![East side of stela C, Quirigua](https://upload.wikimedia.org/wikipedia/commons/7/7a/East_side_of_stela_C%2C_Quirigua.PNG)
The Mesoamerican Long Count calendar is a non-repeating,
vigesimal (base 20) and octodecimal (base 18) calendar used by several
pre-Columbian
In the history of the Americas, the pre-Columbian era spans from the original settlement of North and South America in the Upper Paleolithic period through European colonization, which began with Christopher Columbus's voyage of 1492. Usually, ...
Mesoamerica
Mesoamerica is a historical region and cultural area in southern North America and most of Central America. It extends from approximately central Mexico through Belize, Guatemala, El Salvador, Honduras, Nicaragua, and northern Costa Rica ...
n cultures, most notably the
Maya
Maya may refer to:
Civilizations
* Maya peoples, of southern Mexico and northern Central America
** Maya civilization, the historical civilization of the Maya peoples
** Maya language, the languages of the Maya peoples
* Maya (Ethiopia), a popul ...
. For this reason, it is often 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 a
mythical creation date that corresponds to August 11, 3114
BCE
Common Era (CE) and Before the Common Era (BCE) are year notations for the Gregorian calendar (and its predecessor, the Julian calendar), the world's most widely used calendar era. Common Era and Before the Common Era are alternatives to the or ...
in the
proleptic Gregorian calendar
The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to the dates preceding its official introduction in 1582. In nations that adopted the Gregorian calendar after its official and first introduction, dates occ ...
. The Long Count calendar was widely used on monuments.
Background
The two most widely used calendars in pre-Columbian Mesoamerica were the 260-day
Tzolkʼin
Tzolkʼin (, formerly and commonly tzolkin) is the name bestowed by Mayanists on the 260-day Mesoamerican calendar originated by the Maya civilization of pre-Columbian Mesoamerica.
The tzolkʼin, the basic cycle of the Maya calendar, is a preemi ...
and the 365-day
Haabʼ
The Haabʼ () is part of the Maya calendric system. It was a 365-day calendar used by many of the pre-Columbian cultures of Mesoamerica.
Description
The Haabʼ comprises eighteen months of twenty days each, plus an additional period of five da ...
. The equivalent Aztec calendars are known in
Nahuatl as the
Tonalpohualli and
Xiuhpohualli.
The combination of a Haabʼ and a Tzolkʼin date identifies a day in a combination which does not occur again for 18,980 days (52 Haabʼ cycles of 365 days equals 73 Tzolkʼin cycles of 260 days, approximately 52 years), a period known as the
Calendar Round
The Maya calendar is a system of calendars used in pre-Columbian Mesoamerica and in many modern communities in the Guatemalan highlands, Veracruz, Oaxaca and Chiapas, Mexico.
The essentials of the Maya calendar are based upon a system which had ...
. To identify days over periods longer than this, Mesoamericans used the Long Count calendar.
Long Count periods
![La Mojarra Estela 1 (Escritura superior)](https://upload.wikimedia.org/wikipedia/commons/f/f8/La_Mojarra_Estela_1_%28Escritura_superior%29.jpg)
The Long Count calendar identifies a date by counting the number of days from a starting date that is generally calculated to be August 11, 3114 BCE in the proleptic Gregorian calendar or September 6 in the Julian calendar (or −3113 in astronomical year numbering). There has been much debate over the precise correlation between the Western calendars and the Long Count calendars. The August 11 date is based on the GMT correlation (see
Correlations between Western calendars and the Long Count calendar section elsewhere in this article for details on correlations).
The completion of 13
bʼakʼtuns (August 11, 3114 BCE) marks the Creation of the world of human beings according to the Maya. On this day, Raised-up-Sky-Lord caused three stones to be set by associated gods at Lying-Down-Sky, First-Three-Stone-Place. Because the sky still lay on the primordial sea, it was black. The setting of the three stones centered the cosmos which allowed the sky to be raised, revealing the
Rather than using a base 10 scheme, the Long Count days were tallied in a modified base-20 scheme. In a pure base 20 scheme, 0.0.0.1.5 is equal to 25 and 0.0.0.2.0 is equal to 40. The Long Count is not pure base-20, however, since the second digit from the right (and only that digit) rolls over to zero when it reaches 18. Thus 0.0.1.0.0 does not represent 400 days, but rather only 360 days and 0.0.0.17.19 represents 359 days.
