Structure of the Calendar and the Mayan Number System

Although both the year and lunations are recognized by most human groups around the world and recognition of stellar periodicities is not uncommon, the development or invention of really complex calendars is much more rare.

In Mesoamerica, such a calendar was invented, probably in the 1st or 2nd century a.d. Some components of that invention are still in use among Indian groups today. In its fullest form, among the Mayas, the calendar consisted of three main components: an era count (with one normal base and several alternatives), a 365-day year, and a 260-day period (sometimes called, with no strong basis, a tzolkin), functionally equivalent to the much shorter western week. Mayas and Mayanists normally put the era date first, followed by the 260-day date and the month date. These interlocking parts functioned beautifully to measure time precisely, accurately, and easily over as long a period as was desired. This basic function of a calendar was unmarred by any attempt to "correct" the calendar to make it conform to natural phenomena. The intercalary days or months that have wreaked such havoc with Eurasian attempts to measure time were completely ignored. The arguably impos sible task of creating agreement among Sun, Moon, and stars was considered an irrelevant impediment to time measurement. Mesoamerican astronomers knew the length of the tropical year and various lunar and planetary periodicities with a very high degree of accuracy. Some of the time periods that they employ suggest attempts to measure such phenomena with a precision comparable to a calculation to five decimal places in our society. They did not, however, have our European and modern western preference for making adjustments to the measuring machine. Although evidence will be presented in ยง15.4.2 that the inventor of the calendar had a sophisticated knowledge of contemporary Eurasian calendar-making, this ability to recognize adherence to certain natural phenomena as a defect rather than a valuable goal makes it highly likely that the inventor was a native American (possibly, a Chuh speaker) rather than a Eurasian visiting a new environment.

The heart of the Mesoamerican system was the series of 260 days running endlessly as far into the past or the future as one wished to go, changeable only by the divine decree of a divine ruler or by a "war with heaven." This series consisted of 20 named days combined with 13 numbers (normally 1 to 13, although the Azoyu codices from Guerrero, Mexico, for an unknown reason, run from 2 to 14). The 20 named days in their Mayan and Aztec forms are listed in Table 12.2. Each series runs independently, with numbers repeating the entire series 20 times, the day names running from the 1st to the 20th for 13 times, before the number 1 is combined once again with the 1st day name and the combinations start again. Although the names differ in the many different languages of ancient Mesoamerica, they frequently embody similar or identical concepts. Both the

Table 12.2. Mesoamerican day names.

Aztec English equivalent Yucatec Maya

Table 12.2. Mesoamerican day names.

Aztec English equivalent Yucatec Maya

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