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The Evolution of Mathematics in Ancient China: from the Newly Discovered Shu and Suan Shu Shu Bamboo Texts to the Nine Chapters
The Evolution of Mathematics in Ancient China: From the Newly Discovered Shu and Suan shu shu Bamboo Texts to the Nine Chapters on the Art of Mathematics*,† by Joseph W. Dauben‡ The history of ancient Chinese mathematics and texts currently being conserved and studied at its applications has been greatly stimulated in Tsinghua University and Peking University in Beijing, the past few decades by remarkable archaeological the Yuelu Academy in Changsha, and the Hubei discoveries of texts from the pre-Qin and later Museum in Wuhan, it is possible to shed new light periods that for the first time make it possible to on the history of early mathematical thought and its study in detail mathematical material from the time applications in ancient China. Also discussed here are at which it was written. By examining the recent developments of new techniques and justifications Warring States, Qin, and Han bamboo mathematical given for the problems that were a significant part of the growing mathematical corpus, and which * © 2014 Joseph W. Dauben. Used with permission. eventually culminated in the comprehensive Nine † This article is based on a lecture presented in September of 2012 at the Fairbank Center for Chinese Studies at Har- Chapters on the Art of Mathematics. vard University, which was based on a lecture first given at National Taiwan Tsinghua University (Hsinchu, Taiwan) in the Spring of 2012. I am grateful to Thomas Lee of National Chiaotung University of Taiwan where I spent the academic Contents year 2012 as Visiting Research Professor at Chiaota’s Insti- tute for Humanities and Social Sciences, which provided sup- 1 Recent Archaeological Excavations: The Shu port for much of the research reported here, and to Shuchun and Suan shu shu ................ -
Hawai'i Reader In
Traditional Chinese Culture Edited by Victor H. Mair Nancy S. Steinhardt and Paul R. Goldin University of Hawai'i Press Honolulu 34 | Cao Pi, "A Discourse on Literature" CAO PI (187-226) was the second son of the formidable military dictator Cao Cao (155-220), whose story is told in Romance of the Three Kingdoms fSanguoyanyi'), and the elder brother of the poet Cao Zhi (192-232). He ended the puppet rule of the last Eastern Han emperor and founded the Wei dynasty in 220; thus he is also known as Emperor Wen of the Wei. Like his father and brother, Cao Pi was an accomplished writer and poet. His "Discourse on Literature" (Lun wen) survives from a critical work entided A Treatise on the Classics (Dianlun), of which only some frag- ments are extant. One of the most notable things about this essay is Cao Pi's use of the notion of qi, breath or vital force, as a concept of literary criticism that has had an immense influence on classical Chinese literary thought. "A Discourse on Literature" is itself a beautiful literary composition. It is particularly touch- ing because we see in it a writer who was secretly anxious and insecure about the value of his work and the uncertain possibility of immortal fame. A great deal of the first part of the essay is devoted to the reasoning that one's literary talent is an inherent quality that cannot be learned or obtained by hard efforts (li qiang); in the second part of the essay, he claims that a person may achieve literary immortality by exerting himself (qiang li). -
OECD Reviews of Innovation Policy Synthesis Report
OECD Reviews of Innovation Policy CHINA Synthesis Report ORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENT in collaboration with THE MINISTRY OF SCIENCE AND TECHNOLOGY, CHINA ORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENT The OECD is a unique forum where the governments of 30 democracies work together to address the economic, social and environmental challenges of globalisation. The OECD is also at the forefront of efforts to understand and to help governments respond to new developments and concerns, such as corporate governance, the information economy and the challenges of an ageing population. The Organisation provides a setting where govern- ments can compare policy experiences, seek answers to common problems, identify good practice and work to co- ordinate domestic and international policies. The OECD member countries are: Australia, Austria, Belgium, Canada, the Czech Republic, Denmark, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Japan, Korea, Luxembourg, Mexico, the