Aztec calendar

Please refer to Wikipedia's Aztec calendar, since it was the best known Mesoamerican calendar for the Europeans. Its most famous monument in Mexico is the "Piedra del Sol" which means the "Stone of the Sun." The text under Aztec calendar offers a new solution to it, including its starting point (October 23, 4004 BCE).

The Aztec calendar

This condensed study is taken from Z.A. Simon (1984: 9-31) by permission, in a condensed form. It is known for some scholars for 18 years and it has never been challanged or refuted. It contains the following "new" scientific results:

1) Proof of the nonexistence of intercalary days in the Aztec calendar, verifying Prof. Michael Coe's theory.

2) Establishment of an exact starting date of the calendar (day, month, and year), which was unknown until now (1984).

3) Solution of the contradictory interpretations of the ancient chroniclers: Sahagún and Diego Durán.

4) Mathematical proof of the pre-Columbian contacts between the Mesoamerican and some West-European cultures.

Most of our largest libraries have a few dozen books on the history of Mexico, but these books usually interpret the Aztec calendar very briefly. Besides this, they often emphasize those scientific achievements only that are important for their authors. The wide range of different opinions can be illustrated by one example. A well-known expert on Mexican culture remembers Antonio de León y Gama (1736-1802), who has been called the first Mexican archaeologist. He states that the most important of León y Gama's books for archaeology is the "Descripción histórica y cronológica de las dos piedras." The sculptores of the title are two famous monoliths. Bernal adds that one of them the Stone of the Sun, often and inaccurately called the Aztec calendar and falls into the error of attributing to the stone a calendrical significance, though he never claims that it was used as a calendar. In this situation, despite the correct but brief information of the encyclopeadias, the reader might get easily confused.

In addition to this, some sources introduced certain new terms without proper consistence. Other denominations were superseded, including a few calendrical miscalculations of amateur writers. Due to the apparent lack of coherence, the new results of some interesting papers have been neglected or ignored by the editors of many popular source books. Therefore, a detailed description of the Mexican (Aztec) calendar is necessary for a complete understanding of the question. Therefore we will give that description before examining what experst have said about the problems. It will be concluded with the author's solution and its implications.

It is well-known that the Mayas and Aztecs had a highly developed calendar system. The two basic time cycles that governed Mesoamerican life were the solar calendar and the ritual calendar. In other words, the Mexican calendar is twofold, and comprises a ritual calendar, with a round of 260 days, which was employed in divination and in fixing "movable feasts"; and a solar year, with a round of 365 days, according to which the seasonal feasts were held (Muser, 1978:17 and Joyce, 1970:59).

The solar calendar of 365 days, called the Vague Year (or Civil Year), was composed of 18 months of 20 days each, with a period of 5 days added at the end. The 360-day period was called "xíhuitl" by Aztecs, and "haab" or "tun" by the Maya. The final unlucky days were called "Nemontemi" in Nahuath, and "Uayeb" in Mayan.

Each month had its own special name, and the days were numbered from zero to nineteen. The days of the last month, Uayeb, were numbered from zero to four. In this calendar the Maya counted the days as we do the hours, starting from zero rarther than from one (Ivanoff, 1971: 87).

This solar calendar was inseparable from the Sacred Round, or Sacred Almanac. The priests used this ritual calendar of 260 days, called "Tonalpohualli" by the Aztecs and "tzolkin" by the Maya, primarily for divinatory purposes. The concurrent permutation of the solar and ritual calendars produced the Calendar Round. An exclusively lowland Classic Maya calendar achievement was the Long Count, which permitted an infinite computation of time, backward or forward, from an established starting point (Muser, 1978: 17). By the passing centuries, this simplified system may have became dominant, but we want to know its original form.

As we have already mentioned, in both (solar and ritual) calendars, time elapsed in parallel fashion, simultaneously and continuously. Peter Tompkins (1976: 290) states that each day of the tzolkin was governed by a deity who was thought to influence that day for good or evil, each separate day being regarded by the Maya as an individual god, whose glyph was a stylized portrait of his attributes. The numbers 1 to 13 were also personized as the heads of the gods they represented.

The use of this 260-day calendar was in no way arbitrary. The Mesoamericans possessed the correct knowledge that 260 x 18 was the same as 360 x 13, that 260 x 7 was the same as 364 x5, that 260 x73 was the same as 365 x 52, and that 260 x 1461 (like the Egyptian Sothic cycle!) was the same as 365.25 x 1040. Tompkins adds that to these calendars, which all fell into the 260-day pattern, were added more refinements, in order to calculate the synodic returns of the moon and the planets.

In Mesoamerica the planet Venus looms in the daws sky with exraordinary brilliance. Both the Maya and the Nahua (Nahuatl) astronomers devoted special attention to the planet, and particularly to its heliacal rising. Venus revolves around the sun every 224.7 days, but since the earth is moving along its own orbit, the planet appears at the same place in the sky in 584 days, called synodic period. As 5 x 584 is equal to 8 x 365, the Maya considered five Venus years equal to eight solar years. And as 365 x 104 is equal to both 146 x 260 and 65 x 584, the sacred, the solar, and the venus calendars become coincident every 37,960 days, or 104 years. That is, two Mesoamerican "centuries" of 52 years. (Actually, the Maya knew the Venus cycle to be 583.92 days, instead of a round 584, so they dropped four days every sixty-one Venus years, in order to compensate for the discrepancy and make a round number divisible by 260.)

As astronomers are quick to point out, such an accurate knowledge of the cycle of venus, whose revolutions are by no means regular, points to a long and careful observation.

Furthermore, the Mesoamericans devised a lunar calendar that would fit with the others. Calculating that 405 lunations or 11,960 days was exactly divisible by 260 (or, 260 x 46), they obtained a lunar period of 29.53 days which is practically the same what we know today. This would give them a lunar calendar accurate within a day over a period of 300 years.

Returning to the ritual and the solar calendars, the method of naming the individual days was the same for both, and consisted in the combination of twenty pictorial signs, with the numbers one to thirteen. The signs, according to the four cardinal points, were as follows:

E(ast)... 1 Cipactli (alligator, crocodila, aquatic monster)

N(orth).. 2 Éhecatl (wind, wind god)

W(est)... 3 Calli (house)

S(outh).. 4 Cuetzpalin (lizard)

E..........5 Cóatl (serpent, snake)

N..........6 Miquiztli (death)

W..........7 Mázatl (deer)

S..........8 Tochtli (rabbit)

E..........9 Atl (water)

N.........10 Itzcuintli (dog)

W.........11 Ozomatli (monkey)

S.........12 Malinalli (dead grass

E.........13 Ácatl (reed)

N.........14 Océlotl (ocelot, jaguar)

W.........15 Quauhtli (eagle)

S.........16 Cozcaquauhtli (king buzzard, vulture)

E.........17 Ollin (motion, earthquake)

N.........18 Técpatl (flint, flint knife)

W.........19 Quiáhuitl (rain)

S.........20 Xóchitl (flower)

By combining both series, one gets 1 Alligator as the name of the first day; of the second, 2 Wind; of the third, 3 House, until we reach the day 13 Reed. The following day is called 1 Jaguar; the nex is 2 Eagle, and so on. When the day Flower is reached, it is necessary to start counting the day Alligator over again, with its corresponding number. This calendar was essentially the basis for all other calendrical computations, such as the Mayan, the Zapotec, the Mixtec, the Totonac, the Huaxtec, the Teotihuacán, the Toltec and the Aztec. (Caso, 1958: 66)

Joyce (1970: 61-62) states that these signs ran consecutively in the order given above, one being assigned to each day, and the series was repeated ad infinitum. Conjointly with them were repeated the numeralsone to thirteen, e.g., 1 Cipactli, 2 Eecatl, 3 Calli, and so on to 13 Acatle, which was followed by 1 Ocelotl, 2 Quauhtli, etc. There being no common factorto the numbers 13 and 20, a period of 13 x 20 days, or 260, would elapse before the sign 1 Cipactli would recur. This period of 260 days constituted the divinatory or ritual calendar, known as ''tonalamatl''. The tonalamatl was subdivided in various ways; in some manuscripts each of the twenty 13-day periods, or weeks, is shown separately, together with the figure of a god who was especially associated with the first day, but whose influence was supposed to extend over the whole "week". In some MSS. the tonalamatl is arranged on a different system: in five long horizontal rows of 52 days each. Each row,and each vertical column of five days, is provided with a presiding deity symbol, the influence of which must be assessed.

The Mexicans reckoned 365 days to the solar year, which they divided into 18 months of twenty days each, and a nineteenth period of five days, considered extremely unlucky, at the end of the year. As the days were known by their tonalamatl names, it is obvious that the first 105 days of the year recurred at the end, after the 260-day period. However, it was possible to distinguish between two days of the same name which fell in the same year, owing to the fact that each day was associated with one of a series of nine deities, called lords of the night, a series also repeated ad infinitum, except no "lord" was assigned to any of the five unlucky days at the end of the year, which were called ''nemontemi'' or "useless days." Thus, since the number 260 is not divisible by 9, it was possible to differenciate between two days of the same name falling in one year. And since 9 goes into 360 without a remainder, the commencement of the year coincided with the beginning of the series of "lords of the night."

Nor is this all; a corresponding series of thirteen "lords of day," which, however, is not similarly composed in all manuscripts, accompanied the days (except the nemontemi), and the influences of the day- and night-lord assigned to each day respectively constituted two additional features for the consideration of the would-be interpreter of the tonalamatl.

Since each "month" consisted of twenty days, and there were twenty day-signs, it is obvious that each month in a given year started with the same sign; but that since the last month was followed by the five unlucky days, each year began with a day-sign five days later than the last. Also since 365 is divisible by 13 with 1 as remainder, it follows equally that each year began wit a day-number one in advance of the last.

Further, since there were 20 day-signs, and 5 (the highest common factor of 365 and 20) goes into twenty exactly four times, the year began with on of the four signs only. The four signs mentioned by T.A. Joyce (1970: 63-65), which gave the names to the years, are the signs Tecpatl, Calli, Tochtli and Acatl, recurring in that order. (It is more than probable that the day-number entering into the name of the year was that of the first day, as held by most authorities.) The years were named successively, 1 Tecpatl, 2 Calli, 3 Tochtli, etc., until, after a period of 52 years (taht is, 13 x 4), the same sign recurred with the same number as the name-date of the year. This period of 52 years named ''xiuhmolpilli'' (meaning bundle of years) formed the shorter cycle of the Mexicans.

To understand the calculation of a 52-year cycle, imagine two wheels of time ritating simultaneously. On time wheen recorded days, for which there were 20 names with 13 numbers. The complete name of a day must be accompanied by the appropriate number, such as 4 Reed or 9 Eagle. The other wheel presents a somewhat parallel situation. Eighteen months of 20 days each, to which the dreaded 5-day period of bad luck was added, resulted in a 365-day cycle (18 x 20 plus 5 equals 365), corresponding to our solar year. In order to return to the very same day and month, 52 years would have to elapse. This was the basic computation of time used in Mesoameica. See the diagrammatic illustration in Michael D. Coe, Mexico and in the books of J. Eric S. Thompson.