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The Maya is a Mesoamerican civilization, preceded by Omec culture and succeeded by Aztec. Mayans rose to prominence after the decline of Omnec. Initially established during the Pre-Classic period (c. 2000 BC to 250 AD), according to the Mesoamerican chronology, many Maya cities reached their highest state of development during the Classic period (c. 250 AD to 900 AD), and continued throughout the Post-Classic period until the arrival of the Spanish. The Mayans were known for their written language,  art, architecture, and mathematical and astronomical systems. Though these arts do not originate with the Maya, but their civilisation developed them.  The Maya peoples never disappeared, neither at the time of the Classic period decline nor with the arrival of the Spanish conquistadores and the subsequent Spanish colonization of the Americas. One of the most amazing cultures of the New World inhabited a region encompassing today's Guatemala, Belize, Honduras and El Salvador, and parts of southern Mexico (the states of Yucatan, Campeche, Quintana Roo, Tabasco and Chiapas). Today this area is occupied by the descendants of the ancient Maya, the vast majority of whom have to some extent preserved their cultural heritage and still speak the Mayan language.

Mayan contributions were many. They developed an advanced writing system. The Maya were the first people of the New World to keep historical records. The Maya wrote a mixed script, with ideographic and phonetic elements.

Most of their writing survived on stelae, stone monuments very common in the Maya cities, they recount mostly civil events and record their calendric and astronomical knowledge.

By the time of the Spanish arrival around A.D. 1520, the Mayans were a starkly diminished civilization. Their great cities were abandoned and the remnants of their population widely scattered.

The Maya Calendar

The ancient Mayas invented a  calendar of remarkable accuracy and complexity. They built a pyramid to be used as a calendar: four stairways, each with 91 steps and a platform at the top, making a total of 365, equivalent to the number of days in a calendar year.  The Maya calendar uses three different dating systems in parallel, the Long Count, the Tzolkin, and the Haab. Of these, only the Haab has a direct relationship to the length of the year. The system dates as far back as the 6th century BC. Certain aspects of the calendar system are shared both by earlier civilizations, such as the Olmec and Zapotec as well as later civilizations, such as the Aztec and Mixtec. The reason that the Mayan calendar became so well known because it was well-documented and therefore, the ancient calendar system best understood today.

The Tzolkin Calendar

The first calendar the Mayans used was the Tzolkin calendar. This calendar consisted of 260 days. The Tzolkin calendar was made up of the numbers 20 and 13. There is a numbered week that consists of 13 days. These days are simply numbered 1 to 13. Then, there is a named week that consists of 20 days. These days are Imix, Ik, Akbal, Kan, Chikchan, Kimi, Manik, Lamat, Muluk, Ok, Chuwen, Eb, Ben, Ix, Men, Kib, Kaban, Etznab, Kawak and Ajaw. Because there are only 13 number, by the time Ben is reached, Ix starts over at one and the numbers continue. With the 20 day names and 13 numbered days interlocking and rotating until number one matches up with Imix again, there are 260 days.

The Haab Calendar

The Haab was the solar calendar created by the Mayans. The Haab consisted of 18 “months” of 20 days each, followed by 5 extra days, known as Uayeb. The months are Pop, Wo, Sip, Sotz, Sek, Xul, Yaxkin, Mol, Chen, Yax, Sak, Keh, Mak, Kankin, Muwan, Pax, Kayab, Kumku, and Wayeb. The last five day month ‘Wayeb’ was considered extremely unlucky.

Calendar Round

 

Neither the Tzolk'in nor the Haab' system numbered the years. The combination of a Tzolk'in date and a Haab' date would allow to last for 52 years. 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.

The Long Count Calendar

Since Calendar Round dates can only distinguish in 18,980 days, equivalent to around 52 solar years, the cycle repeats roughly once each lifetime, and thus, a more refined method of dating was needed if history was to be recorded accurately. To measure dates, therefore, over periods longer than 52 years, Mesoamericans devised the Long Count calendar.

The Maya Long Count is a positionally represented linear count of days and in short form can represent a day as 13.0.0.0.0 This is very similiar to the Gregorian Calendar as it is also a positionally represented linear count of days in which a day can be represented as 12.21.2012. The Long Count works on a modified vigesimal system (base-20). Each position increments to the next position (the leftmost position represents the higher numbers as opposed to the Gregorian Calendar) once the position reaches 20 except for the second position which rotates up on 18.

The positional markers of the Gregorian calendar are called days, months and years and we can multiply each by its corresponding values (with special considerations) to get the number of days that have past since the inception date of the calendar. The same holds true for the Long Count. The positional markers (following the highest marker left notation) of the Long Count date 13.0.0.0.0 are called:

13

0

0

0

0

Baktun

Katun

Tun

Uinal

Kin

 

 

These are the Mayan words for periods of time:

 

Day                              Kin (keen)
Month of 20 days        Uinal (wee nal)
Year of 360 days         Tun (toon)
20 Tuns                       K'atun (k' ah toon)
20 K'atuns                   Baktun (bock toon)

 

A particular tzolkin/haab date recurs every 18,980 days, whereas a long count date (assuming that the long count starts over at 0.0.0.0.0 on reaching 13.0.0.0.0) recurs every 1,872,000 days (once in 5,125.37 years). The combination of a long count date and a tzolkin/haab date occurs only once every 136,656,000 days (approximately 374,152 years or 73 Maya eras).

The Mayan Calendar conversion applet below gives the following dates: 
Start of the Mayan calendar (long count cycle):  0.0.0.0.0 [ 4 Ahau 8 Cumku ] is Aug 10, 3113 BC 
End of the Mayan calendar (long count cycle): 13.0.0.0.0 [ 4 Ahau 3 Kankin ] is Dec 21, 2012 AD

 

Mayan Math

 

The Mayan math system is a vigesimal (base-20) system requiring only three symbols representing the numbers zero, one, and five. All other numbers are derived from these three symbols, distinguished by positional notation. Positionally Mayan numbers can be written from either top to bottom or left to right, with the highest value number being in the top position or on the leftmost position, respectively.

An interesting point to note is the Maya were using the concept of zero in their mathematical system over 1,000 years prior to the European adoption of zero around the 11th century.

 

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