The name ''bʼakʼtun'' was invented by modern scholars. The numbered Long Count was no longer in use by the time the Spanish arrived in the
Yucatán Peninsula
The Yucatán Peninsula (, also , ; es, Península de Yucatán ) is a large peninsula in southeastern Mexico and adjacent portions of Belize and Guatemala. The peninsula extends towards the northeast, separating the Gulf of Mexico to the north ...
, although unnumbered
kʼatun
A ''kʼatun'' (, ) is a unit of time in the Maya calendar equal to 20 ''tuns'' or 7200 days, equivalent to 19.713 tropical years. It is the second digit on the normal Maya long count date. For example, in the Maya Long Count date 12.19.13.15.12 (D ...
s and tuns were still in use. Instead the Maya were using an abbreviated
Short Count.
Mesoamerican numerals
![maya](https://upload.wikimedia.org/wikipedia/commons/1/1b/Maya.svg)
Long Count dates are written with Mesoamerican numerals, as shown on this table. A dot represents ''1'' 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.
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) habʼ
atron of Haabʼ month' ("revered was the year-count with the patron
f the month). Next come the 5 digits of the Long Count, followed by the Calendar Round (tzolkʼin and Haabʼ) and
supplementary series
The term supplementary can refer to:
* Supplementary angles
* Supplementary Benefit, a former benefit payable in the United Kingdom
* Supplementary question
A question time in a parliament occurs when members of the parliament ask questions of ...
. The supplementary series is optional and contains lunar data, for example, the age of the moon on the day and the calculated length of current
lunation
In lunar calendars, a lunar month is the time between two successive syzygies of the same type: new moons or full moons. The precise definition varies, especially for the beginning of the month.
Variations
In Shona, Middle Eastern, and Euro ...
. The text then continues with whatever activity occurred on that date.
A drawing of a full Maya Long Count inscription is shown
below.
Earliest Long Counts
The earliest contemporaneous Long Count inscription yet discovered is on Stela 2 at
Chiapa de Corzo,
Chiapas, Mexico, showing a date of 36 BCE, although Stela 2 from
Takalik Abaj
Tak'alik Ab'aj (; ; ) is a pre-Columbian archaeological site in Guatemala. It was formerly known as Abaj Takalik; its ancient name may have been Kooja. It is one of several Mesoamerican sites with both Olmec and Maya features. The site flourishe ...
,
Guatemala might be earlier
Takalik Abaj Stela 2's highly battered Long Count inscription shows 7 ''bak'tuns'', followed by ''k'atuns'' with a tentative 6 coefficient, but that could also be 11 or 16, giving the range of possible dates to fall between 236 and 19 BCE.
Although Takalik Abaj Stela 2 remains controversial, this table includes it, as well as six other artifacts with the eight oldest Long Count inscriptions according to Dartmouth professor Vincent H. Malmström (two of the artifacts contain two dates and Malmström does not include Takalik Abaj Stela 2).
[ Note: Malmström's Gregorian dates are three or four days later than a correlation of 584283 would give (the Wikipedia table has been corrected).] Interpretations of inscriptions on some artifacts differ.
[
Of the six sites, three are on the western edge of the Maya homeland and three are several hundred kilometers further west, leading some researchers to believe that the Long Count calendar predates the Maya. La Mojarra Stela 1, the Tuxtla Statuette, Tres Zapotes Stela C and Chiapa Stela 2 are all inscribed in an Epi-Olmec script, Epi-Olmec, not Maya, style. El Baúl Stela 2, on the other hand, was created in the ]Izapa
Izapa is a very large pre-Columbian archaeological site located in the Mexican state of Chiapas; it is best known for its occupation during the Late Formative period. The site is situated on the Izapa River, a tributary of the Suchiate River, ...
n style.
The first unequivocally Maya artifact is Stela 29 from Tikal
Tikal () (''Tik’al'' in modern Mayan orthography) is the ruin of an ancient city, which was likely to have been called Yax Mutal, found in a rainforest in Guatemala. It is one of the largest archeological sites and urban centers of the pre-C ...
, with the Long Count date of 292 CE (8.12.14.8.15), more than 300 years after Stela 2 from Chiapa de Corzo.
