Mesoamerican Long Count Calendar

The Mesoamerican Long Count calendar is a non-repeating, vigesimal (base-20) calendar used by several Mesoamerican cultures, most notably the Maya. For this reason, it is sometimes known as the Maya (or Mayan) Long Count calendar. Using a modified vigesimal tally, the Long Count calendar identifies a day by counting the number of days passed since August 11, 3114 BCE (Gregorian).[1] Because the Long Count calendar is non-repeating, it was widely used on monuments.

Among other calendars devised in pre-Hispanic Mesoamerica, two of the most widely used were the 365-day solar calendar (Haab' in Mayan) and the 260-day ceremonial calendar, which had 20 periods of 13 days. This 260-day calendar was known as the Tzolk'in to the Maya and tonalpohualli to the Aztecs.

The Haab' and the Tzolk'in calendars identified and named the days, but not the years. The combination of a Haab' date and a Tzolk'in date was enough to identify a specific 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 365 days and 260 days respectively, the whole cycle would repeat itself every 52 Haab' years exactly. This period was known as a Calendar Round.

To measure dates over periods longer than 52 years, the Mesoamericans devised the Long Count calendar.

[edit] Long Count periods
The Long Count calendar identifies a date by counting the number of days from August 11, 3114 BCE in the proleptic Gregorian calendar or September 6 (Julian). Rather than using a base-10 scheme, like Western numbering, the Long Count days were tallied in a base-20 scheme. Thus is equal to 25, and is equal to 40.

The Long Count is not consistently base-20, however, since the second digit from the right only counts to 18 before resetting to zero. Thus does not represent 400 days, but rather only 360 days.

The following table shows the period equivalents as well as Mayan names for these periods.

Table of Long Count units Days Long Count period Long Count period Approx solar years
1 = 1 K'in
20 = 20 K'in = 1 Winal 1/18th
360 = 18 Winal = 1 Tun 1
7,200 = 20 Tun = 1 K'atun 20
144,000 = 20 K'atun = 1 B'ak'tun 395

The Mayan name for a day was k'in. Twenty of these k'ins are known as a winal (or uinal). Eighteen winals or 360 k'in make one tun. Twenty tuns are known as a k'atun. Twenty k'atuns make a b'ak'tun. There are also four rarely-used higher-order periods: piktun, kalabtun, k'inchiltun, and alautun.

[edit] Calculating Long Count dates
Mesoamerican numerals
Long Count dates are written with Mesoamerican numerals, as shown on this table. A dot represents one while a bar equals 5. The shell glyph was used to represent the zero concept. The Long Count calendar required the use of zero as a place-holder, and presents one of the earliest uses of the zero concept in history.


The Long Count dates are written vertically, with the higher periods (i.e. b'ak'tun) on the top and then the number of each successively smaller order periods until the number of days (k'in) are listed. As can be seen at left, the Long Count date shown on Stela C at Tres Zapotes is

7 × 144000 = 1,008,000 days (k'in)
16 × 7200 = 115,200 days (k'in)
6 × 360 = 2,160 days (k'in)
16 × 20 = 320 days (k'in)
18 × 1 = 18 days (k'in)
Total days = 1,125,698 days (k'in)

The date on Stela C, then, is 1,125,698 days from August 11, 3114 BCE, or September 1, 32 BCE.

On Maya monuments, the Long Count syntax is more complex. The date sequence is given once, at the beginning of the inscription, and opens with the so-called ISIG (Introductory Series Initial Glyph) which reads tzik-a(h) hab’ [patron of Haab' month] ("revered was the year-count with the patron [of the month]").[2] Next come the 5 digits of the Long Count, followed by the tzolk'in date written as single glyph, and then by supplementary information. Most of this supplementary series is optional and has been shown to be related to lunar data, for example, the age of the moon on the day and the calculated length of current lunation.[3] The date is concluded by a glyph stating the day and month of the Haab year. The text then continues with whatever activity occurred on that date.

A drawing of a full Maya Long Count inscription is shown below (click here).


Origin of the Long Count calendar
The earliest Long Count inscription yet discovered is on Stela 2 at Chiapa de Corzo, Chiapas, Mexico, showing a date of 36 BCE.[4] This table lists the 6 artifacts with the 8 oldest Long Count dates.

