Calendars: Mesoamerican Calendars
CALENDARS: MESOAMERICAN CALENDARS
In 1555 Bishop Diego de Landa wrote:
The natives of Yucatan were as attentive to the matters of religion as to those of government and they had a high priest whom they called Ah Kin (Daykeeper) Mai …. He was very much respected by the lords … and his sons or nearest relatives succeeded him in office. In him was the key of their learning …. They provided priests for the towns when they were needed, examining them in the sciences … and they employed themselves in the duties of the temples and in teaching them their sciences as well as in writing books about them …. The sciences which they taught were the computation of the years, months and days, the festivals and ceremonies, the administration of the sacraments, the fateful days and seasons, their methods of devotion and their prophecies. (Tozzer, 1941, p. 27)
When he wrote those words, Bishop Diego de Landa correctly perceived the extraordinary attention paid time and calendar by the Maya of Yucatán even several centuries after their classical heyday. It is likely that these Ah Kin were among the elite of Maya culture. One eighth-century scribe from the city of Copán received a royal burial. His remains were found elaborately laid out, ink pots, brushes, and all, next to the ruler he served. Though his trappings seem far more modest in comparison to those of his precontact predecessor, the modern Maya day keeper is still one of the most important and highly regarded members of society. Seated at a cardinally oriented table adorned with bowls of incense and lighted candles, he arranges piles of seeds and crystals drawn from his divining bag in an attempt to "borrow from the days" the answers to questions posed by his clients: Will I be cured of the disease that plagues me? Will my daughter's marriage be successfully consummated? Will my crop tide the family over this year?
Basic Calendrical Units
For the Maya a single word, kin, signified time, day, and sun. In both meaning and glyphic form it suggests that the art of timekeeping was intimately connected with the practice of astronomy. The directions of the petals of the floral design that makes up the kin glyph likely correspond to the extreme positions of the sun along the horizon. Cosmograms also exemplify the spacerelated time system employed by most ancient Mesoamerican cultures. Found on both pre-Columbian and colonial documents, these diagrams can be thought of as exercises in temporal completion. For example, page one of the Féjérvary-Mayer Codex from highland Mexico consists of a quadripartite glyph in the shape of a Maltese cross. Carefully positioned within the symmetric floral design are all the things that belong to each of the four sides of space: gods, plants, trees, birds, even parts of the body; moreover the four directions are color coded. But time is also spatially divided, each region of the world being assigned its share of the twenty days of the Aztec week. The so-called year bearers, the names of successive New Year's Days, are placed one at each of the tips of the cross. Circumscribing the world is the ultimate Mesoamerican number for time: 260 dots, one to each day, arrayed in 20 units of 13. These 260 days make up the Maya tzolkin (called by the Aztecs tonalpohualli ), a ritual calendar known as the "count of the days."
Unique in the world, the number 260 served as the base of practically every Mesoamerican calendar that has survived. Its origin is debatable, but there can be no question that one of its factors, the number twenty, was derived from the number of fingers and toes on the body. The other factor, the number thirteen, represents the number of layers in the Maya heaven. Beyond this, however, it seems that the human body can be further implicated in the origin of the tzolkin. The average duration between human conception and birth is close to 260 days (on average 266). Modern Maya women in highland Guatemala still associate this sacred count with the term of pregnancy. The tzolkin also turns out to be a convenient approximation to the length of the basic agricultural season in many areas of southern Mexico, where it probably originated.
Celestial phenomena are also implicated in establishing Mesoamerica's fundamental time pillar. Nine moons (about 265 days) represent the 9 "bloods" taken away by the moon from pregnant women to give lives to their newborn. Lunar and solar eclipses occur at seasonal intervals commensurate with the tzolkin in the ratio of 2 to 3 (3 times the "eclipse year" of 173.5 days nearly equals 2 times 260 days). Thus the ancient astrologer could easily warn of certain days vulnerable to the occurrence of an eclipse. The planet Venus, the patron star of war in Teotihuacán (the ancient city of highland Mexico built around 100 bce), was also revered by the Maya at a time when the New World's most precise calendar was being developed. The duration of its appearance as morning star averages 263 days—again close to a tzolkin. And if all these harmonies were not enough, in southernmost Mesoamerican latitudes the year is divisible into periods of 260 and 105 days by the (2) days in the annual calendar when the sun passes overhead.
