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1 /* ========================================================================
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2 * Copyright 1988-2006 University of Washington
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3 *
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4 * Licensed under the Apache License, Version 2.0 (the "License");
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5 * you may not use this file except in compliance with the License.
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6 * You may obtain a copy of the License at
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7 *
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8 * http://www.apache.org/licenses/LICENSE-2.0
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9 *
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10 *
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11 * ========================================================================
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12 */
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13
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14 ALL ABOUT CALENDARS
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15
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16 Although one can never be sure of what will happen at some future
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17 time, there is strong historical precedent for presuming that the
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18 present Gregorian calendar will still be in effect within the useful
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19 lifetime of the IMAP toolkit. We have therefore chosen to adhere to
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20 these precedents.
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21
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22 The purpose of a calendar is to reckon time in advance, to show
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23 how many days have to elapse until a certain event takes place in the
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24 future, such as the harvest or the release of a new version of Pine.
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25 The earliest calendars, naturally, were crude and tended to be based
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26 upon the seasons or the lunar cycle.
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27
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28
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29 ANCIENT CALENDARS
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30
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31 The calendar of the Assyrians, for example, was based upon the
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32 phases of the moon. They knew that a lunation (the time from one full
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33 moon to the next) was 29 1/2 days long, so their lunar year had a
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34 duration of 354 days. This fell short of the solar year by about 11
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35 days. (The exact time for the solar year is approximately 365 days, 5
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36 hours, 48 minutes, and 46 seconds.) After 3 years, such a lunar
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37 calendar would be off by a whole month, so the Assyrians added an extra
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38 month from time to time to keep their calendar in synchronization with
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39 the seasons.
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40
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41 The best approximation that was possible in antiquity was a 19-year
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42 period, with 7 of these 19 years having 13 months (leap months). This
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43 scheme was adopted as the basis for the lunar calendar used by the
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44 Hebrews. The Arabs also used this calendar until Mohammed forbade
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45 shifting from 12 months to 13 months; this causes the Muslim holy month
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46 of Ramadan to move backwards through the seasons, completing a cycle
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47 every 32 1/2 years.
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48
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49 When Rome emerged as a world power, the difficulties of making a
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50 calendar were well known, but the Romans complicated their lives because
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51 of their superstition that even numbers were unlucky. Hence their
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52 months were 29 or 31 days long, with the exception of February, which
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53 had 28 days. Every second year, the Roman calendar included an extra
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54 month called Mercedonius of 22 or 23 days to keep up with the solar
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55 year.
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56
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57
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58 JULIAN CALENDAR
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59
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60 Even this algorithm was very poor, so that in 45 BCE, Caesar,
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61 advised by the astronomer Sosigenes, ordered a sweeping reform. By
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62 imperial decree, the year 46 BCE was made 445 days long to bring the
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63 calendar back in step with the seasons. The new calendar, similar to
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64 the one we now use was called the Julian calendar (named after Julius
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65 Caesar).
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66
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67 Months in the Julian calendar were 30 or 31 days in length and
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68 every fourth year was made a leap year (having 366 days) by adding a day
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69 to the end of the year. This leap year rule was not consistantly
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70 applied until 8 CE. The year-ending month of February, never a popular
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71 month, was presently shortened so that Julius Caesar and Emperor
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72 Augustus could each have long months named after them.
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73
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74 Caesar also decreed that the year would start with the first of
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75 January, which since 153 BCE was the day that Roman consuls took office,
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76 and not the vernal equinox in late March. Not everyone accepted that
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77 part of his reform, as we shall see.
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78
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79
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80 GREGORIAN CALENDAR
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81
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82 Caesar's year was 11 1/2 minutes short of the calculations
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83 recommended by Sosigenes and eventually the date of the vernal equinox
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84 began to drift. Roger Bacon became alarmed and sent a note to Pope
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85 Clement IV, who apparently was not impressed. Pope Sixtus IV later
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86 became convinced that another reform was needed and called the German
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87 astronomer, Regiomontanus, to Rome to advise him. Unfortunately,
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88 Regiomontanus died of the plague shortly thereafter and the plans died
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89 as well.