Netherlands, New Zealand, Norway, Poland, Portugal, the Slovak Republic, Spain, Sweden, Switzerland, Turkey, the United Kingdom and the United States. The Commission of the European Communities takes part in the work of the OECD. OECD Publishing disseminates widely the results of the Organisation’s statistics gathering and research on economic, social and environmental issues, as well as the conventions, guidelines and standards agreed by its members. © OECD 2007 No reproduction, copy, transmission or translation of this publication may be made without written permission. Applications should be sent to OECD Publishing: [email protected] 3 Foreword This synthesis report (August 2007 Beijing Conference version) summarises the main findings of the OECD review of the Chinese national innovation system (NIS) and policy. -
Science Without Modernization: China's First Encounter with Useful and Reliable Knowledge from Europe Harriet T
Science Without Modernization: China's First Encounter With Useful And Reliable Knowledge From Europe Harriet T. Zurndorfer Abstract This paper reviews how recent revisionist scholarship on the history of Chinese science and technology has recast the Jesuit enterprise in China. It argues that the Ming and Qing governments' efforts to control the Jesuit-transmitted knowledge in these fields stimulated ever-more interest among local scholars in Chinese traditions of mathematics and astronomy which culminated in the 18th century 'evidential research' movement. But because the scientific knowledge the Jesuits conveyed was already 'out-of-date' before their arrival in China, local scholars never had the possibility to make a complete reassessment of their own mathematical and astronomical practices. As the primary and -- at times the only -- translators of Western scientific thought to China, the Jesuits had an enormous historical impact on how Chinese scholars became trapped in a pre-Copernican universe where Chinese natural philosophy with its focus on metaphysical interpretations of the natural world remained entrenched until the 19th century. Introduction: The History of Chinese Science and Technology in Global Perspective and the 'Great Divergence' In 1603, the famous Chinese intellectual and Christian convert, Xu Guangqi (1562-1633) offered the local magistrate of his native Shanghai county a proposal outlining the methodology to measure the length, width, depth, and water flow of a river. Xu's document (later printed in his collection Nongzheng quanshu [Comprehensive Treatise on Agricultural Administration]; comp. 1639) 1 employed conventional surveying practices as well as calculating techniques based on the Pythagorean theorem. Although it is tempting to attribute Xu's achievement here as a direct consequence of his meeting the Jesuit Matteo Ricci (1552-1610) in Nanjing that same year, it is not certain from extant documentation that this encounter with the European was the defining influence on his water study. -
Astronomy and Calendars – the Other Chinese Mathematics Jean-Claude Martzloff
Astronomy and Calendars – The Other Chinese Mathematics Jean-Claude Martzloff Astronomy and Calendars – The Other Chinese Mathematics 104 BC–AD 1644 123 Jean-Claude Martzloff East Asian Civilisations Research Centre (CRCAO) UMR 8155 The National Center for Scientific Research (CNRS) Paris France The author is an honorary Director of Research. After the publication of the French version of the present book (2009), he has been awarded in 2010 the Ikuo Hirayama prize by the Académie des Inscriptions et Belles-Lettres for the totality of his work on Chinese mathematics. ISBN 978-3-662-49717-3 ISBN 978-3-662-49718-0 (eBook) DOI 10.1007/978-3-662-49718-0 Library of Congress Control Number: 2016939371 Mathematics Subject Classification (2010): 01A-xx, 97M50 © Springer-Verlag Berlin Heidelberg 2016 The work was first published in 2009 by Honoré Champion with the following title: Le calendrier chinois: structure et calculs (104 av. J.C. - 1644). This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. -
Archimedes and Liu Hui on Circles and Spheres Joseph W