Mesoamerican people were further cognizant of the seasonal year. Abhorring fractions, the Maya measured their year, or haab (Aztec, xiuhmolpilli ), at 365 days. They divided the year into eighteen months, each of which was twenty days in length, with a concluding five-day month (an unlucky period thought to reside outside the year). Eschewing leap years, ancient Mesoamericans easily kept track of the anniversary of the tropical year within the haab.
Cycle building emerges as a central theme of Mesoamerican calendrics. The strategy seems to have accumulated small cycles to make bigger and bigger ones. One of the larger cycles was the calendar round, a period of 52 years consisting of 18,980 days, the lowest common multiple of the tzolkin and the haab (52 × 365 = 73 × 260). This time loop thus records the interval over which name and number combinations in both cycles repeat themselves. Perhaps not coincidentally, it is also about equal to the length of a full human life. The completion of a calendar round was quite a momentous occasion. Spanish chronicles record that Aztec priests timed this "year binding" event by proceeding to a special place outside ancient Mexico City called the Hill of the Star. There they carefully watched the Pleiades to see whether they would pass the zenith. If they did, it would be a sign from the gods that time would not come to an end. Instead, a new era would be granted to humanity.
To judge by the archaeological and epigraphic evidence, Maya mathematics was almost exclusively devoted to day keeping. About half a millennium before the beginning of the common era a system of numeration developed in southern Mesoamerica. It probably emanated about 600 bce from the region of Monte Albán, Oaxaca, but was not without Olmec antecedents from the Gulf Coast. The Maya employed only three symbols to produce numbers written in the hundreds of millions: a dot was equivalent to one, and a horizontal bar (uniquely Maya) was equivalent to five, whereas a variety of symbols represented zero. Each of these symbols likely derived from hand gestures.
Unlike its Western counterpart, the Maya zero represented completeness rather than emptiness. Temporally it was regarded as the moment of completion of a cycle, as in the turning of a chain of nines to zeroes on the odometer of an automobile at the conclusion of a large-distance unit traveled. A seashell often represented the Maya zero, perhaps because its roundness was intended to depict the closed, cyclic nature of time. The grasping hand, which like a knot ties up or bundles the days and years together into completed packages, also serves as a zero in many of the inscriptions. The dot and bar numerals probably derived from the tips of the fingers and the extended hand respectively. The Maya expressed large time intervals in a notational system utilizing place values, quite like the Arabic system, which was developed independently in the Middle East after the fall of the Roman Empire.
Structuring Deep Time
Just as it is part of human nature to cling to life, many societies attempt to extend their power, lineage, and legacy. Hierarchically organized societies are in the best position to do this. Often they bureaucratize time, giving it a deep structure that goes beyond the immediate confines of remembered generational experience. The Maya utilized their mathematical system to create history. They accumulated years to make scores of years. Heaping score upon score was a logical extension of their vigesimal (base twenty) system. The "long count" is a five-digit tally that marks an event in lapsed time from the most recent creation. One finds most long counts carved on stelae dating from 100 bce to 900 ce. These display the effigy of a ruler, usually in full regalia, accompanied by a hieroglyphic text that details his or her ancestral history, described in terms of the intervals between seminal events (birth, accession, conquests, marriage, death). To add depth and historical permanence, the dating of these events often seems to have been contrived to fit with repeatable cosmic time markers, such as the reappearance of Venus as morning star, eclipses, and solstices.
To obtain the equivalent in the Gregorian calendar of any long count date appearing in the Maya inscriptions, one must be able to match with certainty at least one long count date with a date in the Gregorian calendar. Until the late twentieth century there had been considerable disagreement about just how to do this. According to the most widely accepted scheme, the so-called Goodman-Martinez-Thompson correlation, the zero point of the most recent starting position of the long count was August 12, 3114 bce, a date on which astronomers have found no momentous celestial event to have occurred. The next cyclic overturn will take place on December 8, 2012.
