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THE GREAT WALL OF CHINA: The World’s Greatest Boundary Monument! John F. Brock, Australia 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). -
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). -
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). -
Full, Original, Version of the Review. the Finally Accepted, Abridged, Version Will Appear in the British Journal for the Histor
Full, original, version of the review. The finally accepted, abridged, version will appear in the British Journal for the History of Mathematics, 2020, vol.35 issue 3 https://www.tandfonline.com/toc/tbsh21/current Cullen, Christopher. Heavenly Numbers. Astronomy and Authority in Early Imperial China. Oxford, UK: Oxford University Press, 2017. Christopher Cullen began his scholarly career as a specialist on the subject of early Chinese astronomy and mathematics with a paper published in the Bulletin of the School of Oriental and African Studies in 1976: “A Chinese Eratosthenes of the flat earth: a study of a fragment of cosmology in Huai nan tzu.” As Cullen explained, he had been inspired to study a short passage of the ca. 120 BC 淮南子 Huai nan zi thanks to a “tantalizing reference” in Needham (SCC, III, 224). What Needham noted there was the fact that the Huai nan zi, an Early Han Daoist collection of essays on a wide variety of subjects, included an account of how gnomons and their shadows could be used to determine the height of the heavens, i.e. the distance to the sun from the (presumed to be flat) earth. Needham pointed out the similarity of the method used in the Huia nan zi to the one Eratosthenes had employed using two gnomons at Alexandria and Syene, a known distance to the south, to calculate the circumference of the of the earth, assumed to be spherical. The challenge Needham posed—that the account in the Huai nan zi was “distinctly obscure, and no satisfactory interpretation has yet bene made”—prompted Cullen to undertake his own thorough study of the text in question: My first efforts to understand the original text led me to the conclusion that it was unique in a number of ways and had points of interest that did not fully appear in the version of Maspero, 1929, 348 ff. -
Mapping Regional Traditions in Chinese Astronomy and Mathematics, 311–618 CE Daniel Patrick Morgan
Mapping Regional Traditions in Chinese Astronomy and Mathematics, 311–618 CE Daniel Patrick Morgan To cite this version: Daniel Patrick Morgan. Mapping Regional Traditions in Chinese Astronomy and Mathematics, 311– 618 CE. On cultures of scientific practice in ancient mathematical sciences, Apr 2019, Paris, France. halshs-02021447 HAL Id: halshs-02021447 https://halshs.archives-ouvertes.fr/halshs-02021447 Submitted on 1 Mar 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Mapping Regional Traditions in Chinese Astronomy and Mathematics, 311–618 CE * Daniel Patrick MORGAN (墨子涵) Paper delivered at On Cultures of Scientific Practice in Ancient Mathematical Sciences, Université Paris Diderot, 10–13 April 2019 Abstract The period of disunion from 311 to 589 CE saw the territories of the former Han Empire (206 BCE–220 CE) carved up into as many as twelve contemporaneous states ruled by a tumultuous succession of some forty different bloodlines, the majority of which were ‘bar- barian’ in origin. As it happens, this was also one of the most fruitful periods in the history of Chinese-language astronomy and mathematics. Experts were divided, working on the same problems in rival capitals, increasingly disconnected in written and oral tradition except as punctuated by violent redistributions of human and material resources by invading armies. -
Of Plates and Rings
of Plates and rings Where is the Dipper tied with the Cord? How is the Axis raised? —Tianwen Part I explained general information about astronomy in China from a very early time and how fengshui instruments are part of that long history. Now we will look at the technical aspects of this information and relate it to our methods. Most people in ancient China used the ordinary or farmer’s calendar of 360 days,1 while experts employed by the ruling classes—such as the imperial astronomer, imperial astrologer, meteorological officer, and timekeeper2—used the astronomical year of 365.25 days. Figure 1. The eastern sky at sunrise at approximately 30°N on The astronomical year is marked on the shi. It counts off the day of the spring equinox in 2300 BCE. (Worthen, 176) roughly a degree (du) per day—that is, time appears as an The observer assumed by the Zhoubi suanjing stood at roughly ° angle. (Cullen, 42) Not until the Jesuits came to China 35 N. (Cullen, 8) did the compass use 360 degrees. A Chinese astronomer stood facing south and observed the celestial objects that crossed the north-south • Inside Plate, Heaven Plate. This is the round plate that meridian in their daily motion from east to west contains the markings on a Luopan. On earlier devices (meridian transits). Any celestial object that fell on the it depicts Beidou, or defines where the ladle piece of meridian was zhong, “centered.” (Cullen, 41–42) the compass rests. All fengshui instruments have in common the following: • Outer Plate, Earth Plate. -
