August 11, 3114 BC marks the beginning of the

current calendric cycle of the Mayan Long Count calendar. The Mayan

calendar is comprised of repeating periods that result from the Mayan

base-20 positional number system.

*The*

Mayans were the first humans to invent a positional number system like

our decimal system—a system based on powers of a number base plus the

idea of a numeral that represents zero. A positional number system must

have some way to represent the value zero. In contrast to our base-10

system, the Mayans chose base-20. So instead of decimal places Mayan

numbers have vigesimal places. Instead of the decimal system of nine

numerals plus zero, Mayan numbers are composed of 19 numerals, plus

zero. In the decimal system, each digit represents a power of ten. In

the Mayan system, each digit represents a power of 20. A positional

number system is a necessity for doing serious mathematics. Imagine

doing even simple addition with a non-positional system like Roman

numerals.

Our Gregorian calendar uses

decimal numbers for years and a messy system based on the arbitrary

values 7, 28, 29, 30, and 31 for weeks and months. We call the periods

of our calendar days, weeks, months, years, decades, centuries, and

millennia.

The Mayan Long Count system is much cleaner. The periods correspond to vigesimal places of a Long Count date and are named

k’in, uinal, tun, k’atun, baktun, piktun, etc., each representing a

power of 20 except the the second place, the uinal, which is base-18.

(This results in the 20×18 = 360 day count in the lowest two places to represent the 360 day Mayan year.)

From the third place on up, the count is purely vigesimal.

The

Mayans actually used three calendars side-by-side. The Tzolkin and the

Ha’ab calendars are designed to keep track of holidays and astronomical

/ planting cycles. Those calendars restart every 52 years and don’t

concern us here. The third calendar, the Maya Long Count calendar,

counts an unlimited number of days from a specified starting point using

a modified base-20 system that accommodates the 360 day Mayan year.

Because this calendar is unlimited, Long Count dates are inscribed in

monuments intended to last for a long time.

Now let’s

connect some of the Mayan Long Count periods with real numbers. The

first vigesimal place, the kin, counts 20 day cycles. The second place,

the uinal, counts base-18. Together, the first and second places roll

over every 360 days, which is the length of the Mayan year, and the

count carries into the third digit. The third digit, tun, counts 20

Mayan years. The fourth digit, k’atun, counts 20 tuns, or 400 Mayan

years, which is 394.25 years on our Gregorian calendar. It is this 394

year cycle that is going to roll over in December 20, 2012, and the next

vigesimal place, the baktun, will increase from 12 to 13. We are now

in the 13th baktun since the start of the Long Count calendar (like

saying we’re in the 21st century in our calendar). The next baktun

begins on December 21, 2012.

A baktun is a period of

144,000 days or 394.25 Gregorian years. The Classic Period of Mayan

history occurred during the 8th and 9th baktuns. The last day of the

13th baktun occurs on Dec 20, 2012 in the Gregorian calendar, which is

12.19.19.17.19 on the Mayan Long Count calendar. The 14th baktun begins

on 13.0.0.0.0 (Long Count) or Dec 21, 2010 (Gregorian).

When

20 baktuns are completed (7,885 years from the starting point in 3114

BCE) a new piktun begins and the baktun starts counting again from

zero. The pictun isn’t normally written on Long Count dates because

it’s assumed. Just like we don’t write leading zeros on Gregorian

years. We don’t write 000002012, just 2012. When 20 pictuns are

completed, or 157,700 years, a new kalabtun begins. In fact there are

two more digits defined beyond these in the Mayan Long Count Calendar,

the k’inchiltun and the alautun. The Mayan Long Count calendar has

places already define and named that carry it another 1.2 billion

years. In our calendar we’re only named periods out to millennia. The

Mayans had a much longer view of time. And even after 1.2 billion years

have elapsed and the named periods of the Mayan calendar are filled,

the calendar still doesn’t end. You just keep adding more digits to the

year, the same as we will do when our year passes 9999.

In

light of this, the idea that the Mayan calendar ends is especially

ridiculous. The Long Count calendar is defined, with named periods, 1.2

billion years out into the future. It would make more sense to say

that our calendar ends in 9999, since we haven’t named any periods

beyond the millennium. But the hoopla about the new baktun (similar to a

century on our calendar) makes for lots of book and movie sales.