More recently, with the discovery in Guatemala of the San Bartolo (Maya site)
San Bartolo is a small pre-Columbian Maya archaeological site located in the Department of Petén in northern Guatemala, northeast of Tikal and roughly fifty miles from the nearest settlement. San Bartolo's fame derives from its splendid Late-P ...
stone block text ( 300 BCE), it has been argued that this text celebrates an upcoming time period ending celebration. This time period may have been projected to end sometime between 7.3.0.0.0 and 7.5.0.0.0 — 295 and 256 BCE, respectively. Besides this being the earliest Maya hieroglyphic text so far uncovered, it would arguably be the earliest glyphic evidence to date of Long Count notation in Mesoamerica.
Correlations between Western calendars and the Long Count
The Maya and Western calendars are correlated by using a Julian day number (JDN) of the starting date of the current creation — 13.0.0.0.0, 4 Ajaw
Ajaw or Ahau ('Lord') is a pre-Columbian Maya civilization, Maya political title attested from epigraphy, epigraphic inscriptions. It is also the name of the 20th day of the ''tzolkʼin'', the Maya divinatory calendar, on which a ruler's ''kʼat ...
, 8 Kumkʼu.[All extant Maya inscriptions that represent this base date wrote it with a "13" bakʼtuns, not "0". But when using "13.0.0.0.0" as a base date in calculations, the "13" bakʼtuns has the numerical value 0, as if it were written as "''0''.0.0.0.0". This is easily confused when the "13" bakʼtuns has the actual value 13 in the ''current'' baktʼun, as in the Maya date for today: (=).] This is referred to as a "correlation constant". The generally accepted correlation constant is the Modified Thompson 2, "Goodman
Goodman or Goodmans may refer to:
Businesses and organizations
* Goodman Games, American publisher.
* Goodman Global, an American HVAC manufacturer.
* Goodman Group, an Australian property company.
* Goodmans Industries, a British electronic co ...
–Martinez– Thompson", or GMT correlation of 584,283 days. Using the GMT correlation, the current creation started on September 6, −3113 ( Julian astronomical) – August 11, 3114 BCE in the Proleptic Gregorian calendar
The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to the dates preceding its official introduction in 1582. In nations that adopted the Gregorian calendar after its official and first introduction, dates occ ...
. The study of correlating the Maya and western calendar is referred to as the correlation question. The GMT correlation is also called the 11.16 correlation.
In ''Breaking the Maya Code'', Michael D. Coe
Michael Douglas Coe (May 14, 1929 – September 25, 2019) was an American archaeologist, anthropologist, epigrapher, and author. He is known for his research on pre-Columbian Mesoamerica, particularly the Maya, and was among the foremost Mayan ...
writes: "In spite of oceans of ink that have been spilled on the subject, there now is not the slightest chance that these three scholars (conflated to G-M-T when talking about the correlation) were not right ...". The evidence for the GMT correlation is historical, astronomical and archaeological:
Historical: Calendar Round dates with a corresponding Julian date
The Julian day is the continuous count of days since the beginning of the Julian period, and is used primarily by astronomers, and in software for easily calculating elapsed days between two events (e.g. food production date and sell by date).
...
are recorded in Diego de Landa
Diego de Landa Calderón, O.F.M. (12 November 1524 – 29 April 1579) was a Spanish Franciscan bishop of the Roman Catholic Archdiocese of Yucatán. Many historians criticize his campaign against idolatry. In particular, he burned almost a ...
's ''Relación de las cosas de Yucatán
''Relación de las cosas de Yucatán'' was written by Diego de Landa around 1566, shortly after his return from Yucatán to Spain. In it, de Landa catalogues Mayan words and phrases as well as a small number of Maya hieroglyphs. The hieroglyphs ...
'' (written circa 1566), the Chronicle of Oxcutzkab and the books of Chilam Balam
The Books of Chilam Balam () are handwritten, chiefly 17th and 18th-centuries Maya miscellanies, named after the small Yucatec towns where they were originally kept, and preserving important traditional knowledge in which indigenous Maya and early ...
. De Landa records a date that is a Tun ending in the Short Count. Oxkutzcab contains 12 Tun endings. Bricker and Bricker find that only the GMT correlation in consistent with these dates. The Book of Chilam Balam of Chumayel contains the only colonial reference to classic long-count dates. The Julian calendar date of 11.16.0.0.0 (November 2, 1539) confirms the GMT correlation.
