when he took over the Directorate of Astronomy in 1072. The situation became even more awkward when he could dislodge few of the timeservers already in the bureau, and was forced to bring in Wei P’u and others from outside the civil service in order to begin work on the calendar reform. It is not yet possible to tell what part of the work was done by Shen and what part by his assistants. Wei surely took responsibility for compiling the system as Shen became increasingly occupied elsewhere in government. Wei bore the brunt of fervent opposition within the bureau. He was even formally accused of malfeasance.

Shen knew that previous Sung astronomical systems had suffered greatly from reliance on old observations. He clearly conceived what new data were needed for the first major advance in centuries. Unabating opposition within the bureau and his own demanding involvements outside it limited the number of important innovations in his Oblatory Epoch (Feng-yuan 奉元) system. It was the official basis of calendar computation from 1075, the year of its completion, to 1094, a period very close to the average for systems of the Northern Sung. That the system was not used longer has little to do with its merits, since except in cases of spectacular failure, Sung astronomical systems changed as rulers changed. Shen’s was replaced when the coming of age of Che-tsung began a new era. The immediate vicissitudes and long-term influence of three special features will give an idea of how historical actualities limited Shen’s astronomical ambitions.

The boldest aspect of Shen’s program was the attempt to predict the apparent positions of the planets—not merely their mean speeds and prominent phenomena—for the first time. The computational tools available did not permit this to be done with a few observations of stationary points, occultations, and maximum elongations. Shen and Wei therefore planned a series of observations of a kind not proposed in Europe until the time of Tycho Brahe, five centuries later: exact coordinates read three times a night for five years. Similar records were to be kept for the moon’s positions, since previous Sung systems had still used the lunar theory of I-hsing, which after 350 years had accumulated considerable error. This program of observing was the most unfortunate casualty of the obstruction within the Bureau. Shen and Wei had no recourse but to produce a conventional planetary theory based mainly on old observations. They were able to correct the lunar error, but even this proposal provoked such an outcry that it could be vindicated only by a public demonstration using a gnomon (116).

A second issue was the central one of eclipse prediction. Previous attempts to add or subtract correction factors had shown the futility of tinkering. It was Wei P’u who "realized that, because the old eclipse technique used the mean sun, [the apparent sun] was ahead of it in the accelerated phase of its motion and behind it in the retarded phase." He therefore incorporated apparent solar motion into the eclipse theory (139). This had been done centuries earlier but abandoned.

A major obstacle in eclipse prediction, as well as in such workaday problems as projecting observations in equatorial coordinates onto the ecliptic, was the absence of spherical geometry. Shen’s evolution of arc-chord-sagitta relations out of some inferior approximations for segment areas given in the arithmetical classics was a first step toward trigonometry. He made it possible in effect to apply sine relations and a fair approximation of cosine relations (301; III, 39, with diagram). The great remaining lack, as in planetary theory, was a mass of fresh observations on which to base new parameters. That this weakness could threaten the continuance of the system became clear in 1076, the year after it was adopted, when the failure of a predicted lunar eclipse to occur left Shen and his associates open to attack. Shen parried with a successful request that students in the Palace Library’s Bureau of Astronomy be ordered to carry out his observational program "for three or five years" and to communicate the results to the original compilers. Whether this expedient could have bypassed the stalemate at the Directorate of Astronomy’s observatory remains unknown, for in the next year Shen’s impeachment aborted it.

In sum, the immediate outcome of the Oblatory Epoch calendar reform was undistinguished, and within half a century the official documents embodying it had been lost. It is impossible to be sure, for instance, to what extent Shen, after inventing arc-sagitta relations, had incorporated them. But enough information survived in proposals, reports, Shen’s writings, and compendia of various sorts for his astronomical system to play a considerable part in the highest achievement of traditional Chinese mathematical astronomy, the Season-Granting (Shou shih 授時) system of Kuo Shou-ching 郭守敬 (1279). Kuo carried out a sustained program of observation using instruments that incorporated Shen’s improvements. He took up Shen’s arc-sagitta formula, greatly improving the cosine approximation, and applied it to the equator-ecliptic transform. Aware of Shen’s emphasis on the continuous variation of quantities in Nature and his criticism of linear interpolation in clepsydra design, Kuo used higher-order interpolation to an unprecedented extent in his calendar reform.

