Wednesday, May 21, 2008


Mayan Calendar

History of Astronomy — The Mayans


The Mayans. Mayan Calendar The Mayans developed astronomy to the point where they could predict eclipses hundreds of years in the future. Their legends say they obtained their astronomical wisdom from the Olmecs. Little is known about the Olmecs, though traces of their culture have been found dating to about 2000 B.C.E. A Mayan stone calendar is shown at left.

The Mayans and Aztecs have a legend of learning great things from a bearded "white man" who came to them sometime after 500 B.C.E. The Aztecs named him Quetzalcoatl, which means "Plumed Serpent." There is some speculation that Quetzalcoatl could have come from Egypt, and that the "Plumed Serpent" represented the cobra with its hood expanded. Mayan legend says that the Yucatan was originally inhabited by "people of the serpent," and their leader's name was "Serpent of the East." Mayans claimed that they got their writing from the Tula, and that their leaders sailed over the sea to the East to learn their wisdom.

Mayans counted using a base 20 system. Their numbers used three symbols: a sea shell for zero, a dot for one, and a bar for five. They also had a small curved symbol that served as a filler around a small number of dots, for aesthetics.

The Mayan Long Calendar. The Mayan timeline began on 13 August 3114 B.C.E. (very near the start of the Egyptian Old Kingdom). This is the starting point of the Mayan Long Calendar. The time divisions in the long calendar were:

  • 1 kin = 1 day
  • 20 kins = unial (20 days)
  • 18 unials = tun (360 days)
  • 20 tuns = katun (7200 days)
  • 20 katuns = baktun (144,000 days, about 394.25 years)
  • 13 baktuns = a Great Cycle (1,872,000 days, about 5,125.25 years)
A Great Cycle, or Age, is also known as a "Sun." Their legends state that at the end of each Sun there is a catastrophe, followed by a renewal. They count time in a cycle of five Suns, which therefore spans 9,360,000 days, or about 25,627 years. Some cite this Five Sun cycle as evidence of Mayan knowledge of precession of the equinoxes.

Mayans believed that we are currently in the Fifth Great Cycle, which will end, and a new First Sun begin, on 23 December 2012. Popular literature abounds with speculation on this event, and its near-coinciding with ecliptic crossing to the north of the Solar System's orbit around the Galatic Center.

The Mayan Vague Year Calendar (Haab). Mayans knew that the length of the Solar Year was about 365.25 days long but, like the Egyptians, they used a calendar of 365 days and did not use leap years. Because this calendar does not follow the true Solar Year, is is referred to as the Vague Year calendar, or Haab.

The Vague Year Calendar is divided into 20 months of 18 days each (360 days total), followed by a five-day period. The days of the month are numbered from 0 to 19. Each month is named after a Mayan god. These are:

  1. Pop
  2. Wo
  3. Sip
  4. Sots'
  5. Sek
  1. Xul
  2. Yaxk'in
  3. Mol
  4. Ch'en
  5. Yax
  1. Sak
  2. Keh
  3. Mak
  4. K'ank'in
  5. Muwan
  1. Pax
  2. K'ayab
  3. Kumk'u
  4. Wayeb

The Mayan Ritual Calendar (Tzolkin). The third Mayan calendar was the Ritual Calendar, or Tzolkin, which had 13 months of 20 days each (260 days total). This 260-day cycle was related to the period of Venus. They Mayans knew that he Evening Star and the Morning Star were the same object, Venus, and had accurate tables of the planet's motion. The 20 days were named as follows:

  1. Imix
  2. Ik
  3. Akbal
  4. Kan
  5. Chicchan
  1. Cimi
  2. Manik
  3. Lamat
  4. Muluc
  5. Oc
  1. Chuen
  2. Eb
  3. Ben
  4. Ix
  5. Men
  1. Cib
  2. Caban
  3. Etz'nab
  4. Cauac
  5. Ahau

The numbers 1 through 13 increased along with the days. So for example the first day in the cycle was 1 Imix, the second was 2 Ik, and so on. After 260 days, every combination of name and number (1-13) would repeat.