The Annals of the Cakchiquels
The ''Annals of the Cakchiquels'' (in es, Anales de los Cakchiqueles, also known by the alternative Spanish titles, ''Anales de los Xahil'', ''Memorial de Tecpán-Atitlán'' or ''Memorial de Sololá'') is a manuscript written in Kaqchikel by Fra ...
contains numerous Tzolkʼin dates correlated with European dates. These confirm the GMT correlation. Weeks, Sachse and Prager transcribed three divinatory calendars from highland Guatemala. They found that the 1772 calendar confirms the GMT correlation. The fall of the capital city of the Aztec Empire, Tenochtitlan
, ; es, Tenochtitlan also known as Mexico-Tenochtitlan, ; es, México-Tenochtitlan was a large Mexican in what is now the historic center of Mexico City. The exact date of the founding of the city is unclear. The date 13 March 1325 was ...
, occurred on August 13, 1521. A number of different chroniclers wrote that this was a Tzolkʼin
Tzolkʼin (, formerly and commonly tzolkin) is the name bestowed by Mayanists on the 260-day Mesoamerican calendar originated by the Maya civilization of pre-Columbian Mesoamerica.
The tzolkʼin, the basic cycle of the Maya calendar, is a preemi ...
( Tonalpohualli) of 1 Snake.
Post-conquest scholars such as Sahagún
Sahagún () is a town and municipality of Spain, part of the autonomous community of Castile and León and the province of León. It is the main populated place in the Leonese part of the Tierra de Campos natural region.
Sahagún contains some ...
and Durán recorded Tonalpohualli dates with a calendar date. Many indigenous communities in the Mexican states of Veracruz, Oaxaca and Chiapas and in Guatemala, principally those speaking the Mayan languages Ixil, Mam, Pokomchí and Quiché, keep the Tzolkʼin and in many cases the Haabʼ. These are all consistent with the GMT correlation. Munro Edmonsen studied 60 Mesoamerican calendars, 20 of which have known correlations to European calendars, and found remarkable consistency among them and that only the GMT correlation fits the historical, ethnographic and astronomical evidence.
Astronomical: Any correct correlation must match the astronomical content of classic inscriptions. The GMT correlation does an excellent job of matching lunar data in the supplementary series
The term supplementary can refer to:
* Supplementary angles
* Supplementary Benefit, a former benefit payable in the United Kingdom
* Supplementary question
A question time in a parliament occurs when members of the parliament ask questions of ...
. For example: An inscription at the Temple of the Sun at Palenque
Palenque (; Yucatec Maya: ), also anciently known in the Itza Language as Lakamhaʼ ("Big Water or Big Waters"), was a Maya city state in southern Mexico that perished in the 8th century. The Palenque ruins date from ca. 226 BC to ca. 799 AD. ...
records that on Long Count 9.16.4.10.8 there were 26 days completed in a 30 day lunation. This Long Count is also the entry date for the eclipse table of the Dresden Codex
The ''Dresden Codex'' is a Maya book, which was believed to be the oldest surviving book written in the Americas, dating to the 11th or 12th century. However, in September 2018 it was proven that the Maya Codex of Mexico, previously known as th ...
.
Using the third method (the Palenque system) the new moon would have been the first evening when one could look to the west after sunset and see the thin crescent moon. Given our modern ability to know exactly where to look, when the crescent Moon is favorably located, from an excellent site, on rare occasions, using binoculars or a telescope, observers can see and photograph the crescent moon less than one day after conjunction. Generally, most observers cannot see the new Moon with the naked eye until the first evening when the lunar phase day is at least 1.5. If one assumes that the new moon is the first day when the lunar phase day is at least 1.5 at six in the evening in time zone UTC−6 (the time zone of the Maya area) the GMT correlation will match many lunar inscriptions exactly. In this example the lunar phase day was 27.7 (26 days counting from zero) at 6 pm after a conjunction at 1:25 am and a new Moon when the lunar phase day was 1.7 at 6 pm on (Julian calendar). This works well for many but not all lunar inscriptions.
Modern astronomers refer to the conjunction of the Sun and Moon (the time when the Sun and Moon have the same ecliptic longitude) as the new moon. Mesoamerican astronomy was ''observational'' not theoretical. The people of Mesoamerica didn't know about the Copernican nature of the solar system — they had no theoretical understanding of the orbital nature of the heavenly bodies. Some authors analyze the lunar inscriptions based on this modern understanding of the motions of the Moon but there is no evidence that the Mesoamericans did.
The first method seems to have been used for other inscriptions such as Quirgua stela E (9.17.0.0.0). Using the third method it should have a moon age of 26 days when in fact it records a new moon. Using the GMT correlation at six AM in time zone −6, this would be 2.25 days before conjunction, so it could record the first day when one could not see the waning moon.