Calendars and Creation
The concept of successive creation-destruction cycles is central to understanding Mesoamerican timekeeping. For example, despite the terrifying effigy at its center, the famous Aztec Sun Stone provides a pictorial narrative of a cyclic cosmogony in which people play an active role. Tonatiuh, the sun god, a flint knife depicting his lolling tongue, grips the firmament with his claws. He cries out for the blood of human sacrificial hearts that he may keep the world in motion. The four panels that surround Tonatiuh represent previous ages, or "suns," as the Aztecs called them. The first cosmogonic epoch (upper right) was the "Sun of Jaguar," named after the day "4 Jaguar" in the 260-day cycle on which it terminated (the head of the jaguar is surrounded by 4 dots within the panel). During this epoch the inhabitants of the earth, the result of the gods' first try at a creation, were giants who dwelled in caves. But they did not till the soil as expected, and so the gods sent jaguars to eat them. In the second sun, the "Sun of Wind," symbolized by the day "4 Wind" (upper left), another less than perfect human race was blown away by the wind. The gods transformed these creatures into apes that they might better cling to the world, an act said to account for the similarity between apes and people. In the third creation, the "Sun of Fire-rain" (the symbol of "4 Rain" is at the lower left), some people were permitted to survive by being transformed into birds to escape from the destruction of the world by volcanic eruptions. The fourth creation, the "Sun of Water," depicted at the lower right, ended with a flood that followed torrential downpours. But this time a transformation from people into fish kept the people from perishing entirely. The symbol "4 Water" marks this epoch. The Aztecs believed they existed in the "fifth sun," of which the symbolic date "4 Movement" houses the effigy of Tonatiuh and the other four ages. (The four large dots of this day sign's coefficient are easily recognizable on the periphery of the four panels that denote the previous suns.) According to most Mesoamerican cosmogonies, the universe was destroyed and re-created anew, each age providing an explanatory temporal framework in which to categorize different forms of life and to relate them to the present human condition.
Two distinct points about Mesoamerican concepts of time emerge in such creation stories. First is the oscillating, repetitive nature of the events taking place. Previous suns were thought to have been creative ventures that failed to achieve the necessary delicate balance between gods and people. Creation time repeats itself, but it is punctuated by periods of destruction. Second, each present contains a piece of the past. Each attempt at creation tries to account for the present state of humankind by referring to what remains in the world. Fish and birds are really human kin, the failed children from archaic creations. People were not destined to dominate them, as Old Testament Genesis requires. Rather, people must revere them, for nature is part of people.
According to the Aztec chronicles, the gods made sacrifices in order to bring about the world in its present condition. They performed these sacrifices at the ancient pyramids of Teotihuacán when, in the aftermath of a struggle among themselves, one of their number sacrificed himself to the ceremonial fire, thus promising to become the first rising sun. Such stories have a Darwinian ring to them: life is a struggle filled with key transitory moments. But unlike the Western view, theirs was a cosmology with a purpose. Human action, in this case blood sacrifice to the gods, was necessary to extend the fifth or present epoch. It mediated the balance of violent forces that might erupt as they still do in the fragile highland environment. After all since the gods sacrificed themselves for people, it is only reasonable that people should offer sacrifice as payment of the debt to them.
Carrying the Burden of Time
Perhaps no monumental imagery better expresses the essence of Maya time than Stela D of Copán. This larger than human-size monolith is dedicated to rituals conducted at the juncture of a series of important time cycles. Eight squared-off images carved in high relief confront the eye at the top of the monument. Each depicts a humanoid figure carrying an animal that represents a bundle of time. They employ tump lines, common devices used by modern Maya peasants to carry a load of wood or a sack of citrus by tying one's pack to a band that presses tightly about the forehead, thus leaving the arms to swing free and perform other tasks. Each porter is a full-figure glyph that represents a number. Thus the uppermost figure in the left block, number nine, is distinguishable by the markings on his youthful chin. He carries a heavy load of baktuns of time, 144,000-day periods consisting of 20 × 20 × 360 days. The old god of number 15, shown in the uppermost right block, hauls katuns (scores of 360-day periods). Fully transliterated, the numbered portion of Stela D reads: It was after the completion of nine baktuns, fifteen katuns, five tuns (360 days), zero uinals (20 days), and zero kin, reckoned since creation day, that such-and-such an event took place. Thus Stela D becomes the resting place of the numbers at the end of their long journey (lubay in Kekchi Maya), who finally let their burden fall 1,405,800 days (3,849 of our Gregorian years) after the last creation. Likewise katun prophecies from postconquest texts repeatedly refer to time as a burden: "This is the removal of his burden … fire is his burden … (In reference to the fifth katun)"; "On the day of the binding of the burden of Lord 5 Ahau." Writes one chronicler, "According to what [the Indians] say [these four first days] are those which take the road and bear the load of the month, changing in time" (Thompson, 1950, pp. 59–61). Time then appears as some sort of essence to be carried or borne along the roadway of eternity, finally seated or brought to rest at various stopping points.