V Chinese Mathematics
V Chinese Mathematics The ancient record of civilization in China began in the more northern Yellow River Valley where the Yangshao culture existed from about 5,000 to 2700 B.C.E. These people lived in the middle and lower parts of the river valley. They cultivated rice and millet, kept pigs, wove baskets and made pottery without a wheel. Their pottery was dyed red with black geometric designs painted on it, and also pictures of fish and human faces. Archeologists have found pottery from these people with the symbols for 1, 2, 5, and 7 painted on the dishes. The next culture, one which evolved from the Yangshao, was the Longshan culture, which thrived from 3,000 to 2,000 B.C.E., approximately. This culture domesticated the water buffalo, sheep and cattle. They made black pottery on a wheel. The pottery was not painted but decorated with grooved or raised rings. From about 2100 to 1600 B.C.E. the Xia (or Hsia) dynasty controlled the Yellow River Valley. Recent discoveries have unearthed a large city with a wall and a moat for defensive purposes surrounding the city. This city has been dated to the early Xia dynasty. It is in Henan Province in today’s China. From about 1500 to 1000 B.C.E the Shang dynasty controlled the area with a capital city at Anyang, also in current day Henan province, just north of the southern bend in the Yellow River. They also used the walled and moated city of the Xia, mentioned above. By 1300 B.C.E. -
Ke-Xin Au Yong
The Ten Mathematical Classics: The Mathematics and Mathematical Education of Pre-Modern China by Ke-Xin Au Yong A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in History Department of History and Classics University of Alberta © Ke-Xin Au Yong, 2018 Abstract The Ten Mathematical Classics were the only imperially prescribed mathematics textbooks in pre-modern China. They were used during the Sui (581 – 618), Tang (618 – 906), and Northern Song (960 – 1127) dynasties at the imperial academy to structure the mathematical training of students. This dissertation explores the contents as well as information about the writers and commentators of these texts in order to arrive at a better understanding of Chinese mathematics and mathematical writers. It also analyzes how mathematical education actually took place, presenting a new perspective on why state-run mathematical education only existed at specific times. Lastly, this dissertation examines the circulation and transmission of the Ten Mathematical Classics. My thesis consists of three central points. Firstly, the history of Chinese mathematics should take into serious account the entire corpus of knowledge and endeavours, such as divination, that historical actors associated indivisibly with what we would consider pure mathematical knowledge. Secondly, the known writers, commentators, and readers of the Ten Mathematical Classics were all highly educated, many of whom were also government officials, so it is over-simplistic to attribute the lack of long-term state-run mathematical education to a general disdain among the Chinese literati for technical subjects. Thirdly, I argue that the state’s decisions to institute or drop mathematical education should be understood within the broader context of the state’s needs at the time, and were directly related to the availability of suitable mathematically skilled candidates who could be recruited into the bureaucracy. -
Proof As a Practice of Mathematical Pursuit in a Cultural, Socio-Political and Intellectual Context
Proof as a practice of mathematical pursuit in a cultural, socio-political and intellectual context Man-Keung Siu Department of Mathematics The University of Hong Kong Abstract Through examples we explore the practice of mathematical pursuit, in particular on the notion of proof, in a cultural, socio-political and intellectual context. One objective of the discussion is to show how mathematics constitutes a part of human endeavour rather than stands on its own as a technical subject, as it is commonly taught in the classroom. As a `bonus', we also look at the pedagogical aspect on ways to enhance understanding of speci¯c topics in the classroom. 1. Prologue: Question 6 of the 29th IMO Proof is, to some extent, as much an individualized activity as a social activity. It is an individualized activity in that a breakthrough or an igniting spark arises from the mental exertion of oneself, though sometimes aided or stimulated through the discussion with fellow mathematicians. It is a social activity in that a proof has to pass the scrutiny of other mathematicians in order to gain approval and acceptance by the mathematical community. Hence, we will begin with an example this author experienced in person. This example highlights the main function of a proof, which is to elucidate rather than just to verify. After that, we will explore, through four examples (in Sections 3,4,5,6), the practice of mathematical pursuit, in particular on the notion of proof, in a cultural, socio-political and intellectual context. Question 6 of the 29th International Mathematical Olympiad, held in Canberra in 1988, reads: \Let a and b be positive integers such that ab + 1 divides a2 + b2 a2 + b2. -
