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The solutions for the various calendars are very different. In the case of calendars as different as the Maya and ancient Egyptian calendar, for example, that is only to be expected, because the calendars themselves are structurally different. |
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There are, however, calendars that resemble each other more closely. When these calendars are solved, structural similarities are observe in their solutions. These similarities suggest looking past a single problem and considering the possibility of solving the problem of solving calendars in general. |
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A single general procedure, which identifies certain key parameters of all calendars and allows any given calendar to be solved by inserting the appropriate constant values as parameters, would eliminate the necessity of developing individual solutions for individual calendars. Such a procedure is the Holy Grail of calendric algorithms. |
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In 1984, D.A. Hatcher published a paper that addressed part of this problem by identifying a method for converting Julian Day numbers and dates in either the Julian or Gregorian calendars. A common set of formulae were used for both calendars. |
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In 1985, Hatcher published a more ambitious paper, which expanded upon the 1984 paper, generalized the distinction between computational and given calendars, and offered a set of generalized equations for solving a wide variety of calendars. Is the Quest complete? |
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The definitive answer is, yes and no. First, the Hatcher equations, as I will call them, do not address all calendars. They are applicable to a set of historical calendars, however. |
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Second, the key to the Hatcher procedure is identifying the point in the calendar year where intercalation occurs and reckoning months and days from zero, rather than one, for computational purposes. Year numbers are kept positive for historical dates. Thus, for the Julian and Gregorian calendars, the computational year begins in March. There may be a fair distance between a given calendar date and its computational cousin. |
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Hatcher distinguishes certain classes of calendars by their structure: |
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Mobile calendars. These calendars have uniform years of 365 days, consisting of 12 uniform months of 30 days and five epagomenal days. This group includes the Egyptian, Armenian, Khwarizmian, and Persian calendars. |
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The Alexandrian, Coptic, and Ethiopic calendars are modified from the Egyptian mobile calendar by the inclusion of a sixth epagomenal day every fourth year, reckoned from the third year of the respective era. |
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Julian calendars. Three calendars are found in this group: Roman, Macedonian, and Syrian. These differ in the date of New Year, so the computational years start in different months. |
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The schematic Islamic calendars. |
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Hatcher treats the three Alexandrian calendars as a case of the mobile calendars. In this work, I treat them as a separate group. |
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