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The Mathematics of the Chinese, Indian, Islamic and Gregorian Calendars
Heavenly Mathematics: The Mathematics of the Chinese, Indian, Islamic and Gregorian Calendars Helmer Aslaksen Department of Mathematics National University of Singapore [email protected] www.math.nus.edu.sg/aslaksen/ www.chinesecalendar.net 1 Public Holidays There are 11 public holidays in Singapore. Three of them are secular. 1. New Year’s Day 2. Labour Day 3. National Day The remaining eight cultural, racial or reli- gious holidays consist of two Chinese, two Muslim, two Indian and two Christian. 2 Cultural, Racial or Religious Holidays 1. Chinese New Year and day after 2. Good Friday 3. Vesak Day 4. Deepavali 5. Christmas Day 6. Hari Raya Puasa 7. Hari Raya Haji Listed in order, except for the Muslim hol- idays, which can occur anytime during the year. Christmas Day falls on a fixed date, but all the others move. 3 A Quick Course in Astronomy The Earth revolves counterclockwise around the Sun in an elliptical orbit. The Earth ro- tates counterclockwise around an axis that is tilted 23.5 degrees. March equinox June December solstice solstice September equinox E E N S N S W W June equi Dec June equi Dec sol sol sol sol Beijing Singapore In the northern hemisphere, the day will be longest at the June solstice and shortest at the December solstice. At the two equinoxes day and night will be equally long. The equi- noxes and solstices are called the seasonal markers. 4 The Year The tropical year (or solar year) is the time from one March equinox to the next. The mean value is 365.2422 days. -
The 100 Years Anglo-Chinese Calendar, 1St Jan. 1776 to 25Th Jan
: THE 100 YEARS ANGLO-CHINESE CALENDAR, 1st JAN., 1776 to 25th JAN., 187G, CORRESPONDING WITH THE 11th DAY of the 11th MOON of the 40th YEAR of the EEIGN KIEN-LUNG, To the END of the 14th YEAR of the REIGN TUNG-CHI; TOGETIIER WITH AN APPENDIX, CONTAINING SEVERAL INTERESTING TABLES AND EXTRACTS. BY IP. LOUE;EIE,0. SHANGHAI rRINTED AT THE " NORTH-CHINA HERALD " OFFICE, 1872. -A c^ V lo ; ; PREFACE. In presenting the 100 Years Anglo-Chinese Calendar to the public, the compiler claims no originality for his work, inasmuch as, since the year 1832,* Calendars in somewhat similar form have been yearly issued from the press in China ; but, as it is doubtful if a complete series of these exists, and as, in the transaction of business, whether official, legal or commercial, between Foreigners and Chinese, and in the study of Chinese History which is now so intimately connected with foreign nations, a knowledge of the corresponding dates is quite necessary, it is hoped that this compilation will be found useful, and especially so in referring to the date of past events, and in deciding the precise day, according to the Chinese and Chris- tian Calendars, on which they occurred. Commencing with the last quarter of the past century (1st January, 1776), the Calendar embraces the peiiod when the first British Embassy (Lord Macartney's in 1793) arrived in China. For convenience sake the Calendar has been divided into 10 parts, each embracing a period of ten years of the Christian era and ends with the close of the 14th year of the present reign Tung-chi, —the 25th January, 1876. -
Transformation of the Dualistic International Order Into the Modern Treaty System in the Sino-Korean Relationship
International Journal of Korean History (Vol.15 No.2, Aug.2010) 97 G Transformation of the Dualistic International Order into the Modern Treaty System in the Sino-Korean Relationship Song Kue-jin* IntroductionG G Whether in the regional or global scale, the international order can be defined as a unique system within which international issues develop and the diplomatic relations are preserved within confined time periods. The one who has leadership in such international order is, in actuality, the superpowers regardless of the rationale for their leading positions, and the orderliness of the system is determined by their political and economic prowess.1 