For a timeline of Guatemalan history, from 15,000 BC to the present, see Guatemala History Timeline.

The Maya Paradise home page displays today’s date in all three Mayan calendars: Tzolkin, Ha’ab, and Long Count. Maya Paradise

*Related*

## Mayan Calendar Doesn’t End on December 20, 2012

August 11, 3114 BC marks the beginning of the

current calendric cycle of the Mayan Long Count calendar. The Mayan

calendar is comprised of repeating periods that result from the Mayan

base-20 positional number system.

Our Gregorian calendar uses

decimal numbers for years and a messy system based on the arbitrary

values 7, 28, 29, 30, and 31 for weeks and months. We call the periods

of our calendar days, weeks, months, years, decades, centuries, and

millennia.

The Mayan Long Count system is much cleaner. The periods correspond to vigesimal places of a Long Count date and are named

k’in, uinal, tun, k’atun, baktun, piktun, etc., each representing a

power of 20 except the the second place, the uinal, which is base-18.

(This results in the 20×18 = 360 day count in the lowest two places to represent the 360 day Mayan year.)

From the third place on up, the count is purely vigesimal.

The

Mayans actually used three calendars side-by-side. The Tzolkin and the

Ha’ab calendars are designed to keep track of holidays and astronomical

/ planting cycles. Those calendars restart every 52 years and don’t

concern us here. The third calendar, the Maya Long Count calendar,

counts an unlimited number of days from a specified starting point using

a modified base-20 system that accommodates the 360 day Mayan year.

Because this calendar is unlimited, Long Count dates are inscribed in

monuments intended to last for a long time.

Now let’s

connect some of the Mayan Long Count periods with real numbers. The

first vigesimal place, the kin, counts 20 day cycles. The second place,

the uinal, counts base-18. Together, the first and second places roll

over every 360 days, which is the length of the Mayan year, and the

count carries into the third digit. The third digit, tun, counts 20

Mayan years. The fourth digit, k’atun, counts 20 tuns, or 400 Mayan

years, which is 394.25 years on our Gregorian calendar. It is this 394

year cycle that is going to roll over in December 20, 2012, and the next

vigesimal place, the baktun, will increase from 12 to 13. We are now

in the 13th baktun since the start of the Long Count calendar (like

saying we’re in the 21st century in our calendar). The next baktun

begins on December 21, 2012.

A baktun is a period of

144,000 days or 394.25 Gregorian years. The Classic Period of Mayan

history occurred during the 8th and 9th baktuns. The last day of the

13th baktun occurs on Dec 20, 2012 in the Gregorian calendar, which is

12.19.19.17.19 on the Mayan Long Count calendar. The 14th baktun begins

on 13.0.0.0.0 (Long Count) or Dec 21, 2010 (Gregorian).

When

20 baktuns are completed (7,885 years from the starting point in 3114

BCE) a new piktun begins and the baktun starts counting again from

zero. The pictun isn’t normally written on Long Count dates because

it’s assumed. Just like we don’t write leading zeros on Gregorian

years. We don’t write 000002012, just 2012. When 20 pictuns are

completed, or 157,700 years, a new kalabtun begins. In fact there are

two more digits defined beyond these in the Mayan Long Count Calendar,

the k’inchiltun and the alautun. The Mayan Long Count calendar has

places already define and named that carry it another 1.2 billion

years. In our calendar we’re only named periods out to millennia. The

Mayans had a much longer view of time. And even after 1.2 billion years

have elapsed and the named periods of the Mayan calendar are filled,

the calendar still doesn’t end. You just keep adding more digits to the

year, the same as we will do when our year passes 9999.

In

light of this, the idea that the Mayan calendar ends is especially

ridiculous. The Long Count calendar is defined, with named periods, 1.2

billion years out into the future. It would make more sense to say

that our calendar ends in 9999, since we haven’t named any periods

beyond the millennium. But the hoopla about the new baktun (similar to a

century on our calendar) makes for lots of book and movie sales.

For a timeline of Guatemalan history, from 15,000 BC to the present, see Guatemala History Timeline.

The Maya Paradise home page displays today’s date in all three Mayan calendars: Tzolkin, Ha’ab, and Long Count. Maya Paradise

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