www.ontologia.net/studies Ontology Studies 10, 2010 21-38 Archimedes and Liu Hui on Circles and Spheres Joseph W. Dauben Department of History Herbert H. Lehman College and Ph.D. Program in History The Graduate Center The City University of New York Reception date / Fecha de recepción: 27-05-2009 Acceptation date / Fecha de aceptación: 22-06-2009 Abstract This article describes the mystery of a long lost codex of Archimedes that resurfaced briefly at the turn of the last century by Johan Ludwig Heiberg. Long enough for the Danish historian of mathematics Heiberg to identify, photograph and eventually transcribe “The Method” and several other works by Archimedes of considerable mathematical interest. In 1879 Heiberg completed his dissertation, Quaestiones Archimedeae, devoted to Archimedes’ life, works, and transmission of his texts. Keywords: Archimedes, Ephodos, Method, Johan Ludwig Heiberg. Resumen. Arquímedes y Hui Liu en torno a círculos y esferas. Este artículo describe el misterio de un códice de Arquímedes perdido hace mucho tiempo que reapareció brevemente a principios del siglo pasado de la mano de Johan Ludwig Heiberg. Tiempo suficiente para que el historiador danés de las matemáticas Heiberg pudiese identificar, fotografiar y, finalmente, transcribir “El Método” y varias otras obras de Arquímedes de interés matemático considerable. En 1879 Heiberg completó su tesis doctoral, Quaestiones Archimedeae, dedicado a la vida de Arquímedes, las obras, y la transmisión de sus textos. Palabras clave: Arquímedes, ephodos, método, Johan Ludwig Heiberg. This story begins with a mystery—the mystery of a long lost codex of Archimedes that resurfaced briefly at the turn of the last century, long enough for the Danish historian of mathematics Johan Ludwig Heiberg to identify, photograph and eventually transcribe “The Method” and several other works by Archimedes of considerable mathematical 22 Ontology Studies 10, 2010 Joseph W. -
The Fundamental Cartographical Technology of Ancient China ─ Forward Intersection
THE FUNDAMENTAL CARTOGRAPHICAL TECHNOLOGY OF ANCIENT CHINA ─ FORWARD INTERSECTION Zilan WANG1 Keling WANG Institute of History and Philosophy of Science University of Wuhan P.R.China Email: [email protected] Institute of Historical Geography University of Wuhan P.R.China Most available ancient Chinese maps were not based on field survey but were compiled indoor using direct or indirect travel and exploration records. The map preparation process can be roughly divided into the following steps. Firstly, the position of a geographical object is marked on the sketch map using its orientation and distance. The orientation data is based on the 8-orientation system in which the circumference is divided into 8 parts. The distance data is mainly based on the Chinese distance unit “Li”, but a smaller unit “Bu” will be used for detailed description. Secondly, the rectification by “intersection” method is carried out in order to minimize the errors in the relative positions of a geographical object caused by the intrinsic “roughness” of the aforementioned spatial model. This “intersection” rectification method, which is similar to the “forward intersection” in modern survey technology, was analyzed in this article from three angles: (1) the simulation study of the 2nd century B.C. survey map “Mawang Dui Map”, (2) the analysis of the traditional survey theory recorded in Zhou Bi Suan Jing and Jiu Zhang Suan Shu (including Liu Hui’s annotation of the latter), and (3) the new interpretation of the Fei Niao model proposed by Shen Kuo. In addition, travel records of “intersection” observation and the technique and historical background of forward intersection were found in related historical and geographical documents. -
A "Chinese Eratosthenes" Reconsidered: Chinese and Greek Calculations and Categories1
134 EASTM 19 (2002) A "Chinese Eratosthenes" Reconsidered: Chinese and Greek Calculations and Categories1 Lisa Raphals [Lisa Raphals is Professor of Chinese and Comparative Literature at the University of California, Riverside. She is author of Knowing Words: Wisdom and Cunning in the Classical Traditions of China and Greece (1992), Sharing the Light: Representations of Women and Virtue in Early China (1998), and a range of studies in comparative philosophy, history of science and early Taoism. Recent and forthcoming publications include: "The Treatment of Women in a Second-Century Medical Casebook" (Chinese Science, 1998), "Arguments by Women in Early Chinese Texts" (Nan Nü, 2001), and "Fate, Fortune, Chance and Luck in Chinese and Greek: A Comparative Semantic History" (Philosophy East & West 2003, forthcoming).] * * * In the third century B.C.E., Eratosthenes of Cyrene (276-196) attempted to calculate the circumference of the earth using gnomon measurements and the properties of similar triangles. His calculation is widely