Monuments such as Stela D attribute the completed cycle of time to the ruler and his dynasty. Stela D gives time a name and proclaims it to belong to the ruler, who is assigned various other titles that connect him to his otherworld ancestors. The side opposite the numbers leaves no doubt that it is the ruler who is being exalted. Dates of his accession, marriage, and victories in battle adorn the glyphic text. So high is the relief on the monument that the ruler seems almost to emerge from the cut stone, appearing larger than life, fully garbed with ritual paraphernalia in hand. He wears an enormous headdress and facial mask, his bloodletting instruments draped from his loincloth. Perhaps the ruler himself once stood before the citizenry in front of his monument performing the rite of genital bloodletting with the spine of a stingray to seal his bond with his ancestors. Here was a demonstration of the continuity of dynastic rulership that also guaranteed the continuity of time.
Two seminal qualities of the Maya concept of time from the dynastic histories comprise these time capsules wrought in stone. First, one has the sense that, whereas the arrow of time points toward the future, it is pushed from behind rather than tugged forward, a stark contrast to the teleological or purposive forward pull of time embedded in the Judeo-Christian tradition. Circumstances in the past, even before the creation of the world, had set the number gods on their journey. It was those four events, enacted in the realm of the ancestor gods, that determined the future course of human history, the creation of the lineage, the journey of the four founders of modern Maya culture to the right place to build the city. Their journey parallels in space the long arduous track along the road of time undertaken by the number gods who bear their ponderous freight. The Popol Vuh, the sacred book of creation of the Quiché Maya, states that the ancient word is the potential and the source for all that is done in the present world. "How should it be sown, how should it dawn?" the gods ask themselves as they contemplate the creative act (D. Tedlock, 1985, p. 73). Events that took place then, by the creators, the founders, the so-called mother-fathers, are responsible for setting time on its course toward the present.
A second seminal quality of Maya time inherent in the monumental inscriptions is more difficult to grasp, especially when contrasting it with the Western historical view of time, which clearly separates human history (arrived at via the testimony of people) from natural history determined from the testimony of things, such as events in the sky, in the landscape, signs in plants and animals. Thus events in the history of the dynasty are directly linked with cosmic events. For example, many of the paramount happenings in the life of 18 Rabbit (called Waxaklahun-Ubah-K'awil in modern orthographies), the name of the ruler depicted on Stela D, are tied directly to the appearance of the planet Venus at key positions in the sky. This habit of creating a single frame for natural and human history is quite common across Mesoamerica. It is reflected especially vividly in the Aztec year annals in which depictions of volcanic eruptions, eclipses, comets, and shooting stars appear linked to victories in battle and the deaths of emperors. Aztec history consists of like-in-kind events, both natural and civic-social, matched up repeatedly over multiple fifty-two-year cycles of time.
In many instances these astronomical events were registered in preferentially aligned calendrical, ceremonial architecture. For example, Temple 22 at Copán possesses a slotlike viewing chamber on its western facade that marks the appearance of Venus at the beginning of the rainy season. Buildings that deviate from the prevailing grid structure and buildings of unusual shape at Uxmal, Chichén Itzá, and other sites also contain Venus alignments. Classic Maya sites in the Petén rain forest include a number of solar "observatories." These specialized architectural assemblages consist of a pyramid on the west side of an open plaza that overlooks three smaller structures on the east. Viewed from the top of the former, the sun rises over each of the latter on seminal dates of the year, for example, the solstices, the equinoxes, and especially dates measured at multiples of twenty days from the passage of the sun across the zenith. In the highlands of Mexico the largest building in the Aztec capital, the Templo Mayor, was deliberately aligned with the sun at the equinox. Such structures might better be conceived as "theaters" than "observatories." They are sacred places that offer the appropriate setting for cosmically timed ritual.
Calendars and Codices
In addition to the monuments, the books (misnamed "codices") constitute a second major medium of information concerning Mesoamerican time and calendars. But here the message is quite different. If the monumental inscriptions, related to a program of public display, were intended to exalt the rulers and legitimize their descent from the gods, the content of the codices seems relatively esoteric and private, consisting of omen-bearing texts to be read only by high-status priests. Only four pre-Columbian codices have survived. Their content, expressed in what have come to be called almanacs, is almost exclusively concerned with divinatory rituals cyclically timed in remarkable detail. In a minority of cases the timings are based on astronomical phenomena encoded in tables that might properly be called ephemerides, even though their content is largely astrological.
The manifold ways the almanacs are laid out, challenging the eye of the reader to dance about the page in order to pursue a temporal journey, bespeak a playful intercourse between time and the Ah Kin. Time's arithmetic flows vertically or zigzaggedly; in some cases the black and red numbers that comprise, respectively, the intervals and resting points in a text are scattered about a single prognostic or divinatory picture like so many loose tokens dropped randomly upon it from above. In many instances the numbers seem to take on an irrational, almost mystical quality akin to the Pythagorean way of dealing with numbers.
One thinks of an almanac in the West as a compilation of useful information, most of it adapted to local space-time. One usually finds in an almanac a calendar for each month that gives all the holidays. There is also astronomical information, such as sunrise, sunset, moon phase tables, and eclipses for the year, coupled with meteorological information and tide tables for major local harbors. Information concerning weather predictions and the positions of the planetary bodies in the signs of the zodiac is also provided. Add to these data nonquantitative information on food recipes and proverbs and the modern almanac, updated and altered slightly from year to year, becomes a handy compendium that both amuses and instructs in practical matters and perhaps offers advice regarding personal behavior.
Maya almanacs feature many of these same aspects. They contain both invocations and divinations that deal with the weather, agriculture, drilling fire with sticks, and disease and medicine in addition to the fates and ceremonies. Their purpose seems to have been to bring all celestial and human activities into the realm of the sacred almanac of 260 days. As is the case in the monumental inscriptions, duration emerges as the support beam in the framework of Maya calendrics in the codices. Each phase seems to be based on a perceived forward movement of time from an event located at the start of the text, to which "distance number" intervals are added. Every round of time in a Maya almanac begins with a starting day name and number in the tzolkin. One then proceeds via black distance numbers to red dates, each accompanied by a picture and glyphic block that convey the appropriate debt payment and (usually) an accompanying omen. The participatory role of the Maya worshiper is also reflected in the content of the codices. The business of laying out the calendar that prescribes Maya ritual behavior must have been complex. A multitude of offerings needed to be made to the gods at the proper places and times when the gods of number dropped their loads, and the periods between ritual events surely were not arbitrary. Long thought to be endlessly cyclical in nature, many almanacs, studies suggest, may have been fixed in real time. And like modern almanacs, they may have undergone repeated revision and recopying.
The most exquisitely complex and esoteric almanacs, termed ephemerides, deal with precise astronomical prediction. Known since its rudimentary elements were deciphered early in the twentieth century, the Venus table in the Dresden Codex chronicles the appearance and disappearance dates of that planet over several centuries. Accompanying pictorials at the middle of each frame show the Venus deity Kukulcan flinging daggers of omen-bearing light on victims who lie impaled below them. A correction table enables the Venus calendar to stay on track for five hundred years with scarcely a day error. Maya astronomers seem to have been attracted by the perfect 8 to 5 commensuration between the Venus cycle of 584 days and the seasonal year of 365 days as well as by the larger commensuration between 65 Venus cycles and two 52-year calendar rounds. Adjacent ephemerides in the Dresden Codex were used to predict eclipses and to chart the movement of Mars, whose 780-day cycle commensurates with the tzolkin in the exact ratio of 3 to 1.