Shen recorded another scheme for reform of the civil calendar that was most remarkable for his time and place. It almost certainly occurred to him in the last decade of his life. The traditional lunisolar calendar was a series of compromises in reconciling two incommensurable quantities. The modern value for the tropical year is 365.2422 days, and that for the synodic month 29.53059 days, so that there are 12.3683 lunar months per solar year. The practical problem was to design a civil calendar with an integral number of days each month, and an integral number of months each year, in such a way that the long-term averages approach the astronomical constants. Hardly two of the roughly one hundred computational systems recorded in early China solved this problem in exactly the same way, just as there was endless tactical variety in other traditional societies, but the strategy was generally the same. Months of twenty-nine and thirty days alternated, with occasional pairs of long months to raise the average slightly. Intercalary thirteenth months were inserted roughly seven times every nineteen years. That comes to 0.3684 additional months per year, an excellent approximation.

By a millennium before Shen’s time the calendar was more than adequate in these respects for every civil need, although attempts to further refine the approximation led to endless retouching. The rhythms of administration, and to some extent of commerce, were of course paramount in the design of the lunisolar calendar, despite pieties about imperial concern for agriculture. Chinese farmers did not need a printed almanac by which to regulate their activity. What they consulted was its notations of lucky and unlucky days. Division of the year by lunar months is, in fact, useless for agriculture, since the seasons that pace the farmer’s work vary with the sun alone. The Chinese calendar also incorporated twelve equal divisions of the tropical year (ch’i, like the Babylonian tithis), further subdivided into twenty-four periods with such names as Spring Begins, Grain Rains, and Insects Awaken. These provided a reliable notation for seasonal change in the part of northern China in which the series originated, but were useless elsewhere. They were included for their antiquity, not because they filled an agricultural need.

Shen’s suggestion was a purely solar calendar, based on the twelve divisions of the tropical year (average 30.43697 days in his system) instead of on the lunation. The civil calendar would thus alternate months of thirty and thirty-one days, with pairs of short months as necessary to approach the average. This would provide truly seasonal months and at the same time do away with "that goitrous excrescence" the intercalary month. "As for the waxing and waning of the moon, although some phenomena such as pregnancy and the tides are tied to them, they have nothing to do with seasons or changes of climate; let them simply be noted in the almanac" (545). Shen was aware that because the lunisolar calendar went back to hoary antiquity "it is by no means appropriate to criticize it." He predicted that his discussion "will call forth offense and derision, but in another time there will be those who use my arguments." This proposal was in fact considered by later scholars the greatest blemish on Shen’s astronomical talent. His posterity appeared in the mid-nineteenth century, with the even more radical solar calendar enacted for a few years by the T’ai-p’ing rebels. His work was cited to justify more respectable proposals between that time and the adoption of the Gregorian calendar in 1912.

Configuration and Change

Despite Shen’s exceptional interest across the board in mathematical quantity and his conventional fondness for numerology, the most obvious of his contributions to understanding the earth and its phenomena are qualitative. I group them below, for convenience, by modern category.

Magnetism. For more than a millennium before Shen’s time, south-pointing objects carved from magnetite were used from time to time in ceremonial and magic. In 1044 a book on military arts recommended, as aids to pathfinding, objects cut from sheet iron and magnetized by thermoremanence. Shen took up the matter of needles rubbed against lodestone by contemporary magi, discussed floating and other mountings, recommended suspension, noted that some needles point north and some south, and asserted that "they are always displaced slightly east rather than pointing due south"—all in about a hundred characters (437; IV.1, 249–250). Noticing the result of what is today called magnetic declination depended not only on trials with a suspended needle but also on the improved meridian determined by Shen’s measurement of the distance between the polestar and true north.

Shen may have been anticipated by geomancers, who practiced a sophisticated proto-science of land configuration and siting, but the dates of texts on which such claims have been based are questionable. The use of compass needles in navigation is recorded shortly after Shen’s death, and later descriptions provide enough detail to show that the twenty-four-point rose that Shen substituted for the old eight compass points (perhaps also under the stimulus of the better meridian, if not of geomantic practice) was widely adopted. He apparently was unaware of the polarity of magnetite itself, since in another article he explained the difference between north-pointing and south-pointing needles as "perhaps because the character of the stone also varies" (588; IV.1, 250).

Cartography. It has been conjectured that Shen was the first to use a compass in mapmaking, although traditional methods would have sufficed. Neither his early maps of Khitan territory nor the atlas of China completed in 1087 have survived to answer this question. But in an enclosure to the latter he did separately record bearings between points using his twenty-four-point compass rose. He also listed rectilinear distances rather than, as customary, distances along established routes. He called the use of distances "as the bird flies" ancient, but we have no earlier record. "Thus although in later generations the maps may be lost, given my book the territorial divisions may be laid out according to the twenty-four directions, and the maps speedily reconstructed without the least discrepancy" (575; III, 576). His great atlas included twenty-three maps drawn to a uniform scale of 1:900,000. The general map was ten by twelve Chinese feet. There is no evidence that the handbook outlasted the maps.