taken as one of the great achievements of Greek science. In "A Chinese Eratosthenes of the flat earth: a study of a fragment of cosmology in Huai Nan tzu ," Christopher Cullen remarks that a comparison of Greek and Chinese calculations provides a good example of the characteristics of success and failure in science. Eratosthenes had two hypotheses of considerable predictive power, despite the fact that he would have found some difficulty in justifying them: (a) the earth is spherical; (b) the sun is for practical purposes at an infinite distance so that its rays reach the earth sensibly parallel. As it will appear, the Chinese author believed neither of these things.2 1 Earlier versions of this paper were presented in the conference "Rethinking Science and Civilization: The Ideologies, Disciplines, and Rhetorics of World History," Stanford University May 21-23, 1999; at the Needham Research Institute, September 10, 1999; and in the Mathematics Colloquium of the University of California at Riverside (April 27, 2000). -
Absence of Geometric Models in Medieval Chinese Astronomy
ABSENCE OF GEOMETRIC MODELS IN MEDIEVAL CHINESE ASTRONOMY JAYANT SHAH Abstract. In 718 A.D., Ch’¨ut’an Hsi-ta (Gautama Siddh¯artha), an Indian astronomer who was appointed an“astronomer royal” in the T’ang court compiled a compendium of omens and divina- tions, called K’aiy¨uan Chan-ching, analogous to Varahamihira’s Br. hatsam. hita. The 104th volume of this work, Chiu-chih li (Nine Upholders Calendrical System) on astronomy was entirely based on the Indian astronomy of the 7th century which in turn was based on the geometric astronomy of the Greeks. A few years later, the emperor asked I-hsing (Yixing in pinyin), a buddhist monk, an as- tronomer and a mathematician, to overhaul the traditional Chinese astronomy. He submitted an astronomical system, called Ta-yen li (Grand Expansion Calendrical System, Dayan li in pinyin) in 727 A.D. Only Ta-yen li was officially adopted. In the 13th century, a Persian astronomer submitted to Khubi- lai Khan an astronomical system, Myriad Year Calendrical System, based on the geometric Islamic astronomy. This too was not of- ficially adopted. Instead, Khubilai Khan ordered a major reform of the traditional Chinese system. The result was Shou-shih li (Granting the Seasons Calendrical System) which held sway over the Chinese astronomy until the arrival of the Jesuits in the 17th century. An analysis of the motion of the Sun and and the lunar paral- lax in Ta-yen li and Shou-shih li shows how little impact foreign imports had on Chinese astronomy. Geometric methods began to make inroads in Chinese astronomy only after the arrival of the Jesuits in the 17th century. -
Chinese Mathematics and ICCM
COMMUNICATION Chinese Mathematics and ICCM Editor’s Note: Notices invites occasional contributions, such as this piece, from its sister publications. Lizhen Ji Introduction distinguished Western math- China is big and growing, and Chinese mathematics is also ematicians such as Wiener, expanding and merging with world mathematics. What is Hadamard, Blaschke, and Os- special about the community of Chinese mathematicians? good were crucial for their How has Chinese mathematics evolved and interacted success. with the outside world? How will it impact the future of Modern Chinese math- mathematics and the global mathematics community in ematics reached another the world? minor golden age in the Though these questions are complex, one good way to 1950s and early 1960s. Then understand them is to take a look at an organization which political turmoil settled in. represents Chinese mathematicians and their friends and collaborators around the world: the International The History of ICCM Congress of Chinese Mathematicians (ICCM), which holds With the open door policy its seventh international conference this August in Beijing. in the 1980s, the Chinese economy and hence Chinese Chern in the early 1990s. A Glimpse at the History of Chinese Mathematics mathematics and sciences China has a long history, and Chinese mathematics also developed rapidly. By the has a long history. Though Chinese mathematics was di- 1990s the time was ripe rectly motivated by applications in astronomy, agriculture, to establish an international platform for mathemati- and commerce, there were systematic expositions of the- cians of Chinese descent and their friends to share and ories and results developed by Chinese people. -
The Great Wall of China : the World’S Greatest Boundary Monument !!!
03-09-2014 THE GREAT WALL OF CHINA : THE WORLD’S GREATEST BOUNDARY MONUMENT !!! THE MOON AS SEEN FROM THE GREAT WALL !!! 1 03-09-2014 TOMB RELIEF FROM THE HAN DYNASTY (202 BC ---6 AD) SHOWING EMPEROR FU XI and his consort NU WA with drawing compass and set square in hand FU XI & NU WA 29 th Century BC 2 03-09-2014 EMPEROR YU THE GREAT C. 2200 TO 2100 BC THE AUTHOR OF THE HAIDAO SUANJING (263 AD) 3 03-09-2014 MEASURING WITH A SET SQUARE LIU HUI (c220-280) 4 03-09-2014 SIGHTING SQUARE SIGHTING STAFF OR GNOMON PLUMB LINE MEASURING ROPE WITH PLUMB BOB ATTACHED 5 03-09-2014 TOWER MEASUREMENTS WERE MUCH THE SAME IN 1247 AS IN 1592 ?!? 1247 1592 1726 WOODCUT FROM THE TU SHU JI CHENG 6 03-09-2014 THE WARRING STATES PERIOD BORDER LINES WITH BOUNDARY WALLS QIN SHI HUANGDI: THE FIRST EMPEROR (221-206 BC) 7 03-09-2014 SOME OF THE 3,000 CHINESE CHARACTERS IN THE MODERN ALPHABET THE GREAT WALL OF THE FIRST EMPEROR 8 03-09-2014 THE FIRST EMPEROR’S “GREAT WALL” TERRACOTTA GUARDIANS OF THE FIRST EMPEROR AT HIS TOMB IN XI’AN 9 03-09-2014 HAN DYNASTY WALL (206 BC- 220 AD) 10 03-09-2014 HAN SILK MAP FROM c. 180 BC HAN SILK MAP FROM c. 180 BC 11 03-09-2014 PEI XIU (223-271) DA MING HUN YI TU 1390 12 03-09-2014 CHINA’S GREAT WALL HERO: QI JIGUANG (1528-1588) 13 03-09-2014 MING GREAT WALL ERECTION GREAT WALL BRICKS FROM 1577 INSCRIBED GREAT WALL BRICKS MING BRICK KILN 14 03-09-2014 TESTING THE GREAT WALL DEFENCES MATTEO RICCI 1552-1610 15 03-09-2014 RICCI WORLD MAP 1602 RICCI WORLD MAP 1602 16 03-09-2014 SALVAGING GREAT WALL MATERIAL DORGON THE MANCHU GREAT -
THE GREAT WALL of CHINA: the World's Greatest Boundary
THE GREAT WALL OF CHINA: The World’s Greatest Boundary Monument! By John F. Brock Keywords: Ancient China, surveyors, Pei Xiu, Liu Hui, The Haidao Suanjing, Great Wall(s) of China, Greatest Boundary Monument. :”… in the endeavors of mathematical surveying, China’s accomplishments exceeded those realized in the West by about one thousand years.” Frank Swetz – last line in The Sea Island Mathematical Manual: Surveying and Mathematics in Ancient China. ABSTRACT It is said that the Great Wall of China is the only manmade structure on Earth which is visible from space (not from the Moon)! The only natural feature similarly identifiable from the outer reaches past our atmospheric zone has been named as Australia’s Great Barrier Reef. This Fig. 1 The moon from The Great Wall instead of natural wonder of the sea is vice versa which cannot actually occur !!! continuous while the Great Wall of China is actually made up of a series of castellated walls mainly erected along ridge lines causing major variations in the levels of its trafficable upper surface. Some of the barriers built are not formed from stone but from rammed earth mounds. The purpose for these walls was primarily to facilitate protection from hostile adjoining tribes and marauding hordes of enemy armies intent on looting and pillaging the coffers of its neighbouring wealthier Chinese Dynasty of the time. As the need for larger numbers of military troops became required to defeat the stronger opponents, which may sometimes have formed alliances, the more astute provincial rulers saw a similar advantage in the unification of the disparate Chinese Provinces particularly during the Ming Dynasty (1368-1644).