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90
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91 In 1545, the Council of Trent authorized Pope Gregory XIII to
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92 reform the calendar once more. Most of the mathematical work was done
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93 by Father Christopher Clavius, S.J. The immediate correction that was
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94 adopted was that Thursday, October 4, 1582 was to be the last day of the
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95 Julian calendar. The next day was Friday, with the date of October 15.
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96 For long range accuracy, a formula suggested by the Vatican librarian
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97 Aloysius Giglio was adopted. It said that every fourth year is a leap
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98 year except for century years that are not divisible by 400. Thus 1700,
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99 1800 and 1900 would not be leap years, but 2000 would be a leap year
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100 since 2000 is divisible by 400. This rule eliminates 3 leap years every
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101 4 centuries, making the calendar sufficiently correct for most ordinary
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102 purposes. This calendar is known as the Gregorian calendar and is the
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103 one that we now use today.
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104
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105 It is interesting to note that in 1582, all the Protestant princes
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106 ignored the papal decree and so many countries continued to use the
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107 Julian calendar until either 1698 or 1752. Britain and its American
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108 colonies went from Wednesday, September 2, 1752 to Thursday, September
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109 14. Prior to the changeover, the British used March 25 as the start of
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110 the new year.
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111
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112 In Russia, it needed the revolution to introduce the Gregorian
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113 calendar in 1918. Turkey didn't adopt it until 1927.
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114
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115
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116 NUMBERING OF YEARS
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117
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118 The numbering of the year is generally done according to an "era",
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119 such as the year of a ruler's reign.
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120
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121 In about 525, a monk named Dionysius Exiguus suggested that the
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122 calculated year of Jesus' birth be designated as year 1 in the Julian
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123 calendar. This suggestion was adopted over the next 500 years and
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124 subsequently followed in the Gregorian calendar.
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125
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126 For the benefit of those who seek religious significance to the
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127 calendar millenium, note that year 1 is too late by at least 4 years.
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128 Herod the Great, named in the Christian Bible as having all children in
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129 Bethlehem put to death in an attempt to kill the infant Jesus, died in 4
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130 BCE.
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131
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132 Nothing particularly significant of an historic or religious nature
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133 happened in Gregorian year 1; however it has become a worldwide standard
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134 as the "common era." In modern times, the terms "CE" (common era) and
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135 "BCE" (before common era) are preferred over the earlier (and, as we
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136 have seen, less accurate) "AD" (anno Domini, "the year of the Lord") and
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137 "BC" (before Christ).
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138
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139 The Hebrew lunar calendar begins at 3760 BCE, the year of creation
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140 in Jewish tradition. The Muslim lunar calendar begins on July 16, 622,
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141 when Mohammed fled from Mecca to Medina.
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142
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143 The Japanese, Taiwanese, and North Koreans use the Gregorian
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144 calendar, but number the year by political era. In Japan, an era
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145 begins when an emperor succeeds to the throne; year 1 of the Heisei
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146 era was 1989 when Emperor Akihito ascended to the throne (the first
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147 few days of 1989 was year 64 of the Shouwa era). In Taiwan, year 1 is
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148 the first full year after the founding of the Republic of China in 1911.
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149 In North Korea, year 1 is the year of the Juche (self-reliance) ideal,
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150 corresponding to the birth year of founder Kim Il-Sung (1912). Thus,
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151 year 2000 is Heisei 12 (Japan), 89th year of the Republic (Taiwan),
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152 and Juche 89 (North Korea).
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153
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154
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155 FURTHER MODIFICATIONS TO THE GREGORIAN CALENDAR
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156
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157 Despite the great accuracy of the Gregorian calendar, it still
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158 falls behind very slightly every few years. The most serious problem
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159 is that the earth's rotation is slowing gradually. If you are very
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160 concerned about this problem, we suggest that you tune in short wave
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161 radio station WWV or the Global Positioning System, which broadcasts
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162 official time signals for use in the United States. About once every
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163 3 years, they declare a leap second at which time you should be
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164 careful to adjust your system clock. If you have trouble picking up
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165 their signals, we suggest you purchase an atomic clock (not part of
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166 the IMAP toolkit).