The Mayan "Calendar Round." Every 52 years, the Vague Calendar and the Ritual Almanac coincide at the same beginning day. The Mayans called this a Calendar Round. They considered this an auspicious time, where the old would end and the new would begin. They rebuilt houses, refaced templed, and performed other such acts on this day. This custom has allowed us to accurately estimate the ages of many of their temples.

Mayans followed a longer cycle of 22 Calendar Rounds, consisting of 13 Heavens (the first 13 Calendar Rounds) followed by 9 Hells (the last 9 Calendar Rounds). The last cycle completed in 1987, placing us now in the first Heaven.

Lost Mayan Culture. Today, much of the ancient Mayan culture is lost forever. Their beliefs conflicted in many ways with the Roman Catholic Church, and the first Archbishop of Mexico claimed to have burned tens of thousands of Mayan books in the 1500s. Apart from remaining temple inscriptions, only four books remain today as the remnant of this ancient culture: the Dresden Codex, the Grolier Codex, the Madrid Codex, and the Paris Codex.

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The Mayan Calendar

What is the Long Count?

    The Long Count is really a mixed base-20/base-18 representation of a number, representing the number of days since the start of the Mayan era. It is thus akin to the Julian Day Number.

    The basic unit is the kin (day), which is the last component of the Long Count. Going from right to left the remaining components are:

    uinal (1 uinal = 20 kin = 20 days)
    tun (1 tun = 18 uinal = 360 days = approx. 1 year)
    katun (1 katun = 20 tun = 7,200 days = approx. 20 years)
    baktun (1 baktun = 20 katun = 144,000 days = approx. 394 years)

    The kin, tun, and katun are numbered from 0 to 19.
    The uinal are numbered from 0 to 17.
    The baktun are numbered from 1 to 13.

    Although they are not part of the Long Count, the Mayas had names for larger time spans. The following names are sometimes quoted, although they are not ancient Maya terms: 1 pictun = 20 baktun = 2,880,000 days = approx. 7885 years
    1 calabtun = 20 pictun = 57,600,000 days = approx. 158,000 years
    1 kinchiltun = 20 calabtun = 1,152,000,000 days = approx. 3 million years
    1 alautun = 20 kinchiltun = 23,040,000,000 days = approx. 63 million years

    The alautun is probably the longest named period in any calendar.

When did the Long Count Start?

    Logically, the first date in the Long Count should be, but as the baktun (the first component) are numbered from 1 to 13 rather than 0 to 12, this first date is actually written

    The authorities disagree on what corresponds to in our calendar. I have come across three possible equivalences: = 8 Sep 3114 BC (Julian) = 13 Aug 3114 BC (Gregorian) = 6 Sep 3114 BC (Julian) = 11 Aug 3114 BC (Gregorian) = 11 Nov 3374 BC (Julian) = 15 Oct 3374 BC (Gregorian)

    Assuming one of the first two equivalences, the Long Count will again reach on 21 or 23 December AD 2012 - a not too distant future.

    The date may have been the Mayas' idea of the date of the creation of the world.

What is the Tzolkin?

    The Tzolkin date is a combination of two "week" lengths.

    While our calendar uses a single week of seven days, the Mayan calendar used two different lengths of week:

    • a numbered week of 13 days, in which the days were numbered from 1 to 13
    • a named week of 20 days, in which the names of the days were:

    0. Ahau 1. Imix 2. Ik 3. Akbal 4. Kan
    5. Chicchan 6. Cimi 7. Manik 8. Lamat 9. Muluc
    10. Oc 11. Chuen 12. Eb 13. Ben 14. Ix
    15. Men 16. Cib 17. Caban 18. Etznab 19. Caunac

    The diagram at right shows the day symbols, in the same order as the table above.