The power that led East Asia in the pre-modern era was China. The pre- modern East Asian regional order is described as the tribute system. The tribute system is built on the premise of installation, so it was important that China designate and proclaim another nation as a tributary state. The system was not necessarily a one-way imposition; it is possible to view the system built on mutual consent as the tributary state could benefit from China’s support and preserve the domestic order at times of political instability to person in power. Modern capitalism challenged and undermined the East Asian tribute GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG * HK Research Professor, ARI, Korea University 98 Transformation of the Dualistic International Order into the ~ system led by China, and the East Asian international relations became a modern system based on treaties. The Western powers brought the former tributary states of China into the outer realm of the global capitalistic system. With the arrival of Western imperialistic powers, the East Asian regional order faced an inevitable transformation. -
Spread of Civilizations in East Asia: Tang & Song Dynasties
Spread of Civilizations in East Asia: Tang & Song Dynasties 500CE-1603CE NOTES Two Golden Ages After the Han dynasty (Wudi, Silk Road) collapsed in 220CE, China remained a divided land for about 400 years. During this period of division, China managed to escape the grim world that Western Europe was experiencing (plague, economic failures, etc.). Farm production in China expanded and technology slowly improved. Buddhism spread, while learning and the arts continued. Even Chinese cities survived despite invaders in the North, as the invaders would often adopt Chinese civilization rather than demolish it. Meanwhile, in the South, various Chinese dynasties rose and fell. THE TANG DYNASTY The first two Tang emperors were father (Li Yuan) and son (Li Shimin), but the son was the main force behind the dynasty. After time, Li Shimin, compelled his aging father to step down and took the throne himself, taking the name Tang Taizong. He was a brilliant general, government reformer, famous historian, and master of the calligraphy brush. He would eventually become the most admired of all Chinese emperors. The Tang Dynasty, under the leadership of Tang Taizong, carried empire building to greater heights, conquering territories deep into Central Asia, as far as present-day Afghanistan. Chinese armies forced neighboring lands of Vietnam, Tibet, and Korea to become tributary states. A tributary state is an independent state that has to acknowledge the supremacy of another state and pay tribute to its ruler. Therefore, while these states remained independent, their rulers had to acknowledge Chinese supremacy and send regular tribute to the Tang emperor. -
The Calendars of India
The Calendars of India By Vinod K. Mishra, Ph.D. 1 Preface. 4 1. Introduction 5 2. Basic Astronomy behind the Calendars 8 2.1 Different Kinds of Days 8 2.2 Different Kinds of Months 9 2.2.1 Synodic Month 9 2.2.2 Sidereal Month 11 2.2.3 Anomalistic Month 12 2.2.4 Draconic Month 13 2.2.5 Tropical Month 15 2.2.6 Other Lunar Periodicities 15 2.3 Different Kinds of Years 16 2.3.1 Lunar Year 17 2.3.2 Tropical Year 18 2.3.3 Siderial Year 19 2.3.4 Anomalistic Year 19 2.4 Precession of Equinoxes 19 2.5 Nutation 21 2.6 Planetary Motions 22 3. Types of Calendars 22 3.1 Lunar Calendar: Structure 23 3.2 Lunar Calendar: Example 24 3.3 Solar Calendar: Structure 26 3.4 Solar Calendar: Examples 27 3.4.1 Julian Calendar 27 3.4.2 Gregorian Calendar 28 3.4.3 Pre-Islamic Egyptian Calendar 30 3.4.4 Iranian Calendar 31 3.5 Lunisolar calendars: Structure 32 3.5.1 Method of Cycles 32 3.5.2 Improvements over Metonic Cycle 34 3.5.3 A Mathematical Model for Intercalation 34 3.5.3 Intercalation in India 35 3.6 Lunisolar Calendars: Examples 36 3.6.1 Chinese Lunisolar Year 36 3.6.2 Pre-Christian Greek Lunisolar Year 37 3.6.3 Jewish Lunisolar Year 38 3.7 Non-Astronomical Calendars 38 4. Indian Calendars 42 4.1 Traditional (Siderial Solar) 42 4.2 National Reformed (Tropical Solar) 49 4.3 The Nānakshāhī Calendar (Tropical Solar) 51 4.5 Traditional Lunisolar Year 52 4.5 Traditional Lunisolar Year (vaisnava) 58 5. -