Studies suggest that other pages of the Dresden Codex as well as certain pages of the Madrid Codex also mark astronomical events. Venus deities, looking much like those in the Dresden, also appear in the Borgia group of codices from highland Mexico. In the Anales de Quauhtitlan, a colonial document from the Mexican highlands, are specific statements about which class of people shall suffer wounds from the piercing rays of Venus, called Quetzalcoatl in the central Mexican pantheon:
And as they (the ancients, the forefathers) learned. When it appears (rises). According to the sign, in which it (rises). It strikes different classes of people with its rays. Shoots them, casts its light upon them. When it appears in the (first) sign, "1 alligator." It shoots the old men and women. Also in the (second) sign, "1 jaguar." In the (third) sign, "1 stag." In the (fourth) sign, "1 flower." It shoots the little children. And in the (fifth) sign, "1 reed." It shoots the kings. Also in the (sixth) sign, "1 death." And in the (seventh) sign, "1 rain." It shoots the rain. It will not rain. And in the (thirteenth) sign, "1 movement." It shoots the youths and maidens. And in the (seventeenth) sign, "1 water." There is universal drought. (Seler, 1904, pp. 384–385)
In stark contrast with the Maya texts, the so-called picture books of highland Mexico, which also include ritual ceremonial prescriptions, have generally been regarded as devoid of real-time astronomical events; that is, the Mexican codices have been characterized as celebrating time cycles, whereas the Maya books were thought to be more event specific. However, this traditional picture has been challenged by studies that offer evidence, specifically in the Codex Borgia, that real-time astronomical events were recorded in the middle of the fifteenth century. Scholars now regard Mesoamerican (especially Maya) mathematical, astronomical, and calendrical achievements to have been rather more like those of the ancient Middle East; that is, closer to the sort of quantitative science that led to modern astronomy.
As the field of Mesoamerican calendrics has remained extraordinarily specialized, most work is in journals such as the Journal for the History of Astronomy, Archaeoastronomy, Supplement to the Journal for the History of Astronomy, Latin American Antiquity. David H. Kelley's Deciphering the Maya Script (Austin, Tex., 1976) and Anthony F. Aveni's Skywatchers: A Revised and Updated Version of Skywatchers of Ancient Mexico (Austin, Tex., 2001) are standard texts that offer broad overviews of Mesoamerican calendrics. Somewhat more specialized are John Justeson's "Ancient Maya Ethnoastronomy: An Overview of the Hieroglyphic Sources," in World Archaeoastronomy, edited by Anthony F. Aveni (Cambridge, U.K., 1989); and Floyd Lounsbury's "Maya Numeration, Computation, and Calendrical Astronomy," in Dictionary of Scientific Biography, edited by Charles Coulston Gillespie, vol. 15, supp. 1, pp. 759–818 (New York, 1978). Alfonso Caso's "Mixtec Writing and Calendar," in Handbook of Middle American Indians, edited by Robert Wauchope, vol. 3 (Austin, Tex., 1965), remains the classic exposition of central Mexican calendrics. See also Rafael Tena's El Calendario Mexica y la cronografía (Mexico City, 1987). On other central Mexican calendars see Javier Urcid's Zapotec Hieroglyphic Writing (Washington, D.C., 2001). Munro S. Edmonson's The Book of the Year: Middle American Calendrical Systems (Salt Lake City, Utah, 1988) offers a pan-Mesoamerican comparative analysis of calendars and calendar glyphs. Contemporary Mesoamerican calendar systems are dealt with in Frank J. Lipp's The Mixe of Oaxaca: Religion, Ritual, and Healing (Austin, Tex., 1991); Barbara Tedlock's Time and the Highland Maya (Albuquerque, N.Mex., 1982; rev. ed. 1992); and Michael P. Closs, ed., Native American Mathematics (Austin, Tex., 1986), which also deals with North American calendars. See also Alfred M. Tozzer, ed. and trans., Landa's Relación de las cosas de Yucatan, vol. 18 (Cambridge, Mass., 1941), Eduard Seler, "The Venus Period in Picture Writings of the Borgian Codex Group," Bulletin of the Bureau of American Ethnology 28: 373–390, Dennis Tedlock's translation of Popol Vuh: The Definitive Edition of the Mayan Book of the Dawn of Life and the Glories of Gods and Kings (New York, 1985), and J. Eric S. Thompson, Maya Hieroglyphic Writing (Washington, D.C., 1950).
Anthony F. Aveni (2005)