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167
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168 Another problem is that the Gregorian calendar represents a year
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169 of 365.2425 days, whereas the actual time taken for the earth to
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170 rotate around the Sun is 365.2421991 days. Thus, the Gregorian calendar
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171 is actually 26 seconds slow each year, resulting in the calendar
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172 being one day behind every 3,300 or so years (a Y3.3K problem).
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173
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174 Consequently, the Gregorian calendar has been modified with a
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175 further rule, which is that years evenly divisible by 4000 are not
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176 leap years. Thus, the year 4000 will not be a leap year. Or, at
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177 least we assume that's what will happen assuming that the calendar
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178 remains unchanged for the next 2000 years.
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179
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180 The modified Gregorian calendar represents a year of 365.24225
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181 days. Thus, the modified Gregorian calendar is actually 4 seconds
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182 slow each year, resulting in the calendar being one day slow every
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183 20,000 or so years. So there will be a Y20K problem.
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184
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185 There is some dispute whether the modified Gregorian calendar was
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186 officially adopted, or if it's just a proposal. Other options (see
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187 below) exist; fortunately no decision needs to be made for several
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188 centuries yet.
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189
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190 There is code in c-client to support the modified Gregorian
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191 calendar, although it is currently disabled. Sometime in the next
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192 2000 years, someone will need to enable this code so that c-client is
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193 Y4K compiliant. Then, 18,000 years from now, someone will have to
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194 tear into c-client's code to fix the Y20K bug.
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195
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196
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197 EASTERN ORTHODOX MODIFICATION OF THE GREGORIAN CALENDAR
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198
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199 The Eastern Orthodox church in 1923 established its own rules to
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200 correct the Julian calendar. In their calendar, century years modulo
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201 900 must result in value of 200 or 600 to be considered a leap year.
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202 Both the Orthodox and Gregorian calendar agree that the years 2000 and
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203 2400 will be leap years, and the years 1900, 2100, 2200, 2300, 2500,
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204 2600, 2700 are not. However, the year 2800 will be a leap year in the
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205 Gregorian calendar but not in the Orthodox calendar; similarly, the
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206 year 2900 will be a leap year in the Orthodox calendar but not in the
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207 Gregorian calendar. Both calendars will agree that 3000 and
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208 3100 are leap years, but will disagree again in 3200 and 3300.
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209
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210 There is code in c-client to support the Orthodox calendar. It
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211 can be enabled by adding -DUSEORTHODOXCALENDAR=1 to the c-client
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212 CFLAGS, e.g.
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213 make xxx EXTRACFLAGS="-DUSEORTHODOXCALENDAR=1"
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214
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215 The Orthodox calendar represents a year of 365.24222222... days.
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216 Thus, the Orthodox calendar is actually 2 seconds slow each year,
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217 resulting in the calendar being one day slow every 40,000 or so years.
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218 The Eastern Orthodox church has not yet made any statements on how the
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219 Y40K bug will be fixed.
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220
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221
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222 OTHER ISSUES AFFECTING THE CALENDAR IN THE FUTURE
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223
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224 The effect of leap seconds also needs to be considered when
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225 looking at the Y3.3K/Y4K, Y20K, and Y40K problems. Leap seconds put
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226 the clock back in line with the Earth's rotation, whereas leap years
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227 put the calendar back in line with the Earth's revolution. Since leap
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228 seconds slow down the clock (and hence the calendar), they actually
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229 bring the day of reckoning for the Gregorian and Orthodox calendars
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230 sooner.
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231
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232 Another factor is that the next ice age (technically, the end of
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233 the current interglacial period; we are in the middle of an ice age
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234 now!) is due around Y25K. It is not known what perturbations this will
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235 cause on the Earth's rotation and revolution, nor what calendar
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236 adjustments will be necessary at that time.
