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Further information: Chinese mathematics and Chinese geography Inverted image of a stone rubbing, comprising a map of eastern China, complete with detailed rivers. The area of the map covered by land features a near perfect grid pattern, which because it does not overlap any text, is clearly the work of the original mapmaker. The Yu Ji Tu, or "Map of the Tracks of Yu", carved into stone in 1137, located in the Stele Forest of Xi'an. This 3 ft (0.91 m) squared map features a graduated scale of 100 li for each rectangular grid. China's coastline and river systems are clearly defined and precisely pinpointed on the map. Yu refers to the Chinese deity described in the geographical chapter of the Book of Documents, dated 5th–3rd centuries BCE. There were many notable improvements to Chinese mathematics during the Song era. The book published in 1261 by the mathematician Yang Hui (c. 1238–1298) provided the earliest Chinese illustration of Pascal's triangle, although it was described earlier around 1100 by Jia Xian.[163] Yang Hui also provided rules for constructing combinatorial arrangements in magic squares, provided theoretical proof for Euclid's forty-third proposition about parallelograms, and was the first to use negative coefficients of 'x' in quadratic equations.[164] Yang's contemporary Qin Jiushao (c. 1202–1261) was the first to introduce the zero symbol into Chinese mathematics;[165] before this blank spaces were used instead of zeroes in the system of counting rods.[166] He is also known for working with the Chinese remainder theorem, Heron's formula, and astronomical data used in determining the winter solstice. Qin's major work was the Mathematical Treatise in Nine Sections published in 1247. Geometry was essential to surveying and cartography. The earliest extant Chinese maps date to the 4th century BCE,[167] yet it was not until the time of Pei Xiu (224–271) that topographical elevation, a formal rectangular grid system, and use of a standard graduated scale of distances was applied to terrain maps.[168][169] Following a long tradition, Shen Kuo created a raised-relief map, while his other maps featured a uniform graduated scale of 1:900,000.[170][171] A 3 ft (0.91 m) squared map of 1137—carved into a stone block—followed a uniform grid scale of 100 li for each gridded square, and accurately mapped the outline of the coasts and river systems of China, extending all the way to India.[172] Furthermore, the world's oldest known terrain map in printed form comes from the edited encyclopedia of Yang Jia in 1155, which displayed western China without the formal grid system that was characteristic of more professionally made Chinese maps.[173] Although gazetteers had existed since 52 CE during the Han dynasty and gazetteers accompanied by illustrative maps (Chinese: tujing) since the Sui dynasty, the illustrated gazetteer became much more common in the Song dynasty, when the foremost concern was for illustrative gazetteers to serve political, administrative, and military purposes.[174] Movable type printing Further information: History of printing in East Asia A rectangular ink on paper diagram with several hundred dots, several of which are organized into constellations, such as a drawn bow (bottom center) and a tree (top left). One of the star charts from Su Song's Xin Yi Xiang Fa Yao published in 1092, featuring cylindrical projection similar to Mercator projection and the corrected position of the pole star thanks to Shen Kuo's astronomical observations.[161][162] Su Song's celestial atlas of five star maps is actually the oldest in printed form.[175] The innovation of movable type printing was made by the artisan Bi Sheng (990–1051), first described by the scientist and statesman Shen Kuo in his Dream Pool Essays of 1088.[176][177] The collection of Bi Sheng's original clay-fired typeface was passed on to one of Shen Kuo's nephews, and was carefully preserved.[177][178] Movable type enhanced the already widespread use of woodblock methods of printing thousands of documents and volumes of written literature, consumed eagerly by an increasingly literate public. The advancement of printing had a deep impact on education and the scholar-official class, since more books could be made faster while mass-produced, printed books were cheaper in comparison to laborious handwritten copies.[70][74] The enhancement of widespread printing and print culture in the Song period was thus a direct catalyst in the rise of social mobility and expansion of the educated class of scholar elites, the latter which expanded dramatically in size from the 11th to 13th centuries.[70][179] The movable type invented by Bi Sheng was ultimately trumped by the use of woodblock printing due to the limitations of the enormous Chinese character writing system, yet movable type printing continued to be used and was improved in later periods. The Yuan dynasty scholar-official Wang Zhen (fl. 1290–1333) implemented a faster typesetting process, improved Bi's baked-clay movable type character set with a wooden one, and experimented with tin-metal movable type.[180] The wealthy printing patron Hua Sui (1439–1513) of the Ming dynasty established China's first metal movable type (using bronze) in 1490.[181] In 1638 the Beijing Gazette switched their printing process from woodblock to movable type printing.[182] Yet it was during the Qing dynasty that massive printing projects began to employ movable type printing. This includes the printing of sixty-six copies of a 5,020 volume long encyclopedia in 1725, the Gujin Tushu Jicheng (Complete Collection of Illustrations and Writings from the Earliest to Current Times), which necessitated the crafting of 250,000 movable type characters cast in bronze.