ÿþ<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <title>The Canada Society of Yi Jing (The Book of Changes)</title> <meta http-equiv="content-type" content="text/html; charset=UTF-8" /> <meta name="keywords" content="Canada Society of Yi Jing, The Book of Changes, Yi Jing, I Ching, Yi" /> <meta name="robots" content="all" /> <meta name="author" content="Serena Deng" /> <meta name="description" content="Canada Society of Yi Jing - The Book of Changes" /> <link href="../includes/css.css" rel="stylesheet" type="text/css" /> <script type='text/javascript' src='../includes/javascript.js'></script> <script type='text/javascript' src='../includes/calendar.js'></script> </head> <body> <div id="main"> <div id="left"> <!-- Left side elements placed here --> <div id="logo"> <!-- Logo image placed here --> <!-- Logo must be at a fixed width of 150px --> <img src="../images/yjlogo.jpg" width="150" height="150" alt="The Canada Society of Yi Jing (The Book of Changes)" /> <img src="../images/space.gif" height="5"> </div> <div id="nav"> <!-- Navigation items placed here --> <!-- Main navigation items should be enclosed by <a> tags --> <!-- Subnavigation items should be in a list (<ul> tags), with each item separated by <a> and then <li> tags --> <!-- Maximum width of images here is 148px --> <div> <a href="index_en.htm">Home</a> <div id="nav01">&nbsp;</div> </div> <div onMouseOver="subNavOpen('nav02')" onMouseOut="subNavClose('nav02')"> <a href="javascript:subNavChange('nav02')"><img class="navarrow" src="../images/arrowd.gif" />About Yi Jing</a> <div id="nav02"><ul> <a href="whatis.htm"><li>What is Yi Jing</li></a> <a href="reducfallacy.htm"><li>Fallacy: A Divination book</li></a> <a href="unilaws.htm"><li>Laws Of the Universe</li></a> </ul></div> </div> <div onMouseOver="subNavOpen('nav03')" onMouseOut="subNavClose('nav03')"> <a href="javascript:subNavChange('nav03')"><img class="navarrow" src="../images/arrowd.gif" />Yijing, Science & Civilization</a> <div id="nav03"><ul> <a href="exampley&s.htm"><li>Yijing and Modern Science</li></a> <a href="exampley&cs.htm"><li>Yijing and Chinese Science</li></a> </ul></div> </div> <div onMouseOver="subNavOpen('nav04')" onMouseOut="subNavClose('nav04')"> <a href="javascript:subNavChange('nav04')"><img class="navarrow" src="../images/arrowd.gif" />The Study of Zhou Yi</a> <div id="nav04"><ul> <a href="handbook.htm"><li>Handbook</li></a> <a href="evidenceyi.htm"><li>New Evidences</li></a> <a href="evidencebased.htm"><li>Evidence-based Interpretation</li></a> <a href="classicalbook.htm"><li>Classical Books</li></a> <a href="bookreview.htm"><li>Book Review</li></a> </ul></div> </div> <div onMouseOver="subNavOpen('nav05')" onMouseOut="subNavClose('nav05')"> <a href="javascript:subNavChange('nav05')"><img class="navarrow" src="../images/arrowd.gif" />History of Yi Academy</a> <div id="nav05"><ul> <a href="profilehistory.htm"><li>Profile History</li></a> <a href="indeterminate.htm"><li>Origin of Indeterminate Analysis</li></a> </ul></div> </div> <div onMouseOver="subNavOpen('nav06')" onMouseOut="subNavClose('nav06')"> <a href="javascript:subNavChange('nav06')"><img class="navarrow" src="../images/arrowd.gif" />Prehistory of Yi Academy</a> <div id="nav06"><ul> <a href="fuxigua_e1.htm"><li>Archaeology of Fu Xi Yi</li></a> <a href="fuxigua_e2.htm"><li>Preshistorical Investigation</li></a> </ul></div> </div> <div onMouseOver="subNavOpen('nav07')" onMouseOut="subNavClose('nav07')"> <a href="javascript:subNavChange('nav07')"><img class="navarrow" src="../images/arrowd.gif" />Yi Divination and Sciences</a> <div id="nav07"><ul> <a href="yidivination_e1.htm"><li>Basic Differences</li></a> <a href="yidivination_e2.htm"><li>Science Basis</li></a> </ul></div> </div> <div onMouseOver="subNavOpen('nav08')" onMouseOut="subNavClose('nav08')"> <a href="javascript:subNavChange('nav08')"><img class="navarrow" src="../images/arrowd.gif" />Traditional Applications of Yijing</a> <div id="nav08"><ul> <a href="yimedicine.htm"><li>Yijing and Chinese Medicine</li></a> <a href="fengshuisci.htm"><li>Feng Shui and Sciences</li></a> <a href="fatecalculation.htm"><li>Fate Calculation and Sciences</li></a> </ul></div> </div> <div onMouseOver="subNavOpen('nav10')" onMouseOut="subNavClose('nav10')"> <a href="javascript:subNavChange('nav10')"><img class="navarrow" src="../images/arrowd.gif" />Members Area</a> <div id="nav10"><ul> <a href="society.htm"><li>Society Board</li></a> <a href="bylaws.htm"><li>Society Bylaws</li></a> <a href="news0205.htm"><li>Monthly Newsletter</li></a> <a href="memberappl.htm"><li>Membership Application</li></a> </ul></div> </div> <a href="links.htm">Links</a> <img src="../images/space.gif" height="5"> </div> <div id="splash"> <!-- Splash items placed here --> <!-- This section is optional; delete the splasharea div area to leave it blank --> <!-- Maximum width of images here is 138px --> <div id="splasharea"> <p>The Canada Society <br /> of Yi Jing <br />(The Book of Changes)<br /> 10939-38 Avenue<br /> Edmonton, AB<br /> Canada T6J 0K6</p> </div> </div> <div id="splashend"> <!-- Additional splash items may be placed here, but this section is fixed at 100 pixels in height; overflow material is hidden --> <!-- Maximum width of images here is 140px --> <p>&nbsp;</p> </div> </div> <div id="content"> <!-- Main page content is placed here --> <!-- h1, h2, p, a, img, ul tags styled --> <!