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237
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238 Hence my use of "or so" in predicting the years that the calendar
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239 will fall behind. The actual point may be anywhere from decades (in the
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240 case of Y3.3K) to millenia (in the case of Y40K) off from these predictions.
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241
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242
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243 MEANINGS OF DAY NAMES
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244
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245 The names of days of the week from a combination of Roman and
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246 Germanic names for celestial bodies:
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247 . Sunday Latin "dies solis" => "Sun's day"
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248 . Monday Latin "dies lunae" => "Moon's day"
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249 . Tuesday Germanic "Tiw's day" => "Mars' day"
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250 . Wednesday Germanic "Woden's day" => "Mercury's day"
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251 . Thursday Germanic "Thor's day" => "Jupiter's day"
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252 . Friday Germanic "Frigg's day" => "Venus' day"
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253 . Saturday Latin "dies Saturni" => "Saturn's day"
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254
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255
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256 MEANINGS OF MONTH NAMES
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257
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258 The names of the months are from the Roman calendar:
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259 . January Janus, protector of doorways
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260 . February Februalia, a time for sacrifice to atone for sins
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261 . March Mars, god of war
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262 . April Latin "aperire" => "to open" buds
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263 . May Maia, goddess of plant growth
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264 . June Latin "juvenis" => "youth"
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265 . July Julius Caesar
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266 . August Augustus Caesar
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267 . September Latin "septem" => "seven"
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268 . October Latin "octo" => "eight"
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269 . November Latin "novem" => "nine"
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270 . December Latin "decem" => "ten"
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271
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272 As you'll notice, the last four months are numbered 7 to 10, which
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273 is an artifact of the time when the new year started in March.
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274
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275
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276 INTERESTING FORMULAE
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277
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278 There's another reason why the historical starting of the new year
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279 is significant. Starting with March, the length of months follows a
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280 mathematical series:
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281 31 30 31 30 31 31 30 31 30 31 31 28
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282
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283 This means that you can calculate the day of week for any
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284 arbitrary day/month/year of the Gregorian calendar with the following
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285 formula (note all divisions are integral):
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286 _ _
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287 | 7 + 31*(m - 1) y y y |
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288 dow = | d + -------------- + y + - - --- + --- | MOD 7
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289 |_ 12 4 100 400_|
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290 where
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291 d := day of month (1..31)
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292 m := month in old style (March = 1..February = 12)
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293 y := year in old style
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294 dow := day of week (Tuesday = 0..Monday = 6)
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295
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296 To convert from new style month/year to old style:
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297 if (m > 2) m -= 2; /* Mar-Dec: subtract 2 from month */
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298 else m += 10,y--; /* Jan-Feb: months 11 & 12 of previous year */
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299
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300 Here's another fun formula. To find the number of days between two
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301 days, calculate a pair of calendar days with the formula (again, all
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302 divisions are integral), using new style month/year this time:
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303 m
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304 m + -
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305 8 y y y
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306 d + 30 * (m - 1) + ----- + y * 365 + - - --- + --- - ld
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307 2 4 100 400
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308
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309 where:
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310 d := day of month (1..31)
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311 m := month in new style (January = 1..December = 12)
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312 y := year in new style
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313 ld := leap day correction factor:
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314 0 for January and February in non-leap years
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315 1 for January and February in leap years
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316 2 for all other months in all years
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317
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318 In C code, the leap day correction factor is calculated as:
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319 (m < 3) ? !(y % 4) && ((y % 100) || !(y % 400)) : 2
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320
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321 It's up to you to figure out how to adapt these formulas for the
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322 Y4K bugfix and the Orthodox calendar. If you're really clever, try to
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323 use these formulae to implement the C library ctime(), gmtime(), and
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324 mktime() functions. Most C library implementations use a table of the
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325 number of days in a month. You don't need it.
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326
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327
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328 ACKNOWLEDGEMENT:
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329
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330 The original version is from an old Digital Equipment Corporation SPR
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331 answer for VMS. Modifications for c-client, and additional information
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332 added by Mark Crispin.
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