Fuls Analysed these inscriptions and found strong evidence for the Palenque system and the GMT correlation however he cautioned: "Analysis of the Lunar Series shows that at least two different methods and formulas were used to calculate the moon's age and position in the six-month cycle ..." which gives eclipse seasons when the Moon is near its ascending or descending node and an eclipse is likely to occur. Dates converted using the GMT correlation agree closely with the Dresden Codex eclipse tables. The Dresden Codex
The ''Dresden Codex'' is a Maya book, which was believed to be the oldest surviving book written in the Americas, dating to the 11th or 12th century. However, in September 2018 it was proven that the Maya Codex of Mexico, previously known as th ...
contains a Venus
Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never f ...
table which records the heliacal risings of Venus. Using the GMT correlation these agree closely with modern astronomical calculations.
Archaeological: Various items that can be associated with specific Long Count dates have been isotope dated. In 1959 the University of Pennsylvania
The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...
carbon dated
Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) is a method for determining the age of an object containing organic material by using the properties of radiocarbon, a radioactive isotope of carbon.
The method was dev ...
samples from ten wood lintels from Tikal
Tikal () (''Tik’al'' in modern Mayan orthography) is the ruin of an ancient city, which was likely to have been called Yax Mutal, found in a rainforest in Guatemala. It is one of the largest archeological sites and urban centers of the pre-C ...
. These were carved with a date equivalent to 741 AD, using the GMT correlation. The average carbon date was 746±34 years. Recently one of these, Lintel 3 from Temple I, was analyzed again using more accurate methods and found to agree closely with the GMT correlation.
If a proposed correlation only has to agree with one of these lines of evidence there could be numerous other possibilities. Astronomers have proposed many correlations, for example: Lounsbury, Fuls, ''et al.'', Böhm and Böhm and Stock.
Today, ( UTC), in the Long Count is (using GMT correlation).
2012 and the Long Count
According to the ''Popol Vuh
''Popol Vuh'' (also ''Popol Wuj'' or ''Popul Vuh'' or ''Pop Vuj'') is a text recounting the mythology and history of the Kʼicheʼ people, one of the Maya peoples, who inhabit Guatemala and the Mexican states of Chiapas, Campeche, Yucatan and ...
'', a book compiling details of creation accounts known to the Kʼicheʼ Maya of the Colonial-era highlands, humankind lives in the fourth world.[Schele & Freidel (1990), pp. 429–30] 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 end of a 13th bʼakʼtun.
The previous creation ended on a Long Count of 12.19.19.17.19. Another 12.19.19.17.19 occurred on December 20, 2012 (Gregorian Calendar), followed by the start of the 14th bʼakʼtun, 13.0.0.0.0, on December 21, 2012. There are only two references to the current creation's 13th bʼakʼtun in the fragmentary Mayan corpus: Tortuguero Monument 6, part of a ruler's inscription and the recently discovered La Corona Hieroglyphic Stairway 2, Block V.
Maya inscriptions occasionally reference future predicted events or commemorations that would occur on dates that lie beyond 2012 (that is, beyond the completion of the 13th ''bʼakʼtun'' of the current era). Most of these are in the form of "distance dates" where some Long Count date is given, together with a Distance Number that is to be added to the Long Count date to arrive at this future date.
For example, on the west panel at the Temple of Inscriptions
The Temple of the Inscriptions (Classic Maya: Bʼolon Yej Teʼ Naah () "House of the Nine Sharpened Spears") is the largest Mesoamerican stepped pyramid structure at the pre-Columbian Maya civilization site of Palenque, located in the modern-day ...
in Palenque
Palenque (; Yucatec Maya: ), also anciently known in the Itza Language as Lakamhaʼ ("Big Water or Big Waters"), was a Maya city state in southern Mexico that perished in the 8th century. The Palenque ruins date from ca. 226 BC to ca. 799 AD. ...
, a section of the text projects into the future to the 80th Calendar Round (CR) 'anniversary' of the famous Palenque ruler Kʼinich Janaabʼ Pakal
Kʼinich Janaab Pakal I (), also known as Pacal or Pacal the Great (March 603 – August 683), was ''ajaw'' of the Maya city-state of Palenque in the Late Classic period of pre-Columbian Mesoamerican chronology. He acceded to the throne in July 6 ...
's accession to the throne (Pakal's accession occurred on a Calendar Round date 5 Lamat 1 Mol, at Long Count 9.9.2.4.8 equivalent to 27 July 615 CE in the proleptic Gregorian calendar
The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to the dates preceding its official introduction in 1582. In nations that adopted the Gregorian calendar after its official and first introduction, dates occ ...