Three-dimensional topographic maps go back at least to Hsieh Chuang 謝 莊 (421–466), who had a demountable wooden model carved, apparently on the basis of an ancient map. In 1075, while inspecting the Khitan border, Shen embodied information gathered from the commander and the results of his own travels in a series of relief maps. He had them modeled, for the sake of portability, in plastic media (wheat paste and sawdust until the weather turned freezing, then beeswax) on wooden bases. These were carried to the capital and duplicated in wood. The government thenceforth required similar models from other frontier regions (472; III, 580).

Shen regularly used both historical research and special on-the-ground surveys to solve such cartographic problems as tracing changes in watercourses (431). Typical of his ingenious topographic survey methods were those used in 1072 to measure the slope of the Pien Canal near the capital. He built a series of dikes in temporary, narrow parallel channels to measure incremental changes in water level (457; III, 577*).

Formation of the earth. In 1074, in the T’ai-hang 太行 mountain range (Hopei), Shen noticed strata of "bivalve shells and ovoid rocks running horizontally through a cliff like a belt. This was once a seashore, although the sea is now hundreds of miles east. What we call our continent is an inundation of silt. . . . This mud year by year flows eastward, forming continental land." A similar stratum had been observed long before by Yen Chen-ch’ing 顏真卿 (708–784), who vaguely suggested its origin in the sea; but Shen—whose duties had made him intimately familiar with the process of silting—opened a new line of investigation by proposing a cause (430; III, 604).

Probably on his southward drought survey earlier in the same year, Shen saw the Yen-tang 雁蕩 range (Chekiang), a series of fantastic rock formations "invisible from beyond the ridgeline [opposite], but towering to the sky when seen from the valleys. If we trace the underlying pattern, it must be that great waters in the valleys have attacked and washed away all the sand and earth, leaving only the great rocks erect and looming." His explanation proceeded to generalize the shaping role of erosion, and then to apply it to the hills that divide streams in the loess country of northwest China—"miniatures of the Yen-tang mountains, but in earth rather than stone" (433; III, 603–604).

Shen reported diverse contemporary finds of petrified plants and animals (373–374; III, 614–618). He remarked particularly on a stony formation he identified as originally a grove of interconnected bamboo roots and shoots, found dozens of feet below ground level at Yenan 延安 (Shensi). He knew from his military service there that the climate was too dry to grow bamboo: "Can it be that in earliest times [literally, ’before antiquity’] the land was lower and the climate moister, suitable for bamboo?" (373). About a century later the great philosopher and polymath Chu Hsi (1130–1200), who knew Shen’s jottings well and often extended ideas from them in his teaching, suggested that the stone of certain mountains was itself petrified silt deposits. But Shen’s notion of prehistoric climatic change, like that of the reshaping of land by erosion, was not pushed further soon after his lifetime.

Atmospheric phenomena. Although Shen did not report important original discoveries of his own, he preserved a number of interesting observations not recorded elsewhere. Perhaps the most important is a vivid description of a tornado (385; translated in Holzman, "Shen Kua," 286). Modern meteorologists questioned its veracity until, in the first decade of the twentieth century, the Sikawei Observatory in Shantung reported phenomena of the same kind, previously thought restricted to the western hemisphere.

Shen transmitted an explanation of the rainbow by Sun Ssu-kung 孫思恭, an elder contemporary in the court who was also considered one of the best mathematical astronomers of his era. "The rainbow is the image [literally, ‘shadow’] of the sun in rain, and occurs when the sun shines upon it." This sentence does not, as often claimed, adduce refraction (pinhole or mirror images were regularly called "shadows"; see 44). Sun’s observations prompted Shen to determine by experiment that the rainbow is visible only opposite the sun (357). Later Chu Hsi, aware of Shen’s account, added that by the time the rainbow appears "the rain ch’i has already thinned out; this in turn is because sunlight has shone on and attenuated the rain ch’i." Ch’i must mean vapor here; the notion of reflections off individual drops is hardly implicit. Shen also recorded the fall of a fist-sized meteorite in more detail and with less mystification than in previous reports. The particulars of its fall came from a careful account by another of Wang An-shih’s associates. The object was recovered and exhibited, but Shen did not claim that he himself had observed that "its color is like that of iron, which it also resembles in weight" (340; III, 433–434).

