When we refer to Mayan astronomy we are really referring to all astronomy (visible to the naked eye), since their knowledge of heavenly bodies was amazingly complete and accurate. The recording of the movements of the stars was effected using a numerical system based on the number 20 (vigesimal), which employed three symbols: a shell for zero, a dot for one unit, and a bar for five units. Numbers were written, exactly as in our system, with multiples of the base identified by their positions; it is often said that Mayan numerals were more convenient than their contemporary Roman numerals, which did not have the zero, but convenience is largely a question of habit.
The Mayas had three calendars: one of 260 days, the Tzolkin, which I mentioned in the previous chapter; a civil one of 365 days, called Haab; and a long-term calendar, based on the smallest common multiple between the years of the other two calendars. The smallest common multiple between 260 and 365 is 18,980 (approximately equal to the days of 52 solar years), and this period was considered a sort of "great year," lasting more than the average life span at that time. It may be that at the end of each such great year the Mayas really feared the end of the world, as some chronicles say. What is certain, however, is only that whenever a new great year commenced, special events took place, such as the renovation of temples.
The Tzolkin assigned to each day a number from 1 to 13 and a name from 20 possibilities (13 x 20 = 260). The reason for the choice of a 260-day period is unknown, and in fact this calendar is conventionally called a religious or sacred calendar for the simple reason that we do not know its origin. As we saw in the previous chapter, however, it is likely that it was established in Copan, or even in the preclassical age, in the 4th century BC, in Izapa. In both these places, 260 is the number of days between the two zenith passages of the sun. Other hypotheses put forward seem rather contrived, such as the theory that the 260 days correspond to the average number of days in the human gestation period, that is, a nonastronomical source for a strictly astronomical thing such as a calendar. Whatever the reason, no definitive explanation has emerged to date.
The Haab, designated by scholars as the civil calendar to distinguish it from the sacred one, consisted of 18 months of 20 days each, plus 5 days considered to be inauspicious, making a total of 365 days. Dates were expressed with groups of figures composed in this way: kin (day), unial (20 days), tun (18 unial = 360 days), katun (20 tun = 7200 days), baktun (20 katun = 144,000 days), exactly as our dates are made up of days, months, and years. For us, the days go from 1 to 31, the months from 1 to 12, and the years go on ad infinitum. For the Mayas, kin, tun, and katun went from 0 to 19, the unial went from 0 to 17, and the baktun went from 1 to 13. Thus, possible dates, consisting of five numbers in succession, were finite in number: the Mayan measure of time was recursive (not cyclical, as it is the date that was repeated). Every period ended in 184.108.40.206.0., which corresponds to approximately 5,125 years; hence, five periods are the equivalent of 26,625 years, a number of years extremely close to a precessional cycle, perhaps not by chance.
The problem of pegging Mayan chronology with ours, that is, of identifying at least one date with a Gregorian equivalent, is clearly crucial for all Mayan historiography. Without this it is impossible to translate the chronology of events described in inscriptions into our dating system and to know therefore when they occurred. I shall not go into detail with regard to this complex problem, whose solution is based on the identification of astronomic events that can be dated with precision and are recorded by the Mayas, such as eclipses (Bricker and Bricker 1983). It is extremely likely, however, that the starting date of the period the Mayas lived through is August 13, 3114 BC, and thus it can be calculated that the final date falls on December 23, 2012. Of course, the fact that the starting date happens to be August 13—one of the dates on which the sun rises at T-east (and passes to the zenith on the parallel of Copan and Izapa)—is strong evidence in favor of the validity of this chronology.
The recursivity of the Mayan calendar has unfortunately given rise to the most fanciful theories, in particular that the Mayas predicted the end of the world, or at least terrible natural calamities, for December 2012. This type of prediction appears, however, only in the Books of Chilam Balam, manuscripts of the 17th and 18th centuries (thus long after the conquest), hand-written in the Maya-Yucatec language but in Roman characters. They contain a tangled web of magic and historical and religious texts in which Mayan traditions and Spanish influence are virtually indistinguishable. Probably the "end of the world" for the true Mayas would not have been so very differently lived from what happened on our New Year of 2000. However, there remains the problem of understanding what logic or event governed the choice of the initial date so far in the past (a problem that, as far as I know, has never been seriously addressed) and, more generally, why the Mesoamerican calendar was recursive.
Yet it is also true that Mayan astronomers, eventually studying our civilization, would have had difficulties in understanding why our calendars go on indefinitely.
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