Maya calendarFrom Wikipedia, the free encyclopedia
The Maya calendar is actually a system of distinct calendars and almanacs used by the Maya civilization of pre-Columbian Mesoamerica, and by some modern Maya communities in highland Guatemala.
These calendars could be synchronised and interlocked in complex ways, their combinations giving rise to further, more extensive cycles. The essentials of the Maya calendric system are based upon a system which had been in common use throughout the region, dating back to at least the 6th century BCE. It shares many aspects with calendars employed by other earlier Mesoamerican civilizations, such as the Zapotec and Olmec, and contemporary or later ones such as the Mixtec and Aztec calendars. Although the Mesoamerican calendar did not originate with the Maya, their subsequent extensions and refinements to it were the most sophisticated. Along with those of the Aztecs, the Maya calendars are the best-documented and most completely understood.
By the Maya mythological tradition, as documented in Colonial Yucatec accounts and reconstructed from Late Classic and Postclassic inscriptions, the deity Itzamna is frequently credited with bringing the knowledge of the calendar system to the ancestral Maya, along with writing in general and other foundational aspects of Maya culture.
The most important of these calendars is one with a period of 260 days. This 260-day calendar was prevalent across all Mesoamerican societies, and is of great antiquity (almost certainly the oldest of the calendars). It is still used in some regions of Oaxaca, and amongst the Maya communities of the Guatemalan highlands. The Maya version is commonly known to scholars as the Tzolkin, or Tzolk'in in the revised orthography of the Academia de las Lenguas Mayas de Guatemala. The Tzolk'in combined with another 365-day calendar (known as the Haab, or Haab' ), to form a synchronised cycle lasting for 52 Haabs, called the Calendar Round. Smaller cycles of 13 days (the trecena) and 20 days (the veintena) were important components of the Tzolk'in and Haab' cycles, respectively.
A different form of calendar was used to track longer periods of time, and for the inscription of calendar dates (i.e., identifying when one event occurred in relation to others). This form, known as the Long Count, is based upon the number of elapsed days since a mythical starting point, and was capable of being extended to refer to any date far into the future. This calendar involved the use of a positional notation system, in which each position signified an increasing multiple of the number of days. The Maya numeral system was essentially vigesimal (i.e., base-20), and each unit of a given position represented 20 times the unit of the position which preceded it. An important exception was made for the second place value, which instead represented 18 × 20, or 360 days, more closely approximating the solar year than would 20 × 20 = 400 days. It should be noted however that the cycles of the Long Count are independent of the solar year.
Many Maya Long Count inscriptions are supplemented by what is known as the Lunar Series, another calendar form which provides information on the lunar phase and position of the Moon in a half-yearly cycle of lunations.
A 584-day Venus cycle was also maintained, which tracked the appearance and conjunctions of Venus as the morning and evening stars. Many events in this cycle were seen as being inauspicious and baleful, and occasionally warfare was timed to coincide with stages in this cycle.
Other, less-prevalent or poorly-understood cycles, combinations and calendar progressions were also tracked. An 819-day count is attested in a few inscriptions; repeating sets of 9- and 13-day intervals associated with different groups of deities, animals and other significant concepts are also known.
With the development of the place-notational Long Count calendar (believed to have been inherited from other Mesoamerican cultures), the Maya had an elegant system with which events could be recorded in a linear relationship to one another, and also with respect to the calendar ("linear time") itself. In theory, this system could readily be extended to delineate any length of time desired, by simply adding to the number of higher-order place markers used (and thereby generating an ever-increasing sequence of day-multiples, each day in the sequence uniquely identified by its Long Count number).
In practice, most Maya Long Count inscriptions confine themselves to noting only the first 5 coefficients in this system (a b'ak'tun-count), since this was more than adequate to express any historical or current date (with an equivalent span of approximately 5125 solar years). Even so, example inscriptions exist which noted or implied lengthier sequences, indicating that the Maya well understood a linear (past-present-future) conception of time.
However, and in common with other Mesoamerican societies, the repetition of the various calendric cycles, the natural cycles of observable phenomena, and the recurrence and renewal of death-rebirth imagery in their mythological traditions were important and pervasive influences upon Maya societies.
This conceptual view, in which the "cyclical nature" of time is highlighted, was a pre-eminent one, and many rituals were concerned with the completion and re-occurrences of various cycles. As the particular calendaric configurations were once again repeated, so too were the "supernatural" influences with which they were associated.
Thus it was held that particular calendar configurations had a specific "character" to them, which would influence events on days exhibiting that configuration. Divinations could then be made from the auguries associated with a certain configuration, since events taking place on some future date would be subject to the same influences as its corresponding previous cycle dates. Events and ceremonies would be timed to coincide with auspicious dates, and avoid inauspicious ones (Coe 1992, Miller and Taube 1993).
The completion of significant calendar cycles ("period endings"), such as a k'atun-cycle, were often marked by the erection and dedication of specific monuments such as twin-pyramid complexes such those in Tikal and Yaxha, but (mostly in stela inscriptions) commemorating the completion, accompanied by dedicatory ceremonies.
A cyclical interpretation is also noted in Maya creation accounts, in which the present world and the humans in it were preceded by other worlds (one to five others, depending on the tradition) which were fashioned in various forms by the gods, but subsequently destroyed. The present world also had a tenuous existence, requiring the supplication and offerings of periodic sacrifice to maintain the balance of continuing existence. Similar themes are found in the creation accounts of other Mesoamerican societies (Miller and Taube, 1993:68-71).
Mayanists have bestowed the name Tzolk'in (in modern Mayan orthography; also and formerly commonly written tzolkin) on the Maya version of the Mesoamerican 260-day calendar. The word was coined based on the Yukatek Maya language, with an intended meaning of "count of days" (Coe 1992). The actual names of this calendar as used by the pre-Columbian Maya peoples are not known. The Aztec calendar equivalent was called by them Tonalpohualli, in the Nahuatl language.
The Tzolk'in calendar combines twenty day names with the thirteen numbers of the trecena cycle to produce 260 unique days. It was used to determine the time of religious and ceremonial events and for divination. Each successive day was numbered from 1 up to 13 and then starting again at 1. Separately from this, each day was given a name in sequence from a list of 20 day names:
The system started with 1 Imix', which was followed by 2 Ik', 3 Ak'b'al and so on up to 13 B'en. The trecena day numbers then started again at 1 while the named-day sequence continued onwards, and so the next entries in the combined sequence were 1 Ix, 2 Men, 3 K'ib', 4 Kab'an, 5 Etz'nab', 6 Kawak, then 7 Ajaw. With all twenty named days used, these now began to repeat the cycle while the numbered portion continued, so the next day after 7 Ajaw was 8 Imix'. The repetition of these interlocking 13- and 20-day cycles therefore took 260 days to complete (that is, for every possible combination of number/named day to occur once).
The Maya believed that each day of the Tzolk'in had a character that influenced events; in some regions these beliefs are still current. A Mayan shaman-priest, whose name meant "day keeper", read the Tzolk'in to predict the future. When a child is born, the day keeper interprets the Tzolk'in cycle to predict the baby’s destiny. For example, a child born on the day of Ak'b'al is thought to be feminine, wealthy, and verbally skillful. The birthday of Ak'b'al (along with several other days) is also thought to give the child the ability to receive messages with the supernatural world through somatic twitches of "blood lightning", so he or she might become a shaman-priest or a marriage spokesman.
Origin of the Tzolk'in
The exact origin of the Tzolk'in is not known, but there are several theories. One theory is that the calendar came from mathematical operations based on the numbers thirteen and twenty, which were important numbers to the Maya. The number twenty was the basis of the Maya counting system, taken from the number of human fingers and toes. (See Maya numerals). Thirteen symbolized the number of levels in the Upperworld where the gods lived, and the number of "major joints" on the human body (three per limb, plus the neck). The numbers multiplied together equal 260. Another theory is that the 260-day period came from the length of human pregnancy. This is close to the average number of days between the first missed menstrual period and birth, unlike Naegele's rule which is 40 weeks (280 days) between the last menstrual period and birth. It is postulated that midwives originally developed the calendar to predict babies' expected birth dates.
The Haab' was the Maya solar calendar made up of eighteen months of twenty days each plus a period of five days ("nameless days") at the end of the year known as Wayeb' (or Uayeb in 16th C. orthography). Bricker (1982) estimates that the Haab' was first used around 550 BCE with the starting point of the winter solstice.
The Haab' month names are known today by their corresponding names in colonial-era Yukatek Maya, as transcribed by 16th century sources (in particular, Diego de Landa and books such as the Chilam Balam of Chumayel). Phonemic analyses of Haab' glyph names in pre-Columbian Maya inscriptions have demonstrated that the names for these twenty-day periods varied considerably from region to region and from period to period, reflecting differences in the base language(s) and usage in the Classic and Postclassic eras predating their recording by Spanish sources.