).[Gregorian, using GMT correlation JDN=584283.] It does this by commencing with Pakal's birthdate 9.8.9.13.0 8 Ajaw 13 Pop (24 March ) and adding to it the Distance Number 10.11.10.5.8.[Schele (1992, pp. 93–95)]
This calculation arrives at the 80th Calendar Round since his accession, a day that also has a CR date of , but which lies over 4,000 years in the future from Pakal's time—the day 21 October in the year 4772. The inscription notes that this day would fall eight days after the completion of the 1st ''piktun'' (since the creation or zero date of the Long Count system), where the ''piktun'' is the next-highest order above the ''bʼakʼtun'' in the Long Count. If the completion date of that ''piktun''—13 October 4772—were to be written out in Long Count notation, it could be represented as 1.0.0.0.0.0. The 80th CR anniversary date, eight days later, would be 1.0.0.0.0.8 5 Lamat 1 Mol.
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 have no record or knowledge that he Mayawould think the world would come to an end" in 2012. ''USA Today'' writes 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 in Crystal River, Florida
Crystal River is a city in Citrus County, Florida, United States. The population was 3,108 in the 2010 census. According to the U.S. Census estimates of 2018, the city had a population of 3,162. The city was incorporated in 1903 and is the self p ...
. To render December 21, 2012, as a doomsday event or moment of cosmic shifting, she says, is 'a complete fabrication and a chance for a lot of people to cash in.[ "There will be another cycle," says E. Wyllys Andrews V, director of the ]Tulane University
Tulane University, officially the Tulane University of Louisiana, is a private research university in New Orleans, Louisiana. Founded as the Medical College of Louisiana in 1834 by seven young medical doctors, it turned into a comprehensive pub ...
Middle American Research Institute (MARI). "We know the Maya thought there was one before this, and that implies they were comfortable with the idea of another one after this."
Converting between the Long Count and western calendars
Calculating a Western calendar date from a Long Count
It is important to know the difference between the Julian and Gregorian calendars when calculating a Western calendar date from a Long Count date.
Using as an example the Long Count date of 9.10.11.17.0 (Long Count date mentioned on the Palenque Palace Tablet), first calculate the number of days that have passed since the zero date (August 11, 3114 BCE; GMT correlation, in the Proleptic Gregorian calendar
The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to the dates preceding its official introduction in 1582. In nations that adopted the Gregorian calendar after its official and first introduction, dates occ ...
, September 6, −3113 Julian astronomical).
Then add the GMT correlation to the total number of days.
: 1,372,300 + 584,283 = 1,956,583
This number is a Julian day.
To convert a Julian day to a Proleptic Gregorian calendar
The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to the dates preceding its official introduction in 1582. In nations that adopted the Gregorian calendar after its official and first introduction, dates occ ...
date:
From this number, subtract the nearest smaller Julian Day Number (in the table below), in this case 1,940,206, which corresponds to the year 600 CE.
: 1,956,583 – 1,940,206 = 16,377
Next, divide this number by 365 days (vague year).
: 16,377 / 365 = 44.86849
The remainder is 44.86849 years, which is 44 years and 317 days. The full year date is 644 CE. Now calculate the month and day number, taking into account leap days over the 44 years. In the Gregorian Calendar, every fourth year is a leap year with the exception of centuries not evenly divisible by 400 (e.g. 100, 200, 300). When the year is divisible by 400 (e.g. 400, 800, etc.), do not add an extra day. The calculated year is 644 CE. The number of leap days, keeping in mind that the year 600 is not a leap year, is 10. Subtracting that from 317 remainder days is 307; in other words, the 307th day of the year 644 CE, which is November 3.
To summarize: the Long Count date 9.10.11.17.0 corresponds to November 3, 644 CE, in the Proleptic Gregorian calendar
The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to the dates preceding its official introduction in 1582. In nations that adopted the Gregorian calendar after its official and first introduction, dates occ ...
.
To convert a Julian day to a Julian/Gregorian astronomical date (Proleptic Julian calendar
The proleptic Julian calendar is produced by extending the Julian calendar backwards to dates preceding AD 8 when the quadrennial leap year stabilized. The leap years that were actually observed between the implementation of the Julian calendar in ...
before 46 BCE):
Use an astronomical algorithm such as the Method of Meeus to convert the Julian day to a Julian/Gregorian date with astronomical dating of negative years:
In this example:
input: Julian day ''J''
''J'' = ''J'' + 0.5 ''// 1,956,583.5''
''Z'' = integer part of ''J'' ''// 1,956,583''
''F'' = fraction part of ''J'' ''// 0.5''
if ''Z'' < 2,299,161 then ''// Julian?''