CALENDRICAL CALCULATIONS the Ultimate Edition an Invaluable
Cambridge University Press 978-1-107-05762-3 — Calendrical Calculations 4th Edition Frontmatter More Information CALENDRICAL CALCULATIONS The Ultimate Edition An invaluable resource for working programmers, as well as a fount of useful algorithmic tools for computer scientists, astronomers, and other calendar enthu- siasts, the Ultimate Edition updates and expands the previous edition to achieve more accurate results and present new calendar variants. The book now includes algorithmic descriptions of nearly forty calendars: the Gregorian, ISO, Icelandic, Egyptian, Armenian, Julian, Coptic, Ethiopic, Akan, Islamic (arithmetic and astro- nomical forms), Saudi Arabian, Persian (arithmetic and astronomical), Bahá’í (arithmetic and astronomical), French Revolutionary (arithmetic and astronomical), Babylonian, Hebrew (arithmetic and astronomical), Samaritan, Mayan (long count, haab, and tzolkin), Aztec (xihuitl and tonalpohualli), Balinese Pawukon, Chinese, Japanese, Korean, Vietnamese, Hindu (old arithmetic and medieval astronomical, both solar and lunisolar), and Tibetan Phug-lugs. It also includes information on major holidays and on different methods of keeping time. The necessary astronom- ical functions have been rewritten to produce more accurate results and to include calculations of moonrise and moonset. The authors frame the calendars of the world in a completely algorithmic form, allowing easy conversion among these calendars and the determination of secular and religious holidays. Lisp code for all the algorithms is available in machine- readable form. Edward M. Reingold is Professor of Computer Science at the Illinois Institute of Technology. Nachum Dershowitz is Professor of Computational Logic and Chair of Computer Science at Tel Aviv University. © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-05762-3 — Calendrical Calculations 4th Edition Frontmatter More Information About the Authors Edward M. -
Tributary Trade and China's Relations with the West Author(S): J
Tributary Trade and China's Relations with the West Author(s): J. K. Fairbank Reviewed work(s): Source: The Far Eastern Quarterly, Vol. 1, No. 2 (Feb., 1942), pp. 129-149 Published by: Association for Asian Studies Stable URL: http://www.jstor.org/stable/2049617 . Accessed: 09/10/2012 18:50 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Association for Asian Studies is collaborating with JSTOR to digitize, preserve and extend access to The Far Eastern Quarterly. http://www.jstor.org TRIBUTARY TRADE AND CHINA'S RELATIONS WITH THE WEST J.K. FAIRBANK HarvardUniversity UNTIL a centuryago, China's foreign relations were suzerain-vassal relationsconducted through the ancient forms of thetributary system. This traditionalChinese basis fordiplomacy was finallyturned upside down by the "unequal" treatiesof the period1842-1858, but vestigesof the old Chineseway of dealingwith the barbarians survived much longer and today still forma considerablethough latent portion of the heritageof Chinese diplomats.It is ofcourse a truismthat tribute was notexactly what it seemed, and thatboth diplomacy and internationaltrade were conductedwithin the tributaryframework. The followingessay offers a preliminaryinterpretation of theorigin, function, and significanceof thisgreat Chinese institution.' CHINESE CULTURAL DOMINANCE IN EAST ASIA The tributarysystem was a naturalexpression of Chinesecultural ego- centricity.Ever since the bronzeage, when the civilizationof the Shang dynasty(c. -
Zar-O Zur: Gold and Force: Safavid Iran As a Tributary Empire
