To the basic Mesoamerican system of recording time the Maya added three things: an era date, periods of time, and the concept of zero. The era date, 4 Ahau 8 Cumku, August 11, 3114 B.C. is the first day of this humanity.
4 Ahau is its name in the Tzolkin ritual calendar of 260 days and 8 Cumku in the Haab or solar calendar of 365 days. We, too, give names to days from two calendars. We could say that Sunday 25 December is our era date; Sunday being its name in the calendar of the week and 25 December its name in the solar calendar.
Like the era date in our contemporary calendar -- the birth of Jesus -- the Maya era date was neither the beginning of time nor was it the first day of a year. Nor were people using the calendar when it started. In both calendars events are recorded that occurred before the era date.
A day named 4 Ahau 8 Cumku re-occurs every 52 years -- yet usually, when mentioned, it is referring to the era date in 3114 B.C. In our calendar we repeat the names of days every 14 years -- at least that’s how many calendars there used to be in the front of phone books, which some readers may remember.
The Mayas grouped the days that have elapsed since the era date into periods of time. The smallest is Kin, which means sun -- one sun equals one day. Twenty Kins equal a Uinal -- a 'month' of twenty days. The Uinal goes nicely with the Maya vigesimal, base twenty, mathematical system. (If we got our decimal system from the Arabs counting their ten fingers, perhaps the Mayas came up with their system by counting fingers and toes). The Haab calendar has 18 months of 20 days and one last month of five days. The Tzolkin has 13 numbers that combine with 20 names; so the twenty-day Uinal fits nicely with both of the basic Mesoamerican calendars.
The Mayas would have appreciated a 400-day year; it would have been perfect -- twenty months of twenty days! Alas, there are only 365 days in a year. So they took the closest multiple of twenty, 360 Kins, and called it a Tun. That is the only deviation from their mathematical system. From then on periods of time increase by multiples of twenty. Twenty Tuns make up a Katun, 7,200 days. Twenty Katuns, a Baktun, 144,000 days. These five periods of time -- Kin, Uinal, Tun, Katun, and Bactun -- can keep track of all the days elapsed since the era date in 3114 B.C.
In Maya hieroglyphics, periods of time are referred to with numbers written in a vertical column -- the smallest unit is at the bottom. This is difficult to do in our horizontal system of writing. Therefore, in contemporary books Maya dates are written left to right with the largest period of time first and dots between the periods of time. Today's date in the Maya calendar is 220.127.116.11.0 -- according to the Maya ap on my iPod.
That means that between the era date and today, 12 Bactuns, 19 Katuns, 18 Tuns, 11 Uinals, and 0 Kin have passed; and today’s name is 11 Ahau 8 Yaxkin wherein 11 Ahau is the name of the day in the Tzolkin and 8 Yaxkin the name in the Haab.
Days have names; months do too. Each Haab 365-day year receives the name of the first day of the year -- allowing individual years to be identified within a 52-year cycle. Because of the makeup of the calendar there are only four days on which years can begin -- they are called year bearers; interestingly they are days in the Tzolkin.
Demonstrating a certainty that the period of time will reach completion, Katuns are named the last day of the Katun -- again from the Tzolkin calendar -- always a number from 1 to 13 followed by the name Ahau.
I haven't heard of names for Bactuns -- they are referred to with numbers perhaps because Bactuns are longer than a human lifetime. We live in Bactun 12.
There are periods of time longer than Bactuns, each 20 times the previous period, and there are Maya dates carved in stone that include those longer and larger periods.
The longest Maya date, found so far, is on a stela at the base of the tallest pyramid at Coba on which the era date is recorded, August 11, 3114 B.C. It is written in a way that recalls the Tzolkin calendar and its twenty cycles (periods of time) set at thirteen: 18.104.22.168.22.214.171.124.126.96.36.199.188.8.131.52.13.13.
The four zeros at the end of that date refer to Katuns, Tuns, Uinals, and Kins. According to Linda Schele, arithmetically the thirteens are also zeros. Four hundred Tuns after the era date the 'last' of the thirteens turned over to become 1. For the largest period of time on the Coba stela to change to 1 will "take slightly under 142 nonillion years, or in our number system, 142 followed by thirty-six zeros." This is farther into the future than the Big Bang is into the past!
December 21, 2012, will be a milestone in timekeeping, a day on which a small part of the odometer of time will reset to zeros -- 184.108.40.206.0 -- but the gods of time will keep on walking with the Sun making their way towards Bactun 14. Just as there are only 13 names for Katuns, yet it takes 20 to make up a Bactun, likewise these first thirteen Bactuns will be joined by seven more to form the first Pictun.