''A'' = ''Z''
else
''alpha'' = floor((''Z'' - 1,867,216.25) / 36,524.25) ''// 15''
''A'' = ''Z'' + 1 + ''alpha'' - floor(''alpha'' / 4.0) ''// 2,436,129''
''// The floor operation rounds a decimal number down to the next lowest integer.''
''// For example, floor(1.5) = 1 and floor(−1.5) = -2''
end if
''B'' = ''A'' + 1524 ''// 1,958,107''
''C'' = floor((''B'' - 122.1) / 365.25) ''// 5,360''
''D'' = floor(365.25 × ''C'') ''// 1,957,740''
''E'' = floor((''B'' - ''D'') / 30.6001) ''// 11''
''day'' = ''B'' - ''D'' - floor(30.6001 × ''E'') + ''F'' ''// 31.5''
if ''E'' < 14 then
''month'' = ''E'' - 1 ''// 10''
else
''month'' = ''E'' - 13
end if
if ''month'' > 2 then
''year'' = ''C'' - 4716 ''// 644''
else
''year'' = ''C'' - 4715
end if
return (''year'', ''month'', ''day'')
In this example the Julian date is noon October 31, 644. The Method of Meeus is not valid for negative year numbers (astronomical), so another method such as the method of Peter Baum should be used.
Calculating a full Long Count date
A full Long Count date not only includes the five digits of the Long Count, but the 2 character Tzolkʼin and the two-character Haabʼ dates as well. The five digit Long Count can therefore be confirmed with the other four characters (the "calendar round date").
Taking as an example a Calendar Round date of 9.12.2.0.16 (Long Count) 5 Kibʼ (Tzolkʼin) 14 Yaxkʼin (Haabʼ). 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 Kumkʼu and show how the date 5 Kibʼ 14 Yaxkʼin is derived.
Calculating the Tzolkʼin date portion
The Tzolkʼin date is counted forward from 4 Ajaw. To calculate the numerical portion of the Tzolkʼin date, add 4 to the total number of days given by the date and then divide total number of days by 13.
: (4 + 1,383,136) / 13 = 106,395 (and 5/13)
This means that 106,395 whole 13 day cycles have been completed and the numerical portion of the Tzolkʼin date is 5.
To calculate the day, divide the total number of days in the long count by 20 since there are twenty day names.
:1,383,136 / 20 = 69,156 (and 16/20)
This means 16 day names must be counted from Ajaw. This gives Kibʼ. Therefore, the Tzolkʼin date is 5 Kibʼ.
Calculating the Haabʼ date portion
The Haabʼ date 8 Kumkʼu is the ninth day of the eighteenth month. There are 17 days to the start of the next year.
Subtract 17 days from the total, to find how many complete Haabʼ years are contained.
:1,383,136 − 17 = 1,383,119
by 365
:1,383,119 / 365 = 3,789 and (134/365)
Therefore, 3,789 complete Haabʼ have passed and the remainder 134 is the 135th day in the new Haabʼ, since a remainder of 0 would indicate the first day.
Find which month the day is in. Dividing the remainder 134 by 20, is six complete months and a remainder of 14, indicating the 15th day. So, the date in the Haabʼ lies in the seventh month, which is Yaxkʼin. The fifteenth day of Yaxkʼin is 14, thus the Haabʼ date is 14 Yaxkʼin.
So the date of the long count date 9.12.2.0.16 5 Kibʼ 14 Yaxkʼin is confirmed.
Piktuns and higher orders
There are also four rarely used higher-order periods above the bʼakʼtun: ''piktun'', ''kalabtun'', ''kʼinchiltun'' and ''alautun''. All of these words are inventions of Mayanists. Each one consists of 20 of the lesser units.
Many inscriptions give the date of the current creation as a large number of 13s preceding 13.0.0.0.0 4 Ahau 8 Kumkʼu. For example, a Late Classic monument from Coba
Coba ( es, Cobá) is an ancient Maya city on the Yucatán Peninsula, located in the Mexican state of Quintana Roo. The site is the nexus of the largest network of stone causeways of the ancient Maya world, and it contains many engraved and sculp ...