Each day in the Haab' calendar was identified by a day number within the month followed by the name of the month. Day numbers began with a glyph translated as the "seating of" a named month, which is usually regarded as day 0 of that month, although a minority treat it as day 20 of the month preceding the named month. In the latter case, the seating of Pop is day 5 of Wayeb'. For the majority, the first day of the year was 0 Pop (the seating of Pop). This was followed by 1 Pop, 2 Pop ... 19 Pop, 0 Wo, 1 Wo and so on.
As a calendar for keeping track of the seasons, the Haab' was crude and inaccurate, since it treated the year as having 365 days, and ignored the extra quarter day (approximately) in the actual tropical year. This meant that the seasons moved with respect to the calendar year by a quarter day each year, so that the calendar months named after particular seasons no longer corresponded to these seasons after a few centuries. The Haab' is equivalent to the wandering 365-day year of the ancient Egyptians. Some argue that the Maya knew about and compensated for the quarter day error, even though their calendar did not include anything comparable to a leap year, a method first implemented by the Romans.
The five nameless days at the end of the calendar called Wayeb' were thought to be a dangerous time. Foster (2002) writes "During Wayeb, portals between the mortal realm and the Underworld dissolved. No boundaries prevented the ill-intending deities from causing disasters." To ward off these evil spirits, the Maya had customs and rituals they practiced during Wayeb'. For example, people avoided leaving their houses or washing or combing their hair.
Neither the Tzolk'in nor the Haab' system numbered the years. The combination of a Tzolk'in date and a Haab' date was enough to identify a date to most people's satisfaction, as such a combination did not occur again for another 52 years, above general life expectancy.
Because the two calendars were based on 260 days and 365 days respectively, the whole cycle would repeat itself every 52 Haab' years exactly. This period was known as a Calendar Round. The end of the Calendar Round was a period of unrest and bad luck among the Maya, as they waited in expectation to see if the gods would grant them another cycle of 52 years.
Since Calendar Round dates can only distinguish within 18980 days, equivalent to around 52 solar years, the cycle repeats roughly once each lifetime, and thus, a much more refined method of dating was needed if their history was to be recorded accurately.
The Long Count employs the use of number series, roughly base 20 and is constructed by counting whole number of days alone. The Mayan name for a day was k'in; twenty of these k'ins are known as a winal (or uinal); eighteen winals make one tun; twenty tuns are known as a k'atun, twenty k'atuns make a b'ak'tun. (Four rarely-used higher-order cycles are known as Piktun, Kalabtun, K'inchiltun, and Alautun.)
Correlations between Western calendars and the Maya calendar
Only one day in one calendar system has to be firmly established in the other to be able to translate all dates in one system to the other. The commonly-established way of expressing the correlation between the Maya calendar and the Gregorian or Julian calendars is to give the offset in days from the start of the Julian Period to the Maya creation on 0.0.0.0.0 4 Ajaw 8 Kumk'u.
The most commonly accepted correlation is the "Goodman, Martinez, Thompson" correlation (GMT correlation). The GMT correlation establishes that the 0.0.0.0.0 creation date occurred on 3114 BCE 6 September (Julian) or 3114 BCE 11 August (Gregorian), Julian day number (JDN) 584283, the number of days since the start of the Julian Period. This correlation fits the astronomical, ethnographic, carbon dating, and historical sources. However, there have been other correlations that have been proposed at various times. All of the following are only of historical interest, except that by Floyd Lounsbury, two days after the GMT correlation, which is still used by a few Maya scholars.
Today, 17:33, Monday 22 January 2007 (UTC), in the Long Count is 22.214.171.124.0.
Many of the books about the Maya and most of the software available for Maya calendar conversions uses the proleptic Gregorian calendar. In this system all Julian calendar dates are revised into the Gregorian calendar, rather than left in the Julian calendar which was in use before it. This is how one converts the Long Count 0.0.0.0.0 to August 11, 3114 BCE.
The use of software that is based on the proleptic Gregorian calendar can be problematic for:
1. Historical research. For example the G.M.T. correlation is based dates in both calendars in the Chronicle of Oxcutzcab, Bishop Diego de Landa's Relacion and the book of Chilam Balam of Tizimin. If one were to try to correctly derive the G.M.T. correlation by using these dates in a program that used the proleptic Gregorian calendar it would fail because the Gregorian calendar had not yet been invented.