Chapter 2 Zar-o Zur: Gold and Force: Safavid Iran as a Tributary Empire Rudi Matthee Introduction The first decade of the twenty-first century saw a plethora of scholarly writings on the concept of empire and its historical manifestations. Pro- pelled by the terrible events of 9/11 and the overseas wars the United States launched in their wake, this renewed attention to an old state struc- ture introduced and sought to generalize the proposition that, despite its habitual denial-cum amnesia with regard to its status, America consti- tutes a latter-day global empire. Within half a decade, forced to keep pace with evolving events, the emerging discussion changed course to fasten onto the notion that, barely begun, the end of the American empire was already in sight, that America’s imperial decline had set in as soon as its imperial status culminated. Safavid Iran, with a lifespan of 221 years, might sound like a remote and unlikely homologue. Yet, with the caveat that time in the modern world is compressed, that developments playing out over a decade today might have taken a century or more in the past, the simile is, on second thought, perhaps not an unreasonable one: The Safavids, too, “declined” (and collapsed) soon after attaining their peak. That, at least, is one of the arguments I advanced in an article pub- lished in 2010 in which I posed the question of whether the Safavids - 35 - Rudi Matthee presided over an empire at all.1 The very question might seem strange, yet the reason for posing it was simple: In the traditional literature, -
Downloaded License
Journal of the history of International Law (2021) 1–32 brill.com/jhil Making International Law Truly ‘International’? Reflecting on Colonial Approaches to the China-Vietnam Dispute in the South China Sea and the Tribute System So Yeon Kim PhD Researcher, Faculty of Law, University of Cambridge, Cambridge, UK [email protected] Received: 22 August 2020 | Revised: 20 December 2020 | Accepted: 31 January 2021 Abstract Before non-European regions adopted international law, a different set of law of ter- ritory governed the non-European regions. Notwithstanding their differences, inter- national courts and tribunals have approached non-European territorial disputes through a single lens of Eurocentric international law. The general claim of this article is that international courts and tribunals should approach non-European territorial disputes with special consideration to account for the region’s historical system. This article case studies the China-Vietnam dispute in the South China Sea to advance this claim. Through the case study, I argue that East Asian concepts of sovereignty do not equate with those employed by Eurocentric international law. I then suggest guide- lines for considering regional systems when ruling on non-European territorial dis- putes. If international courts and tribunals do not change their legal approach, this not only distorts the historical realities of the non-European regions but also results in unfair dispute settlements. Keywords Tribute System – Territorial Disputes – Law of Territory – Paracel Islands Dispute – South China Sea © So Yeon Kim, 2021 | doi:10.1163/15718050-12340183 This is an open access article distributed under the terms of the CC BY 4.0Downloaded license. -
The End of Time: the Maya Mystery of 2012
THE END OF TIME ALSO BY ANTHONY AVENI Ancient Astronomers Behind the Crystal Ball: Magic, Science and the Occult from Antiquity Through the New Age Between the Lines: The Mystery of the Giant Ground Drawings of Ancient Nasca, Peru The Book of the Year: A Brief History of Our Seasonal Holidays Conversing with the Planets: How Science and Myth Invented the Cosmos Empires of Time: Calendars, Clocks and Cultures The First Americans: Where They Came From and Who They Became Foundations of New World Cultural Astronomy The Madrid Codex: New Approaches to Understanding an Ancient Maya Manuscript (with G. Vail) Nasca: Eighth Wonder of the World Skywatchers: A Revised and Updated Version of Skywatchers of Ancient Mexico Stairways to the Stars: Skywatching in Three Great Ancient Cultures Uncommon Sense: Understanding Nature’s Truths Across Time and Culture THE END OF TIME T H E Ma Y A M YS T ERY O F 2012 AN T H O N Y A V E N I UNIVERSI