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Shen Kuo (Chinese: Chen Gua ; 1031-1095), courtesy name Cunzhong (Cun Zhong ) and pseudonym Mengqi (now usually given as Mengxi) Weng (Meng Xi Weng ), was a Han Chinese polymathic scientist and statesman of the Song dynasty (960-1279). Excelling in many fields of study and statecraft, he was a mathematician, astronomer, meteorologist, geologist, zoologist, botanist, pharmacologist, agronomist, archaeologist, ethnographer, cartographer, encyclopedist, general, diplomat, hydraulic engineer, inventor, academy chancellor, finance minister, governmental state inspector, poet, and musician.

Shen Kuo was born in Qiantang (modern-day Hangzhou) in the year 1031. His father Shen Zhou (Chen Zhou ; 978-1052) was a somewhat lower-class gentry figure serving in official posts on the provincial level; his mother was from a family of equal status in Suzhou, with her maiden name being Xu (Xu ). Shen Kuo received his initial childhood education from his mother, which was a common practice in China during this period. She was very educated herself, teaching Kuo and his brother Pi (Pi ) the military doctrines of her own elder brother Xu Tang (Xu Dong ; 975-1016). Since Shen was unable to boast of a 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 to achieve in his studies, subsequently passing the imperial examinations and enter the challenging and sophisticated life of an exam-drafted state bureaucrat.  From about 1040 AD, Shen's family moved around Sichuan province and finally to the international seaport at Xiamen, where Shen's father accepted minor provincial posts in each new location. Shen Zhou also served several years in the prestigious capital judiciary, the equivalent of a federal supreme court. Shen Kuo took notice of the various towns and rural features of China as his family traveled, while he became interested during his youth in the diverse topography of the land. He also observed the intriguing aspects of his father's engagement in administrative governance and the managerial problems involved; these experiences had a deep impact on him as he later became a government official. Since he often became ill as a child, Shen Kuo also developed a natural curiosity about medicine and pharmaceutics.  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). 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 (400 km2) of swampland into prime farmland. Shen Kuo noted that the success of the silt fertilization method relied upon the effective operation of sluice gates of irrigation canals.  The new Chancellor Cai Que (Cai Que ; 1036-1093) held Shen responsible for the disaster and loss of life. Along with abandoning the territory which Shen Kuo had fought for, Cai ousted Shen from his seat of office. Shen's life was now forever changed, as he lost his once reputable career in state governance and the military. 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 ink brush 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. Shen was also pardoned by the court for any previous faults or crimes that were claimed against him.  In his more idle years removed from court affairs, Shen Kuo enjoyed pastimes of the Chinese gentry and literati that would indicate his intellectual level and cultural taste to others. As described in his Dream Pool Essays, Shen Kuo enjoyed the company of the "nine guests" (Jiu Ke , jiuke), a figure of speech for the Chinese zither, the older 17x17 line variant of weiqi (known today as go), Zen Buddhist meditation, ink (calligraphy and painting), tea drinking, alchemy, chanting poetry, conversation, and drinking wine. These nine activities were an extension to the older so-called Four Arts of the Chinese Scholar.  According to Zhu Yu's book Pingzhou Table Talks (Ping Zhou Ke Tan ; Pingzhou Ketan) of 1119, Shen Kuo had two marriages; the second wife was the daughter of Zhang Chu (Zhang Chu ), 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 themselves 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. Shen Kuo permanently moved to the Dream Brook Estate in 1088, and in that same year he completed his life's written work of the Dream Pool Essays, naming the book after his garden-estate property. It was there that Shen Kuo spent the last several years of his life in leisure, isolation, and illness, until his death in 1095.  In the broad field of mathematics, Shen Kuo mastered many practical mathematical problems, including many complex formulas for geometry, circle packing, and chords and arcs problems employing trigonometry. Shen addressed problems of writing out very large numbers, as large as 1043. Shen's "technique of small increments" laid the foundation in Chinese mathematics for packing problems involving equal difference series. Sal Restivo writes that Shen used summation of higher series to ascertain the number of kegs which could be piled in layers in a space shaped like the frustum of a rectangular pyramid. In his formula "technique of intersecting circles", he created an approximation of the arc of a circle s given the diameter d, sagitta v, and length of the chord c subtending the arc, the length of which he approximated as s = c + 2v2/d. Restivo writes that Shen's work in the lengths of arcs of circles provided the basis for spherical trigonometry developed in the 13th century by Guo Shoujing (1231-1316). He also simplified the counting rods technique by outlining short cuts in algorithm procedures used on the counting board, an idea expanded on by the mathematician Yang Hui (1238-1298). Victor J. Katz asserts that Shen's method of "dividing by 9, increase by 1; dividing by 8, increase by 2," was a direct forerunner to the rhyme scheme method of repeated addition "9, 1, bottom add 1; 9, 2, bottom add 2".  Shen wrote extensively about what he had learned while working for the state treasury, including mathematical problems posed by computing land tax, estimating requirements, currency issues, metrology, and so forth. Shen once computed the amount of terrain space required for battle formations in military strategy, 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. Shen wrote about the earlier Yi Xing (672-717), 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.  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-Haytham (965-1039) was the first to experiment with camera obscura, Shen Kuo was the first to attribute geometrical and quantitative properties to the camera obscura, just several decades after Ibn al-Haytham's death. Using a fitting metaphor, Shen compared optical image inversion to an oarlock and waisted drum. He also discussed focal points and noted that the image in a concave mirror is inverted. Shen, who never asserted that he was the first to experiment with camera obscura, hints in his writing that camera obscura was dealt with in the Miscellaneous Morsels from Youyang written by Duan Chengshi (d. 863) during the Tang Dynasty (618-907), in regard to the inverted image of a Chinese pagoda by a seashore.
Shen Kuo