2. Astronomical research. For example, to study ancient observations on stelae or in the codices, one may convert a Long Count to days, months, and years. This date would then be entered into an astronomy program. The astronomy program will use the standard Julian/Gregorian calendar so this will cause a major error.
Obviously this is a nontrivial issue and since most researchers will buy computer software to do Maya calendar conversions it is imperative for them to know which system their program uses.
Calculating Long Count dates
Long count dates list number of the highest order period first (B'ak'tun) and then the number of each successively smaller order periods until the number of days (k'in) are listed. Then the Calendar Round date is given.
A typical Calendar Round date is 126.96.36.199.16 5 Kib' 14 Yaxk'in. One can check whether this date is correct by the following calculation.
It is perhaps easier to find out how many days there are since 4 Ajaw 8 Kumk'u, and show how the date 5 Kib' 14 Yaxk'in is derived.
Calculating the Tzolk'in date portion
The Tzolk'in date is counted forward from 4 Ajaw. To calculate the numerical portion of the Tzolk'in date, we must add 4 to the total number of days given by the date, and then divide total number of days by 13.
(4 + 1383136) / 13 = 106395 and 5/13
This means that 106395 whole 13 day cycles have been completed, and the numerical portion of the Tzolk'in date is 5.
To calculate the day, we divide the total number of days in the long count by 20 since there are twenty day names.
1383136 / 20 = 69156 and (16/20)
This means 16 day names must be counted from Ajaw. This gives Kib'. Therefore, the Tzolk'in date is 5 Kib'.
Calculating the Haab' date portion
The Haab' date 8 Kumk'u is the ninth day of the eighteenth month. Since there are twenty days per month, there are eleven days remaining in Kumk'u. The nineteeth and last month of the Haab' year contains only five days, thus, there are sixteen days until the end of the Haab' year.
If we subtract 16 days from the total, we can then find how many complete Haab' years are contained.
1383136 - 16 = 1383120
Dividing by 365, we have
1383120 / 365 = 3789 and (135/365)
Therefore, 3789 complete Haab' have passed, with 135 days into the new Haab'.
We then find which month the day is in. Dividing the remainder 135 days by 20, we have six complete months, plus 15 remainder days. So, the date in the Haab' lies in the seventh month, which is Yaxk'in. The fifteenth day of Yaxk'in is 14, thus the Haab' date is 14 Yaxk'in.
So the date of the long count date 188.8.131.52.16 5 Kib' 14 Yaxk'in is confirmed.
2012 and the Maya Calendar
The end of the 13th b'ak'tun is conjectured to have been of great significance to the Maya, but does not necessarily mark the end of the world according to their beliefs, but a new beginning or time of re-birth. According to the Popol Vuh, a book compiling details of creation accounts known to the Quiché Maya of the colonial-era highlands, we are living in the fifth world. The Popol Vuh describes the first four creations that the gods failed in making and the creation of the successful fifth world where men were placed.
The last creation ended on a long count of 184.108.40.206.19. Another 220.127.116.11.19 will occur on 20 December 2012, and it has been discussed in many New Age articles and books that this will be the end of this creation, the next pole shift or something else entirely. However, the Maya abbreviated their long counts to just the last five vigesimal places. There was an infinite number of larger units that were usually not shown. When the larger units were shown (notably on a monument from Coba), the end of the last creation is expressed as 18.104.22.168.22.214.171.124.126.96.36.199.188.8.131.52.184.108.40.206.220.127.116.11.0, where the units are obviously supposed to be 13s twenty places larger than that b'ak'tun. In this age we are only approaching 0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.18.104.22.168.0, and the larger places would all need to similarly roll over to 13 again to match the date of the new creation.
This is confirmed by a date from Palenque, which projects forward in time to 22.214.171.124.0.0, which will occur on 13 October, 4772 (a Friday). The Classic Period Maya likely did not believe that the end of this age would occur in 2012. According to the Maya, there will be a baktun ending in 2012, a significant event being the end of a 13th 400 year period, but not the end of the world.
Another important calendar for the Maya was the Venus cycle. The Maya were skilled astronomers, and could calculate the Venus cycle with extreme accuracy. There are six pages in the Dresden Codex (one of the Maya codices) devoted to the accurate calculation of the location of Venus.
The Maya were able to achieve such accuracy by careful observation over many years. The Venus cycle was especially important because the Maya believed it was associated with war and used it to divine good times for coronations and war.
Maya rulers planned for wars to begin when Venus rose. The Maya also possibly tracked other planets’ movements, including those of Mars, Mercury, and Jupiter.
what is the mayan numeral for half?