## Maya Long Count

The Maya were the most enduring of the Mesoamerican civilizations. The origins of Maya society can be traced back to at least 400 b.c.e. in the lowlands of the Yucatan peninsula, when existing small villages—which, in the dry north, were built close to cenotes, sink holes full of vital water formed by the collapse of underground caves—started to develop into more sprawling towns with monumental structures at their centers. This process accelerated, with social elites beginning to gain power, during what is known as the Late Preclassic, or Late Formative, period, which lasted until about c.e. 250. In the Classic period that followed, the political structure of the Maya lowlands developed into a patchwork of city states—anywhere from about twenty-five to about sixty of them at different times—creating a continually shifting network of wars and alliances. Each political center was also a religious one, with ceremonial buildings and pyramids surrounding a large central plaza. But the ninth century brought change. Many of the largest Maya cities were suddenly abandoned for no clearly apparent reason. One of the exceptions was Chichen Itza, which endured and even reached its apex in the ensuing Postclassic period, from about c.e. 900-1300. Maya de-scendents, speaking dialects of the Maya language, continue to live in southern Mexico, Guatemala, and adjacent countries.

That the Maya peoples were prepossessed with astronomy is beyond dispute, although the motivation seems to have been primarily astrological. The Maya shared the general Mesoamerican concern with calendrical cycles, taking to tremendous lengths the quest to find coincidence between different numbers of cycles of different celestial bodies. However, one of their most incredible achievements was the adoption, development, and extensive use of the linear calendar known as the Long Count. Underlying this was a set of time units—baktuns (periods of four hundred years), katuns (twenty years), tuns (years of 360 days), uinals (twenty days) and kins (days)—and each progressive day was simply expressed as a number of each unit. For example, 9.17.19.13.16 meant nine baktuns, seventeen katuns, nineteen tuns, thirteen uinals and sixteen days.

One crucial prerequisite, without which Long Count dates could never have been recorded and, arguably, the Long Count is unlikely even to have been conceived, is a system for recording numbers using a fixed base. Modern (Arabic) numerals use a decimal (base ten) system, so that 8,945 signifies 5 units + 4 tens + 9 hundreds (10 x 10) + 8 thousands (10 x 10 x 10). The Maya did the same, except they used different symbols to express the digits and used a base of twenty. Thus, when they wrote (in their own vigesimal, rather than decimal, notation) 1.2.7.5 this signified 5 units + 7 twenties + 2 four-hundreds (20 x 20) + 1 eight-thousand (20 x 20 x 20)—in other words, the same number. (The use of base twenty makes sense: our base ten derives from counting using the fingers and thumbs, and people have twenty digits on their hands and feet.) To represent the individual numerical digits, the Maya used bars and dots. Each dot counted one and each bar five. Thus the digit seven was represented by a bar and two dots. When reading Maya numbers it is essential to remember that each set of bars and dots represents a single digit. In a base-twenty system, we need symbols for all the digits from one to nineteen, and so the largest, nineteen, was represented by three bars and four dots. Finally, in any fixed-base notation we need a symbol for zero. The Maya used a stylized nut, shell, or other variants. More esoteric ways of recording numbers also existed, such as representing each digit from 0 to 19 as a deity's head shown in profile with distinctive attributes.

Before any society can develop a fixed-base recording system for numbers, they must develop two concepts: first, the idea that the position of a digit can be used to signify value—that is, depending on its place, a digit can represent units, twenties, four-hundreds, etc.; second, the concept of zero in order to concoct a symbol to represent it. Once these bridges are crossed, two major advantages soon emerge. The first is the ease with which one can do simple arithmetic. It is a trivial matter to multiply a Maya numeral by twenty by simply adding a zero on the end, and other sums are easily solved using straightforward rules, just as with modern numbers; but they would be frightfully difficult using, say, Roman numerals. The second advantage is the ability to represent arbitrarily large numbers (since it is always possible to add further digits). It is this ability that aided the conceptualization of the long periods of time that underlie the Long Count.

The relationship between Long Count dates and base-twenty numbers fell out naturally, since each time unit was twenty times larger than the next smaller one, with the single exception of the tun, which is eighteen rather than twenty uinals in order to achieve a "year" not too different in length from the real one. In fact, all written records that have come down to us are calendrical, and in these the Maya used a modified vigesimal system to express all numbers, in which the third-to-last digit was 18, rather than 20, times the second-to-last one.

The significance for us of Long Count dates is that they permit us to date sites and artifacts. The significance for the ancient Maya was that they could achieve a grand conception of history. On the first point, most Maya calendrical inscriptions give the Long Count and Calendar Round (haab plus tzolkin) date. One of the main challenges is to find events, dated according to the Long Count, that can also be dated within our own (Gregorian) calendar to permit a correlation between the two. Astronomical events such as eclipses are one possibility; recorded events soon after the conquest are another. Once the correlation is determined any Long Count date can be converted to a Gregorian one. The issue of finding the definitive correlation has occupied Maya scholars for many decades.

On the second point, since the Long Count was a linear calendar, the Maya could conjure up key (mythical) historical events and assign them dates that seemed significant within the Long Count, such as the beginning of a new baktun. Even more fundamentally, they had to fix a zero date for the whole scheme—an assumed date of creation. The date chosen corresponds in the Gregorian calendar to about August 13, 3114 b.c.e. (depending upon the correlation). One explanation of why this particular date was chosen is that it was obtained by retrogressing the Calendar Round and other observed astronomical cycles in order to reach a date of key (perceived) astronomical significance.

The Long Count could also be extended into the future and provided a source of prognostication. It is commonly believed that the ancient Maya even predicted the end of the world, which would occur at the end of bak-tun 13, around December 21, 2012. However it now seems more likely that they considered the present era would contain 20 baktuns, or a complete pic-tun of 8,000 years, giving the world considerably longer.

A more sobering thought is that without the historical evidence of Maya inscriptions and the few books that only survive through fortunate ac cident, we would know little or nothing of the existence—let alone the distinctiveness or complexities—of Maya astronomy and calendrics. Although a few anomalous round towers, such as the Caracol at Chichen Itza, have been suggested as possible observatories, there is no convincing archaeological evidence of any Maya astronomical measuring instruments.

See also:

Calendars.

Caracol at Chichen Itza; Dresden Codex; Gregorian Calendar; Mesoameri-can Calendar Round.

References and further reading

Aveni, Anthony F. Stairways to the Stars: Skywatching in Three Great Ancient Cultures, 125-127. New York: Wiley, 1997.

Aveni, Anthony F. Skywatchers, 136-139, 210-214. Austin: University of Texas Press, 2001.

Coe, Michael D. The Maya (4th ed.), 172-176. London: Thames and Hudson, 1987.

Tedlock, Barbara. "Maya Astronomy: What We Know and Why We Know It." Archaeoastronomy: The Journal of Astronomy in Culture 14 (1) (1999), 39-58.

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