, Stela 1. The date of creation is expressed as 13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.0.0.0.0, where the units are 13s in the nineteen places larger than the bʼakʼtun. Some authors think that the 13s were symbolic of a completion and don't represent an actual number.
Most inscriptions that use these are in the form of distance dates and Long Reckonings – they give a base date, a distance number that is added or subtracted and the resulting Long Count.
The first example below is from Schele (1987). The second is from Stuart (2005 pp. 60, 77)
Palenque Temple of the Cross, tablet, Schele (1987 p.)
12.19.13.4.0 8 Ajaw 18 Tzek in the prior era
6.14.0 Distance number linking to the "era date"
13.0.0.0.0 4 Ajaw 8 Kumkʼu
Palenque Temple XIX, South Panel G2-H6 Stuart (2005 pp. 60, 77)
12.10.1.13.2 9 Ikʼ 5 Mol (seating of GI in the prior era)
2.8.3.8.0
1.18.5.3.2 9 Ikʼ 15 Keh (rebirth of GI, this date also in Temple of the Cross)
The tablet of the inscriptions contains this inscription:
9.8.9.13.0 8 Ajaw 13 Pop
10.11.10.5.8
1.0.0.0.0.8
The Dresden codex
The ''Dresden Codex'' is a Maya book, which was believed to be the oldest surviving book written in the Americas, dating to the 11th or 12th century. However, in September 2018 it was proven that the Maya Codex of Mexico, previously known as th ...
contains another method for writing distance numbers. These are Ring Numbers. Specific dates within the
Dresden codex are often given by calculations involving Ring Numbers. Förstemann identified these, but Wilson (1924) later clarified the way in which they operate. Ring Numbers are intervals of days between the Era Base date 4 Ajaw 8 Kumkʼu and an earlier Ring Base date, where the place-holder for the numeral of days in the interval is circled by an image of a tied red band. Added to this earlier Ring Base date is another count of days forward, which Thompson refers to as a Long Round, leading to a final date within the Long Count that is given as an entry date to be used within a specific table in the codex.
Ring number (12) 12.12.17.3.1 13 Imix 9 Wo (7.2.14.19 before (13) 13.0.0.0.0)
distance number (0) 10.13.13.3.2
Long Count 10.6.10.6.3 13 Akʼbal 1 Kankʼin
Ring number (portion of the DN preceding era date) 7.2.14.19
Add Ring number to the ring number date to reach 13.0.0.0.0
Thompson contains a table of typical long reckonings after Satterwaite.[ table from Thompson]
The "Serpent Numbers" in the Dresden codex pp. 61–69 is a table of dates using a base date of 1.18.1.8.0.16 in the prior era (5,482,096 days).
See also
* Aztec calendar
* Maya astronomy
Maya astronomy is the study of the Moon, planets, Milky Way, Sun, and astronomical phenomena by the Precolumbian Maya Civilization of Mesoamerica.
The Classic Maya in particular developed some of the most accurate pre-telescope astronomy in the ...
* Maya calendar
The Maya calendar is a system of calendars used in pre-Columbian Mesoamerica and in many modern communities in the Guatemalan highlands, Veracruz, Oaxaca and Chiapas, Mexico.
The essentials of the Maya calendar are based upon a system which had ...
* Maya codices
Maya codices (singular ''codex'') are folding books written by the pre-Columbian Maya civilization in Maya hieroglyphic script on Mesoamerican bark paper. The folding books are the products of professional scribes working under the patronage of ...
* Mesoamerican calendars
Mesoamerican calendars are the calendrical systems devised and used by the pre-Columbian cultures of Mesoamerica. Besides keeping time, Mesoamerican calendars were also used in religious observances and social rituals, such as for divination.
T ...
Notes
References
Bibliography
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External links
Coba Stela 1 (Schele #4087)
partial illustration from the Linda Schele Drawings Collection of the monument from Coba with an expanded Long Count date
(Uses the proleptic Gregorian calendar.)
* 1897 text by Cyrus Thomas.
{{DEFAULTSORT:Mesoamerican Long Count Calendar
Long Count
Long count or slow count is a term used in boxing. When a boxer is knocked down in a fight, the referee will count over them and the boxer must rise to their feet, unaided, by the count of ten or else deemed to have been knocked out. A long count ...
Maya Classic Period
Specific calendars
Chronology
Obsolete calendars
2012 phenomenon
it:Calendario maya#Il Lungo computo