    As the named week is 20 days and the smallest Long Count digit is 20 days, there is synchrony between the two; if, for example, the last digit of today's Long Count is 0, today must be Ahau; if it is 6, it must be Cimi. Since the numbered and the named week were both "weeks," each of their name/number change daily; therefore, the day after 3 Cimi is not 4 Cimi, but 4 Manik, and the day after that, 5 Lamat. The next time Cimi rolls around, 20 days later, it will be 10 Cimi instead of 3 Cimi. The next 3 Cimi will not occur until 260 (or 13 x 20) days have passed. This 260-day cycle also had good-luck or bad-luck associations connected with each day, and for this reason, it became known as the "divinatory year."

    The "years" of the Tzolkin calendar are not counted.

When did the Tzolkin Start?

    Long Count corresponds to 4 Ahau. The authorities agree on this.

What is the Haab?

    The Haab was the civil calendar of the Mayas. It consisted of 18 "months" of 20 days each, followed by 5 extra days, known as Uayeb. This gives a year length of 365 days.

    The names of the month were:

    1. Pop 7. Yaxkin 13. Mac
    2. Uo 8. Mol 14. Kankin
    3. Zip 9. Chen 15. Muan
    4. Zotz 10. Yax 16. Pax
    5. Tzec 11. Zac 17. Kayab
    6. Xul 12. Ceh 18. Cumku

    In contrast to the Tzolkin dates, the Haab month names changed every 20 days instead of daily; so the day after 4 Zotz would be 5 Zotz, followed by 6 Zotz ... up to 19 Zotz, which is followed by 0 Tzec.

    The days of the month were numbered from 0 to 19. This use of a 0th day of the month in a civil calendar is unique to the Maya system; it is believed that the Mayas discovered the number zero, and the uses to which it could be put, centuries before it was discovered in Europe or Asia.

    The Uayeb days acquired a very derogatory reputation for bad luck; known as "days without names" or "days without souls," and were observed as days of prayer and mourning. Fires were extinguished and the population refrained from eating hot food. Anyone born on those days was "doomed to a miserable life."

    The years of the Haab calendar are not counted.

    The length of the Tzolkin year was 260 days and the length of the Haab year was 365 days. The smallest number that can be divided evenly by 260 and 365 is 18,980, or 365×52; this was known as the Calendar Round. If a day is, for example, "4 Ahau 8 Cumku," the next day falling on "4 Ahau 8 Cumku" would be 18,980 days or about 52 years later. Among the Aztec, the end of a Calendar Round was a time of public panic as it was thought the world might be coming to an end. When the Pleaides crossed the horizon on 4 Ahau 8 Cumku, they knew the world had been granted another 52-year extension.

When did the Haab Start?

    Long Count corresponds to 8 Cumku. The authorities agree on this.

Did the Mayas Think a Year Was 365 Days?

    Although there were only 365 days in the Haab year, the Mayas were aware that a year is slightly longer than 365 days, and in fact, many of the month-names are associated with the seasons; Yaxkin, for example, means "new or strong sun" and, at the beginning of the Long Count, 1 Yaxkin was the day after the winter solstice, when the sun starts to shine for a longer period of time and higher in the sky. When the Long Count was put into motion, it was started at, and 0 Yaxkin corresponded with Midwinter Day, as it did at back in 3114 B.C.E. The available evidence indicates that the Mayas estimated that a 365-day year precessed through all the seasons twice in or 1,101,600 days.

    We can therefore derive a value for the Mayan estimate of the year by dividing 1,101,600 by 365, subtracting 2, and taking that number and dividing 1,101,600 by the result, which gives us an answer of 365.242036 days, which is slightly more accurate than the 365.2425 days of the Gregorian calendar.

    (This apparent accuracy could, however, be a simple coincidence. The Mayas estimated that a 365-day year precessed through all the seasons twice in days. These numbers are only accurate to 2-3 digits. Suppose the days had corresponded to 2.001 cycles rather than 2 cycles of the 365-day year, would the Mayas have noticed?)

    In ancient times, the Mayans had a tradition of a 360-day year. But by the 4th century B.C.E. they took a different approach than either Europeans or Asians. They maintained three different calendars at the same time. In one of them, they divided a 365-day year into eighteen 20-day months followed by a five-day period that was part of no month. The five-day period was considered to be unlucky.

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