Archaeological site Name Gregorian Date
(based on August 11)
Long Count digits Location
Chiapa de Corzo Stela 2 December 10, 36 BCE Chiapas, Mexico
Tres Zapotes Stela C September 3, 32 BCE Veracruz, Mexico
El Baúl Stela 1 March 6, 37 CE Guatemala
Abaj Takalik Stela 5 May 20, 103 CE Guatemala
' ' ' ' June 6, 126 CE ' '
La Mojarra Stela 1 July 14, 156 CE Veracruz, Mexico
' ' ' ' May 22, 143 CE ' '
Near La Mojarra Tuxtla Statuette March 15, 162 CE Veracruz, Mexico

Of the 6 sites, three are on the western edge of the Maya homeland and three are several hundred kilometers further west, leading most researchers to believe that the Long Count calendar predates the Maya.[5] La Mojarra Stela 1, the Tuxtla Statuette, Tres Zapotes Stela C, and Chiapa Stela 2 are all inscribed in an Epi-Olmec, not Maya, style.[6] El Baúl Stela 2, on the other hand, was created in the Izapan style. The first unequivocally Maya artifact is Stela 29 from Tikal, with the Long Count date of 292 CE (, more than 300 years after Stela 2 from Chiapa de Corzo.[7]

[edit] Correlations between Western calendars and the Long Count calendar
JDN correlations
to the Maya creation date
(after Thompson 1971, et al.) Name Correlation
Willson 438,906
Smiley 482,699
Makemson 489,138
Spinden 489,384
Teeple 492,662
Dinsmoor 497,879
-4CR 508,363
-2CR 546,323
Stock 556,408
Goodman 584,280
Martinez-Hernandez 584,281
GMT 584,283
Lounsbury 584,285
Pogo 588,626
+2CR 622,243
Kreichgauer 626,927
+4CR 660,203
Hochleitner 674,265
Schultz 677,723
Ramos 679,108
Valliant 679,183
Weitzel 774,078
A list of the start dates for 13 Baktuns Long Count Proleptic Gregorian Calendar Date August 11, 3114 BCE November 13, 2720 BCE February 16, 2325 BCE May 21, 1931 BCE August 23, 1537 BCE November 26, 1143 BCE February 28, 748 BCE June 3, 354 BCE September 5, 41 CE December 9, 435 March 13, 830 June 15, 1224 September 18, 1618 December 21, 2012
There have been various methods proposed to allow us to convert from a Long Count date to a Western calendar date. These methods, or correlations, are generally based on dates from the Spanish conquest, where both Long Count and Western dates are known with some accuracy.

The commonly-established way of expressing the correlation between the Maya calendar and the Gregorian or Julian calendars is to provide number of days from the start of the Julian Period (Monday, January 1, 4713 BCE) to the start of creation on (4 Ajaw, 8 Kumk'u).

The most commonly accepted correlation is the "Goodman, Martinez, Thompson" correlation (GMT correlation). The GMT correlation establishes that the creation date occurred on 3114 BCE September 6 (Julian) or 3114 BCE August 11 (Gregorian), Julian day number (JDN) 584283. This correlation fits the astronomical, ethnographic, carbon dating, and historical sources. However, there have been other correlations that have been proposed at various times, most of which are merely of historical interest, except that by Floyd Lounsbury, two days after the GMT correlation, which is in use by some Maya scholars, such as Linda Schele.

Today, 15:12, Saturday April 19, 2008 (UTC), in the Long Count is (GMT correlation).

[edit] 2012 and the Long Count
According to the Popol Vuh, a book compiling details of creation accounts known to the K'iche' Maya of the Colonial-era highlands, we are living in the fourth world.[8] The Popol Vuh describes the first three creations that the gods failed in making and the creation of the successful fourth world where men were placed. In the Maya Long Count, the previous creation ended at the start of a 13th b'ak'tun.

The previous creation ended on a long count of Another will occur on December 20, 2012, followed by the start of the thirteenth b'ak'tun,, on December 21, 2012.[9]

[edit] Significance within the New Age movement
Two figures within the New Age, the artist and theorist José Argüelles and the late ethnobotanist and psychonaut Terence McKenna, have publicized theories concerning the significance of the end of the cycle. (They arrived at their conclusions separately from one another.) They have jointly inspired a number of articles and books that this will be the end of this creation, the next pole shift or, as McKenna speculated in his theories, the end of history and events as "novel" as the origin of life on Earth, which we could not possibly imagine. Other, more mundane speculations involve a worldwide catastrophe, such as a pole shift. The idea of the significance of the date has also increasingly passed into popular culture.

[edit] Refutation
In this age we are approaching the same count again, only there is a common misconception of the Maya's practice of abbreviating their dates to five vigesimal places. According to the Maya there will be a baktun ending in 2012, a significant event being the end of the 13th 394 year period, but not the end of the world.[10]

[edit] Inscriptions beyond 2012
Maya stelae occasionally show dates beyond 2012. Most of these are in the form of "distance dates", where a Long Count date is given with a distance date to be added. For example, on the Tablet of Inscriptions from Palenque the following Long Count date was found: 8 Ahau 13 Pop (24 March 603 Gregorian) with a distance date of The resulting date is given as 5 Lamat 1 Mol,[11] or 21 October 4772 – almost 3,000 years into the future. The king Pacal of Palenque predicted that on this date the eightieth Calendar Round anniversary of his accession will be celebrated, suggesting he did not believe the world would end in 2012.[12]

[edit] Summary
Despite the publicity generated by the 2012 date, Susan Milbrath, curator of Latin American Art and Archaeology at the Florida Museum of Natural History, stated that "We [the archaeological community] have no record or knowledge that [the Maya] would think the world would come to an end" in 2012.[13]

"For the ancient Maya, it was a huge celebration to make it to the end of a whole cycle," says Sandra Noble, executive director of the Foundation for the Advancement of Mesoamerican Studies, Inc. in Crystal River, Florida. To render December 21, 2012, as a doomsday or moment of cosmic shifting, she says, is "a complete fabrication and a chance for a lot of people to cash in."[14]

[edit] Calculating a full Long Count date
As stated, a full Long Count date not only includes the 5 digits of the Long Count, but the 2-character Tzolk'in and the 2-character Haab' dates as well. The 5 digit Long Count can therefore be confirmed with the other 4 characters (the "calendar round date").

Taking as an example a Calendar Round date of (Long Count) 5 Kib' (Tzolk'in) 14 Yaxk'in (Haab'). 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.

9 × 144000 = 1296000
12 × 7200 = 86400
2 × 360 = 720
0 × 20 = 0
16 × 1 = 16
Total days = 1383136 k'in

[edit] 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'.

[edit] 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 nineteenth 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 5 Kib' 14 Yaxk'in is confirmed.

[edit] Piktuns and higher orders
As mentioned in the Syntax section, there are also four rarely-used higher-order periods above the b'ak'tun: piktun, kalabtun, k'inchiltun, and alautun.

It is a matter of dispute whether the first piktun occurs after 13 or after 20 b'ak'tun. Most Mayanists think that in the majority of inscriptions, where only the last five Long Count positions are used, the count recycles at 13 b'ak'tuns, whereas, if longer cycles are used, the count continues to the end of the 20th b'ak'tun (b'ak'tun 19) before a pictun is registered.[citation needed] In the same way, the fact that a 13-katun cycle was used, didn't negate the fact that there are 20 katuns in a b'ak'tun.

The inscription on Quirigua stela F, or 6, shows a Long Count date of 1 Ahau 3 Zip (15 March 761 Gregorian). The huge distance date of is subtracted and the resulting date is given as (18.) 1 Ahau 13 Yaxkin, which is equivalent to a day over 90 million years in the past. However, there is another distance date on Quirigua Stela D or 4, that gives a date of 7 Ahau 18 Pop (17 February 766 Gregorian), to which is added, to give a date of (13.) This is over 400 million years after the date the stela was erected! It was by calculating a number of these distance dates that Eric Thompson was able to determine that the date of creation in 3114 BCE – was actually in the extended version.

At Yaxchilan, on a temple stairway, there is an inscription that includes four levels above the alautuns. The inscription reads: 3 Muluc 17 Mac. This is equivalent to 19 October 744, but the higher cycles do not conform to Thompson’s calculation. The same applies to a Late Classic monument from Coba, Stela 1. The date of creation is expressed as, where the units are 13s in the nineteen places larger than the b'ak'tun.[

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