Current Mayan Date
The Mayans had an elaborate calendrical system, no longer in use, which obviously evolved in complete isolation from those of the old world. This system ended with the fall of the Mayan civilization. Most of the remaining knowledge of it was destroyed by the Spanish during the conquest. It was not until very recently, during the 1990s, that archeologists have finally been able to fill in many of the gaps in our knowledge of Mayan civilization, including the calendrical system.
The Mayans were skilled mathematicians, and this shows in their calendar; besides having a concept of zero, they also had a firm grasp of modular arithmetic; they also worked extensively in base 20. However, despite their great skill at observing the heavens, their calendar has no relationship to lunar or seasonal cycles, and is only synchronized with the solar cycle year approximately. The Mayans were aware of this discrepancy; they simply didn't feel the compelling need to synchronize their calendar with the sun that Old World civilizations did.
The Mayans used three separate calendars. The Long Count was pricipally used for historical purposes, since it can define any date for millenia in the past and future. The Haab was a civil calendar based on a year of 360 days consisting of 18 periods of 20 days. Five days were added at the end of the Haab year to approximately synchronize it with the solar year. The Tzolkin calendar was used for ceremonial purposes, which had 20 periods of 13 days. The Tzolkin calendar went through a complete cycle every 260 days. The signficance of this cycle is unknown; it may be connected with the orbit of Venus, which has a period of 263 days. The Haab and Tzolkin dates did not have a year component; however, a combined Haab and Tzolkin date specify a unique day within a 52 year cycle.
It's the end of the world as we know it...
There is a great deal of nonsense that has been written about the Mayan long count. It has been claimed (most egregiously, in a Discovery Channel TV series) that it will 'come to an end' in the near future, and along with it will arrive a Mayan apocalypse, a pole shift, earth change, cosmic convergence, whatever. Given the completely cyclic nature of the long count, this is an idiotic characterization. Once any given cycle ends, another begins, endlessly. The full long count is currently only at baktun 12; there are still 8 baktuns (or about three thousand years) before it turns over. The current Katun will increment about ten years from now (18.104.22.168.0 will be on December 21st, 2012). However, there is no reason that date should be any more cosmologically significant than the end of the common era millenium was!
For one thing, this is a theoretical reconstruction of the Mayan calendar, since it hasn't been in use for hundreds of years. The Mayan epoch shown above was hotly debated by archeologists for many decades. The date shown is a consensus date, originally proposed by J.E.S. Thompson, and supported by carbon dating and other methods. However, this particular date for the Mayan epoch could still be off by some amount, possibly by years. Thus any eschatological theories based on this calendar would have to be adjusted accordingly. This is similar to the Christian era, which may be off by several years since we don't have Jesus' birth certificate in hand; so any predictions of the end of the world based on when that calendar ticks over were just as absurd. Furthermore, the assumption that some occurance of the Christian millenium marks the expiration date of the Universe is based on base 10 math: the fact that the Mayans adopted a base 20 system shows how arbitrary this assumption is. And anyway, last time I checked, the date is now 2000 and counting, and the universe is still here...
The long count was broken down into five components:
The zero day of the Mayan calendar is the date given above as the 'Mayan Epoch'. The significance of this particular date, which far exceeds any known historical horizon for Mayan civilization, is unknown. No recorded Mayan date preceeds baktun 7, and most of the historical Mayan events occurred during baktun 9 (from 435-830 C.E.).
Even longer dates with more components have been found. This includes enough additional base 20 components to write dates millions of years in the past or future, even though no such dates actually occur in the Mayan inscriptions, just contemporary dates with more digits in front of them. Imagining that kind of chronological depth to the universe is another Mayan accomplishment, similar to Hindu and Buddhist chronologies which encompass not just millenia, but billions of years of cosmic history.
Each Haab date consists of a one of twenty day numbers, (numbered from 0 to 19), and a 'month' or uinal name, of which there are 18. The uinal names are as follows:
Five days were added at the end of the year: this Uinal was called Uayeb. There is no year component to the Haab date.
The Tzolkin was a cycle of 260 days, consisting of a day number from 1 to 13 and one of 20 day names. In this case both the day number and the day name are incremented each day, that is, both advance in parallel. Since 13 and 20 do not divide evenly, it is 260 days before a particular Tzolkin date repeats. There is no year component to the Tzolkin date.
This is a list of the Tzolkin day names: