Thursday, December 20, 2012

Mayan Calendars

The Maya are famous for their calendar system which, unfortunately, has been seized upon by many people who are peddling nonsense about this calendar predicting the end of the world on the winter solstice (December 21) of 2012. Since that's tomorrow, let’s tale a look at this a bit more closely.

The Maya actually had three different versions of calendars - the Tzolk’in, the Haab', and the Calendar Round.

The Tzolk’in

The first calendar was 260 days long and called the Tzolk’in. It was believed to be a religious calendar but no one knows for sure. Why 260 days? Many researchers believe that it was established in Copan – a major early Mayan site in Honduras near the Guatemalan border. It’s the time between passages of the Sun through the zenith (the point directly overhead at 90° of altitude).

The Sun is never directly overhead here in New York. It’s directly overhead exactly once if you live on the Tropic of Cancer (23.5° N latitude) on the summer solstice (because of the 23.5° tilt of the Earth’s axis). It’s directly overhead twice a year at latitudes between 0° (the equator) and 23.5° (the Tropic of Cancer). According to Wikipedia, Copan is located at 14° 50’ 24” N latitude and 089° 08’ 24” W longitude. The Sun passed through the zenith around noon on April 30 and again on August 13 in the year 426 CE (the date of the founding of Copan). The span of time from August 13 to April 30 is exactly 260 days.

While not all researchers agree with this explanation, it does work out nicely. Some have also argued that 260 days is the average number of days between the first missed menstrual period and birth (although this obviously isn’t very exact). Others have argued that it’s the number of days between planting and harvesting in agriculture (very contrived, in my opinion, since it depends on what you plant, weather, etc.).

The Tzolk’in is subdivided into 20 names of days (reflecting the vigesimal, or base-20, system of the Maya) with each day assigned a number from 1-13. This gives a total of (20x13) = 260 days. Each of the 20 names is also associated with a glyph. For example, the ninth named day is Muluk (“water”) and the glyph is shown at upper right. The fourteenth named day is Ix (“jaguar”) and the glyph is shown at lower right. Below is a table of all 20  day names and their meanings.
 
 
The way the Maya assigned names and numbers to days in the Tzolk’in calendar is complicated. It starts with Imix-1, Ik’-2, Ak’bal-3, K’an-4, … Eb-12, Ben-13, Ix-1, Men-2, …Ahaw-7, Imix-8, … Manik’-13, Lamat-1, Muluk-2, etc. In this way, every unique combination is hit.

The Haab'

The second calendar is called the Haab' and it was 365 days in length – the approximate length of the tropical year. The Haab' was a civil calendar and consisted of 18 months of 20 days each (there’s that 20 again!) which gives (18x20) = 360 days. An extra 5 days (called the Weyeb) were tacked on and these were considered unlucky days (other cultures have had this exact same system) where the veil between the mortal realm and the underworld disappeared.
 
One problem with the Haab' is that it ignored the extra ¼ day in the tropical year so the solstices and equinoxes occurred on different dates by a ¼ day each year (the ancient Egyptian calendar and the modern Muslim calendar do the same thing). Even though this calendar did not mark the true length of the tropical year, the Maya did know its length which they determined to be 365.2420 days (a value that compares well with modern knowledge).


Dates were specified as day (0-19) and then the month name. The year began with 0-Pop. Full dates in the Haab’ calendar were given as k’in (the day), uinal (the month name consisting of 20 kin), tun (the 365 day year consisting of 18 uinal), the k’atun (a cycle of 20 tun), and the b’ak’tun (a cycle consisting of 20 k’atun). There were then 13 b’ak’tun in a cycle before it begins all over again. This is referred to as the Long Count.
 
Long Count dates are written by modern scholars in the following format:
 
     e.d.c.b.a
 
Where:
 
     a = A cycle from 0-19 kin (equivalent to our 20 days in a month) – 20 days
     b = A cycle from 0-17 uinal (equivalent to 18 months in a year) – 360 days
     c = A cycle from 0-19 tun (equivalent to a cycle of 20 years) – 7,200 days
     d = A cycle from 0-19 katun (equivalent to a cycle of 20 tun) – 144,000 days
     e = A cycle from 1-13 baktun (equivalent to a cycle of 13 katun) – 1,872,000 days

So a long count date ranges from 0.0.0.0.0 to 13.0.0.0.0. The date of 0.0.0.0.0 supposedly dates to the Mayan creation on August 13, 3114 BCE (on our modern Gregorian calendar). Note that August 13 is the date the Sun passes through the zenith in Copan as discussed above. Since a complete cycle of 13 b'ak'tun is 1,872,000 days, the cycle ends in (1,872,000 / 365.24219) = 5,125.37 years. This corresponds to December 23 (not the 21st), 2012 CE (cue spooky music).

Archaeologists have worked very hard to find some data points where we can convert the Maya Long Count dates to Gregorian calendar dates. They’ve been able to do this with Mayan records of eclipses (we can calculate when they occurred with reference to our calendar). There are no reputable Mayan scholars or astronomers who believe anything untoward is going to happen at the end of the Long Count (other than the rolling over and start of a new Long Count cycle).

One interesting thing about the Long Count is that 5 Long Count cycles of 5,125 years is 25,625 days, the approximate length of the precessional cycle – this is the cycle of the wobble of the Earth and shifting of the Pole Star over time. Many believe the Maya knew of this cycle (as did the ancient Babylonians).
 
The Calendar Round
 
The Maya also had a third cycle, called the Calendar Round, which is the multiple of the 260-day Tzolk’in and the 365 day Haab’. It was therefore (260x360) = 18,980 days or 52 Haab’ years. The end of the Calendar Round was a time of anxiety as they waited to see if the gods would grant them another cycle (it would only occur once in anyone’s life). This was also a time when many of their temples were renovated.
 
End of the World?
 
So will the world end when the Long Count resets to zero?  NO!  Plain and simple.  I'll post "I told you so!" on the 24th (just in case the 23rd is the more accurate date).  What gets lost in all of this is how freaking smart the ancient Maya were in figuring out these calendar systems and matching them to astronomical observations (all before calculators and such).  Pretty cool.

So anyway, I'll be waiting out the apolcalypse by having a few beers on Friday (or maybe I'll live it up at the end with some single malt scotch) and celebrating the solstice and the start of lengthening days (even though winter begins).

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