T Y PRESS OF COLOR A DO For Dylan © 2009 by Anthony Aveni Published by the University Press of Colorado 5589 Arapahoe Avenue, Suite 206C Boulder, Colorado 80303 All rights reserved Printed in the United States of America The University Press of Colorado is a proud member of the Association of American University Presses. The University Press of Colorado is a cooperative publishing enterprise supported, in part, by Adams State College, Colorado State University, Fort Lewis College, Mesa State College, Metropolitan State College of Denver, University of Colorado, University of Northern Colorado, and Western State College of Colorado. -
Earth Ascending (Jose Arguelles)
Contents Foreword by Charles T. Tart viii Introduction to the Second Edition ix Part I: Geomancy is to History, What Grammar is to Language Two Introductory Essays I. The Roots of Unity: Geomancy and World Order 2 II. From Geomancy to Holonomics 15 The Discovery of the Psi Bank 15 The Search for History 18 The Holonomic Equation: Art, Science, and Sacred Order 23 Part II: The Maps I. Nature Presents Itself 28 Prelude: The Code, the Key, the Model 1. Psi Bank Matrix, the Warp Demonstrating the Fourfold Polar Seasonal Pattern of the Binary Triplet Configuration 30 2. Binary Triplet Configuration-The Code and the Key 32 3. Resonant Field Model, Derived from Binary Triplet Configuration 34 4. Psi Bank Matrix Generated as Binary Resonance of Radiation Belts 36 5. Ceomantic Flow Chart and Model of Evolved Psi Rings 38 6. Holonomic Brain and Demonstration of Psi Circulation within Electromagnetic Field 40 7. I Ching as Description of Holonomic Space-Time Matrix and as Description of Genetic Code 42 8. Random Psi Transmission Example: Ben Franklin's Magic Square with an Array of 8 and Pulse of 260 44 9. Tzolkin, the Mayan Version of the Sacred Calendar Written in Binary Mathematical Notation with Mayan Day Glyphs 46 II. Man Learns from Nature 48 Prelude: From Primary Attunement to Psychosensory Elaboration 10. Rhythmic Movement of the Sacred Calendar as Pattern of Primary Attunement 50 11. Shaman Shirt and Tree of Life: Interpenetration of Man and Nature 52 12. Aboriginal Attunement Templates 54 13. Primary Attunement and Geomancy 56 14. -
Traditional Chinese Calendar: an Exceptional Timepiece Bearing the Emblem of an Ox
Blancpain –Villeret collection December 2020 Ref. 00888I-3431-55B Traditional Chinese Calendar: an exceptional timepiece bearing the emblem of an ox Blancpain celebrates Chinese New Year with a limited series of 50 watches dedicated to this tradition and its festivities. The Year of the Metal Ox begins on February 12th 2021 and ends on January 31st 2022. Housed in a precious platinum case, the Traditional Chinese Calendar bearing the emblem of the ox features an exclusive complication appearing on an elegant Grand Feu enamel dial. Forged in noble platinum, the 50-piece limited-edition Traditional Chinese Calendar watch pays homage to the age-old culture of the Middle Kingdom. The Grand Feu enamel dial of this exceptional timepiece reveals the complexity of a display combining Chinese calendar indications with those of the Gregorian calendar and moon phases – all specialities of the Manufacture Blancpain. Unlike the Gregorian calendar, whose unit of measurement is based on the solar day, the traditional lunisolar Chinese calendar is based on the lunar cycle as well as exact astronomical observations of the sun’s longitude. Thus, in addition to the hours and minutes, date and moon phases, Blancpain's Traditional Chinese Calendar watch offers the main indications of the traditional Chinese calendar: double hours, days, months and leap months, zodiac signs, five elements and ten heavenly stems. The latter, combined with the 12 earthly branches – symbolised by the animals of the zodiac – produce 60 different pairs forming the sexagesimal cycle of the Chinese time measurement system. Despite their complex combination, these functions are clearly displayed on a dial with Roman gold numerals and hollowed-out sage leaf-shaped hands.