[183] By the 19th century the European style printing press replaced the old Chinese methods of movable type, while traditional woodblock printing in modern East Asia is used sparsely and for aesthetic reasons. Hydraulic and nautical engineering Main article: Science and technology of the Song dynasty The most important nautical innovation of the Song period seems to have been the introduction of the magnetic mariner's compass, which permitted accurate navigation on the open sea regardless of the weather.[170] The magnetized compass needle – known in Chinese as the "south-pointing needle" – was first described by Shen Kuo in his 1088 Dream Pool Essays and first mentioned in active use by sailors in Zhu Yu's 1119 Pingzhou Table Talks. A diagram of the pound lock system, from a bird's eye perspective and from a side perspective. The bird's eye view illustrates that water enters the enclosed area through two culverts on either side of the upper lock gate. The side view diagram illustrates how the elevation is higher before reaching the top gate than it is afterwards. A plan and side view of a canal pound lock, a concept pioneered in 984 by the Assistant Commissioner of Transport for Huainan, the engineer Qiao Weiyo.[184] There were other considerable advancements in hydraulic engineering and nautical technology during the Song dynasty. The 10th-century invention of the pound lock for canal systems allowed different water levels to be raised and lowered for separated segments of a canal, which significantly aided the safety of canal traffic and allowed for larger barges.[185] There was the Song-era innovation of watertight bulkhead compartments that allowed damage to hulls without sinking the ships.[74][186] If ships were damaged, the Chinese of the 11th century employed drydocks to repair them while suspended out of the water.[187] The Song used crossbeams to brace the ribs of ships in order to strengthen them in a skeletal-like structure.[188] Stern-mounted rudders had been mounted on Chinese ships since the 1st century, as evidenced with a preserved Han tomb model of a ship. In the Song period, the Chinese devised a way to mechanically raise and lower rudders in order for ships to travel in a wider range of water depths.[188] The Song arranged the protruding teeth of anchors in a circular pattern instead of in one direction.[188] David Graff and Robin Higham state that this arrangement "[made] them more reliable" for anchoring ships.[188] Structural engineering and architecture Main article: Architecture of the Song dynasty A wide, octagonal pagoda. It has four tall, functional floors made of brick, and an additional five, short, purely decorative floors made of wood. Each floor is separated by an eave, and the top five floor's eaves look as if they were simply stacked right on top of one another. The 42-metre (138 ft) tall, brick and wood Lingxiao Pagoda of Zhengding, Hebei, built in 1045. Architecture during the Song period reached new heights of sophistication. Authors such as Yu Hao and Shen Kuo wrote books outlining the field of architectural layouts, craftsmanship, and structural engineering in the 10th and 11th centuries, respectively. Shen Kuo preserved the written dialogues of Yu Hao when describing technical issues such as slanting struts built into pagoda towers for diagonal wind bracing.[189] Shen Kuo also preserved Yu's specified dimensions and units of measurement for various building types.[190] The architect Li Jie (1065–1110), who published the Yingzao Fashi ('Treatise on Architectural Methods') in 1103, greatly expanded upon the works of Yu Hao and compiled the standard building codes used by the central government agencies and by craftsmen throughout the empire.[191] He addressed the standard methods of construction, design, and applications of moats and fortifications, stonework, greater woodwork, lesser woodwork, wood-carving, turning and drilling, sawing, bamboo work, tiling, wall building, painting and decoration, brickwork, glazed tile making, and provided proportions for mortar formulas in masonry.[192][193] In his book, Li provided detailed and vivid illustrations of architectural components and cross-sections of buildings. These illustrations displayed various applications of corbel brackets, cantilever arms, mortise and tenon work of tie beams and cross beams, and diagrams showing the various building types of halls in graded sizes.[194] He also outlined the standard units of measurement and standard dimensional measurements of all building components described and illustrated in his book.[195] A painting of people boating in a lake. There is a small island in the center of the lake, connected to the mainland by an arched bridge. The entire lake is surrounded by a low wall. Games in the Jinming Pool, silk painting by Zhang Zeduan, depiction of Kaifeng, Northern Song era. Grandiose building projects were supported by the government, including the erection of towering Buddhist Chinese pagodas and the construction of enormous bridges (wood or stone, trestle or segmental arch bridge). Many of the pagoda towers built during the Song period were erected at heights that exceeded ten stories. Some of the most famous are the Iron Pagoda built in 1049 during the Northern Song and the Liuhe Pagoda built in 1165 during the Southern Song, although there were many others. The tallest is the Liaodi Pagoda of Hebei built in 1055, towering 84 m (276 ft) in total height. Some of the bridges reached lengths of 1,220 m (4,000 ft), with many being wide enough to allow two lanes of cart traffic simultaneously over a waterway or ravine.[196] The government also oversaw construction of their own administrative offices, palace apartments, city fortifications, ancestral temples, and Buddhist temples.