Products of the earth. Shen’s responsibilities with respect to fiscal policy gave him a detailed knowledge of important commodities, their varieties, and the circumstances of their production, as may be seen from his descriptions of tea (208) and salt (50, 221, 224, 422). Inflammable seepages from rock had been known a millennium before Shen’s time, and for centuries had been used locally as lamp fuel and lubricant. While Commissioner near Yen-chou in 1080-1081, he noted the blackness of soot from petroleum. Good ink was then made by burning pine resin, but Shen knew that North China was being rapidly deforested. He remarked that, in contrast with the growing scarcity of trees, "petroleum is produced inexhaustibly within the earth." He began an industry to manufacture the solid cakes of carbon ink used for writing and painting throughout China. The name Shen coined for petroleum is the one used today, and the source in Shensi province that he developed is still exploited. In the same article he quoted a poem of his that is among the earliest records of the economic importance of coal, then beginning to replace charcoal as a fuel (421; III, 609, partial).

Optical phenomena. Shen did not directly link his interest in image formation with his worldly concerns. The play of his curiosity over old artifacts, not the improvement of naked-eye astronomical instruments, motivated him.

In the canons of the Mohist school (ca. 300 B.C.) is a set of propositions explaining the formation of shadows and of optical images (considered a kind of shadow) in plane, convex, and concave mirrors. Most scholars believe that one proposition concerns pinhole images, although textual corruption and ambiguity make this uncertain. These propositions are in many respects physically correct, although very schematic. They do not presuppose rays of light.

Shen asked himself why a concave mirror forms an inverted image. He suggested that an "obstruction" (ai 礙), analogous to an oarlock, constricts the "shadow" to a shape like that of a narrow-waisted drum (more or less two cones apex to apex, the second constituting the inverted image). Like the Mohists, Shen clearly believed that inversion takes place before the image is reflected. He expressly likened the inverted image to that of a moving object formed on the wall of a room through a tiny opening in a paper window. Aware for the first time that there is a range of distances from a concave mirror within which no image is formed (that is, between the center of curvature and the focal point), he explained that this blank region, corresponding to the pinhole, is the locus of "obstruction" (44). Shen’s pinhole observation was adventitious, but his approach to the burning-mirror settled the details by experiment.

Two other observations of optical interest are found under the rubric "Artifacts and Implements." The first, in the Sequel to Brush Talks, noted that when the ancients cast bronze mirrors, they made the faces just convex enough that, regardless of size, every mirror would reflect a whole face. By Shen’s time this refinement had been abandoned and the reasoning behind the curvature forgotten, so that collectors were having the faces of old mirrors scraped flat (327; IV.1, 93).

The second jotting is the oldest record of a Far Eastern curiosity still being investigated: "magic mirrors," or, as Shen called them, "transparent mirrors." Shen described a bronze mirror with the usual smooth, polished face and an inscription integrally cast in relief on its back. When this mirror was used to reflect the sun onto a wall, the inscription appeared within the image. Shen cited with approval an anonymous explanation: "When the mirror is cast, the thinner parts cool first. The raised design on the back, being thicker, cools later and the shrinkage of the bronze is greater. Although the inscription is on the obverse, there are imperceptible traces of it on the face, so that it becomes visible within the light." He noted that this explanation is incomplete, because he had tried mirrors in his own and other collections that were physically indistinguishable from the "transparent" ones and found that they did not cast images (330; IV.1, 94*). His doubt was justified, although the approach taken by his informant was at least as good as those of some modern metallurgists.

Manipulation of the cooling rate can only accentuate the effect. The variation in thickness appears to be primarily responsible for the image in this sort of mirror, the most common among several types extant. Filing considerable bronze off the face of the mirror after casting is the key. This releases tensions in the metal and gives rise to slight deformations that produce the image.

Productive Techniques and Materials

The technologies of Shen’s time, like their European counterparts, were not cumulative and linked to science, but independent artisanal traditions transmitted from master to pupil. Shen left so many unique and informative accounts of ancient and contemporary processes among his jottings that Brush Talks has become a major source for early technology. Shen’s interests in contemporary techniques can in most cases be linked to broad concerns of his official career; but the exceptional richness of his record bespeaks a rare curiosity, and the trenchancy of his descriptions a seriousness about mechanical detail unusual among scholar-officials. His notes on techniques that had been lost before his time reflect the application of this technical curiosity and seriousness to archaeology, which was just becoming a branch of antiquarianism in the eleventh century.

Most of Shen’s cultured contemporaries keenly appreciated good workmanship, but saw no reason to notice the artisans responsible for it, except occasionally when condescending to them. Shen wrote about resourceful craftsmen and ingenious laborers with much the same admiration he