On Their Own Terms
On Their Own Terms On Their Own Terms Science in China, 1550–1900 Benjamin A. Elman Harvard University Press Cambridge, Massachusetts, and London, England 2005 Copyright © 2005 by the President and Fellows of Harvard College All rights reserved. Printed in the United States of America Library of Congress Cataloging-in-Publication Data Elman, Benjamin A., 1946– On their own terms : science in China, 1550–1900 / Benjamin A. Elman. p. cm. Includes bibliographical references and index. ISBN 0-674-01685-8 (alk. paper) 1. Science—China—History—16th century. 2. Science—China— History—17th century. 3. Science—China—History—18th century. 4. Science—China—History—19th century. I. Title. Q127.C5E38 2005 509'.51—dc22 2004059654 For Susan Naquin and Nathan Sivin and in memory of my mother, Rachel Elman Contents List of Maps, Illustrations, and Tables xi Chinese Dynasties xv Abbreviations xix Preface xxi I Introduction 1 Prologue 3 Finding the Correct Conceptual Grid 4 What Should Be the Literati Theory of Knowledge? 5 Late Ming Classicism in the Context of Commercial Expansion 9 Printing Technology and Publishing 16 Naturalization of Anomalies in Ming China and Early Modern Europe 20 1. Ming Classification on the Eve of Jesuit Contact 24 Ordering Things through Names 24 Collecting the Collectors 34 Late Ming Statecraft, Mathematics, and Christianity 53 Collecting Things in Texts 57 II Natural Studies and the Jesuits 61 2. The Late Ming Calendar Crisis and Gregorian Reform 63 Development of the Ming Astro-calendric Bureau 65 Evolution of the Late Ming Calendar Crisis 73 Gregorian Reform 80 Jesuits and Late Ming Calendar Reform 84 3. -
Astronomy and Mathematics in Ancient China: the Zhou Bi Suan Jing
This is a study and translation of the Zhou bi suanjing, a Chinese work on astronomy and mathematics which reached its final form around the first century AD. The author provides the first easily accessible introduction to the developing mathematical and observational practices of ancient Chinese astronomers and shows how the generation and validation of knowledge about the heavens in Han dynasty China related closely to developments in statecraft and politics. NEEDHAM RESEARCH INSTITUTE STUDIES • I Astronomy and mathematics in ancient China: the Zhou bi suanjing The Needham Research Institute Studies series will publish important and original new work on East Asian culture and science which develops or links in with the publication of the Science and Civilisation in China series. The series will be under the editorial control of the Publications Board of the Needham Research Institute. Astronomy and mathematics in ancient China: the Zhou bi suanjing Christopher Cullen Senior lecturer in the History of Chinese Science and Medicine, School of Oriental and African Studies, University of London CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 2RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521550895 © Cambridge University Press 1996 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1996 This digitally printed first paperback version 2006 A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Cullen, Christopher. -
Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chongnimsa˘ and Kamunsa˘ Buddhist Temples
religions Article Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chongnimsa˘ and Kamunsa˘ Buddhist Temples Juhwan Cha 1 and Young Jae Kim 2,* 1 School of Architecture, Tsinghua University, Beijing 100084, China; [email protected] 2 The Department of Heritage Conservation and Restoration, Korea National University of Cultural Heritage, Buyeo 33115, Korea * Correspondence: [email protected] Received: 14 January 2019; Accepted: 8 March 2019; Published: 18 March 2019 Abstract: Ancient books on East Asian mathematics introduced to the Korean Peninsula enrich our understanding of the arithmetic notions that mold the creative thought processes of the ancients. They believed that all objects in the universe could be composed of circles and squares and all items could be expressed in terms of geometrical profiles. Through the combination of circles and squares, the ancient East Asians expressed the order of the world and unraveled it mathematically. These principles are evident in the construction principles of early Korean stone pagodas. In particular, the square p root of 2 ( 2) is a very important number in the delineation represented in the consolidation of inscribed and circumscribed circles with squares. Further, the square root of 2 is applied as a design principle in the construction of the stone pagodas at the temples Chongnimsa˘ and Kamunsa.˘ This article demonstrates that the ancients on the continuous impact of the Jiuzhang Suanshu and the Zhoubi Suanshu constructed the pagodas complying with design principles based on the arithmetic and p geometric proportional systems of 2 times, which are intended to adjust compositional proportions and the gradual decrease in length to shape the tripartite partition of the foundation, the pagoda body, and the finial in stone pagodas.