[197] The professions of the architect, craftsman, carpenter, and structural engineer were not seen as professionally equal to that of a Confucian scholar-official. Architectural knowledge had been passed down orally for thousands of years in China, in many cases from a father craftsman to his son. Structural engineering and architecture schools were known to have existed during the Song period; one prestigious engineering school was headed by the renowned bridge-builder Cai Xiang (1012–1067) in medieval Fujian province.[198] A diagram showing multiple elaborately carved triangular brackets attached to each of the vertical support beams inside of a building. Bracket arm clusters containing cantilevers, from Li Jie's building manual Yingzao Fashi, printed in 1103. Besides existing buildings and technical literature of building manuals, Song dynasty artwork portraying cityscapes and other buildings aid modern-day scholars in their attempts to reconstruct and realize the nuances of Song architecture. Song dynasty artists such as Li Cheng, Fan Kuan, Guo Xi, Zhang Zeduan, Emperor Huizong of Song, and Ma Lin painted close-up depictions of buildings as well as large expanses of cityscapes featuring arched bridges, halls and pavilions, pagoda towers, and distinct Chinese city walls. The scientist and statesman Shen Kuo was known for his criticism of artwork relating to architecture, saying that it was more important for an artist to capture a holistic view of a landscape than it was to focus on the angles and corners of buildings.[199] For example, Shen 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.[199] There were also pyramidal tomb structures in the Song era, such as the Song imperial tombs located in Gongxian, Henan province.[200] About 100 km (62 mi) from Gongxian is another Song dynasty tomb at Baisha, which features "elaborate facsimiles in brick of Chinese timber frame construction, from door lintels to pillars and pedestals to bracket sets, that adorn interior walls."[200] The two large chambers of the Baisha tomb also feature conical-shaped roofs.[201] Flanking the avenues leading to these tombs are lines of Song dynasty stone statues of officials, tomb guardians, animals, and mythological creatures. Archaeology Further information: List of Chinese inventions § A In addition to the Song gentry's antiquarian pursuits of art collecting, scholar-officials during the Song became highly interested in retrieving ancient relics from archaeological sites, in order to revive the use of ancient vessels in ceremonies of state ritual.[202] Scholar-officials of the Song period claimed to have discovered ancient bronze vessels that were created as far back as the Shang dynasty (1600–1046 BCE), which bore the written characters of the Shang era.[203] Some attempted to recreate these bronze vessels by using imagination alone, not by observing tangible evidence of relics; this practice was criticized by Shen Kuo in his work of 1088.[202] Yet Shen Kuo had much more to criticize than this practice alone. Shen objected to the idea of his peers that ancient relics were products created by famous "sages" in lore or the ancient aristocratic class; Shen rightfully attributed the discovered handicrafts and vessels from ancient times as the work of artisans and commoners from previous eras.[202] He also disapproved of his peers' pursuit of archaeology simply to enhance state ritual, since Shen not only took an interdisciplinary approach with the study of archaeology, but he also emphasized the study of functionality and investigating what was the ancient relics' original processes of manufacture.[202] Shen used ancient texts and existing models of armillary spheres to create one based on ancient standards; Shen described ancient weaponry such as the use of a scaled sighting device on crossbows; while experimenting with ancient musical measures, Shen suggested hanging an ancient bell by using a hollow handle.[202] A heavily tarnished bronze bowl adorned with several carvings of squares that curl in on themselves at the bottom. It has three stubby, unadorned legs and two small, square handles coming off from the top rim. Scholars of the Song claim to have collected ancient relics dating back as far as the Shang dynasty, such as this bronze ding vessel. Despite the gentry's overriding interest in archaeology simply for reviving ancient state rituals, some of Shen's peers took a similar approach to the study of archaeology. His contemporary Ouyang Xiu (1007–1072) compiled an analytical catalogue of ancient rubbings on stone and bronze which pioneered ideas in early epigraphy and archeology.[81] During the 11th century, Song scholars discovered the ancient shrine of Wu Liang (78–151 AD), a scholar of the Han dynasty (202 BC – 220 AD); they produced rubbings of the carvings and bas-reliefs decorating the walls of his tomb so that they could be analyzed elsewhere.[204] On the unreliability of historical works written after the fact, scholar-official Zhao Mingcheng (1081–1129) stated "...the inscriptions on stone and bronze are made at the time the events took place and can be trusted without reservation, and thus discrepancies may be discovered."[205] Historian R.C. Rudolph states that Zhao's emphasis on consulting contemporary sources for accurate dating is parallel with the concern of the German historian Leopold von Ranke (1795–1886),[205] and was in fact emphasized by many Song scholars.[206] The Song scholar Hong Mai (1123–1202) heavily criticized what he called the court's "ridiculous" archaeological catalogue Bogutu compiled during the Huizong reign periods of Zheng He and Xuan He (1111–1125).[207] Hong Mai obtained old vessels from the Han dynasty and compared them with the descriptions offered in the catalogue, which he found so inaccurate he stated he had to "hold my sides with laughter."[208] Hong Mai pointed out that the erroneous material was the fault of Chancellor Cai Jing (1047–1126), who prohibited scholars from reading and consulting the written histories.[208] |
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