-- Maximum width of images here is 430px --> <h1>What is the Earliest Chinese Origin of Indeterminate Analysis -- Find out the Truth of the Mystery behind the Ta Yen Shu</h1> <p>by Deng Honghai</p> <p> As Dr. Joseph Needham, the author of Science and Civilisation in China, pointed out, indeterminate analysis was always a marked mathematical interest of Chinese. Why had Chinese been so interested in this mathematical field? Although giving an excellent introduction to the post-4th century Chinese mathematicians contributions to this field, he did not examine this question because his research was limited within the available Chinese mathematical literatures. </p> <p> Fortunately, he connected time indeterminate analysis with Ta yen shu ('YMˆSˆ Great Extension Mathematics) and introduced two important works in its study and application: I Ching s(NLˆ) Ta Yen Li Shu ('YMˆÆføf Book of the Ta Yen Calendar) and Chhin Chiu Shao s(æy]Nö—) Shu Shu Chiu Chang (xeøf]Nàz Nine Chapters of Mathematics). The former only contains the results from the calendrical calculation by applying the Ta yen shu; the latter focused on how to apply the Ta yen shu to calendrical calculation and other public works. </p> <p> He realized that the name Ta yen shu was derived from an obscure statement in the I Ching (Book of Changes) that the  Great Extension Number ('YMˆKNxe)  is 50. Having known the mathematical procedure of the classical method of consulting the oracle of the I-Ching, he concluded:  indeterminate analysis was connected with, if not actually derived from, an ancient method of divination using yarrow stalks. (Joseph Needham: Science and Civilisation in China, Cambridge at the University Press, 1959, P. 119-122).His conferment of the connection between indeterminate analysis and the classical method of divination using yarrow stalks is correct. However, since he could not understand the statement, he could not further find the truth of the development of indeterminate analysis in China. </p> <p> In fact, Chhin Chiu Shao already indicated in his book that the classical method of divination using yarrow stalks was one of the applied disciplines of the Ta yen shu, just like the calendrical calculation as one of its applied disciplines. Because the classical method of divination had been deified since the Xia dynasty, the truth of Ta yen shu was lost. He approached the historical development and extensive applications of the Ta yen shu since remote antiquity. Although having shown his mathematical proof, he did not have archaeological evidences to prove his logical conclusion. </p> <p> This paper will have both mathematical and archaeological evidences to prove the natural reasonability of the statement in the I Ching (Book of Changes) that the  Great Extension Number  is 50. The statement means that as a key number in Fu Xi numbering system, 50 is so important that a set basic parameters of the ancient Sifen (äSÛVRÆf four quadrantal) Calendar, the algebraic formulation of the Pythagoras theorem (þR¡€š[t) and it applications in terrestrial and celestial measurements, and the mathematics of circle and square (¹eWSˆ) and its applications in article makings and engineering and so on were derived from it. This was the reason for Chinese to be so interested in this mathematical field. Based on these evidences, the process of evolution of the Ta yen shu from an ancient method of calendrical calculation to the classical method of divination using yarrow stalks will logically and historically be recovered and hence the truth of the mystery behind the Ta Yen Shu will be found out. </p> <p>&nbsp;</p> </div> <div id="right"> <!-- Right side elements placed here --> <div id="rightnav"> <table> <th><a href="../Yi_Jing_EN/indeterminate.htm">Eng</a></th> <th><a href="../Yi_Jing_TC/indeterminate_bg5.htm">A~SO</a></th> <th><a href="../Yi_Jing_SC/indeterminate_GB.htm">€{SO</a></th> </table> </div> <div id="rightwhite"> <!-- Whitespace, ignore --> <div id="cornertl"> <!-- Top left page corner decoration; do not modify --> <img src="../images/cornertl.gif" /> </div> <!-- Top right page corner decoration; do not modify --> <div id="cornertr"> <img src="../images/cornertr.gif" /> </div> </div> <div id="rightmain"> <div id="righttext"> <!-- Right blurb items, such as ads or related items, here --> <!-- Maximum width of images is 130px --> <h1>Your inputs are always welcome!</h1> <p> You are welcome to input your comments, suggestions, supports and donations. </p> <p> There is a bank account of our society for raising funds. </p> <p> All proceeds will be used to fund publishing the books mentioned above, developing international cooperation on the theme, promoting Universe Yi research and education. </p> <p> You can contact us by mail via our mailing address on the left side of the page or email at <a href="javascript:antiSpam('jvs','shaw.ca')">jvs@shaw.ca</a>. </p> </div> <p><CENTER> <SCRIPT LANGUAGE="JavaScript"> getBgn(); </SCRIPT> </CENTER></P> </div> <div id="rightend"> <!-- Additional blurb area; items may be placed here but this section is fixed at 100 pixels in height; overflow material is hidden --> <!-- Maximum width of images is 140px --> <p>&nbsp;</p> </div> </div> <div id="footer"> <!-- Page copyright information; do not modify --> <!-- Bottom left page corner decoration; do not modify --> <div id="cornerbl"> <img src="../images/cornerbl.gif" /> </div> <div> <p id="foottext"> &copy; 2004 The Canada Society of Yi Jing (The Book of Changes). 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