Saturday, August 27, 2011

The Longest Count

Stela One, Coba, Yucatan, Mexico

In a previous posting I discussed the Mayan calendar and of course the Mayan long count.1 Since the supposed ending of the world in 2012 was supposedly predicted by the Maya perhaps exactly what the Mayan long count was about should be examined. Now in the Mayan long count dates were given by giving the number of days that had passed since August 11, 3114 B.C.E., (B.C.).2 This was the so called long count which is usually transcribed into 5 numbers as in The number given is in fact the beginning of the Mayan long count.

The Mayan calendar worked like this.

Kin = 1 day
Winal = Month (20 Kins)
Tun = 360 days (18 Winals)
K’atun = 7200 days (20 Tuns)
Bak’tun = 144,000 days (20 Ka’tuns or 400 Tuns)

Thus dates would start by giving the number of Kins than Winals than Tuns than K’atuns than Bak’tuns. Thus a set of 5 numbers. For example 13. (Bak’tuns) 0. (K’atuns) 0. (Tuns) 0. (Winals) 0. (kins) or, (August 11, 3114 B.C.E.), which is the beginning of the conventional Mayan long count. However what happened on that date is not that the next day the 14th Bak’tun begins but the Bak’tun number resets to 0.

Why? The Mayan’s were in love with numbers and loved to play numerical and astronomical games with their calendar.

As indicated above the beginning date of the long count was not a zero date but, so that obviously this date is not the start of the calendar. For the last little while it has been common to talk about the date December 21, 2012, ( as the Mayan end of the world and the Mayan date has the creation date. Sorry neither is the end or beginning of creation.3 Above the Bak’tun the Maya had other figures thus above the Bak’tun we have:

“Pictun” = 2,880,000 days (20 Bak’tuns, 8,000 Tuns)
“Kalabtun” = 57,600.00 days (20 “Pictuns”, 160,000 Tuns)
“K’inchiltun” = 1,152,000,000 days (20 “Kalabtun”, 3,200,000 Tuns)
“Alawtun” = 23,040,000,000 days (20 “K’inchiltun”, 64,000,000 Tuns)

The reason I put those names in quotation marks is because those names were given to those quantities by Mayan Archaeologists, what the Maya actually called them is not known.4

Now the figures so far given go into tens of millions of years but there are still higher numbers whose names aren’t known in fact there are 15 higher magnitudes of numbers the names of which are unknown. The highest of which has a value of 754,974,720,000,000,000,000,000,000,000 days or 2,097,152,000,000,000,000,000,000,000 Tuns!5

So how did the Maya calculate their truly huge number of years? Well to begin. The full long count of which the one we know of consisted of only 5 numbers is a short hand for the actual long count which consisted of 24 different numbers. The Bak’tun was the Mayan century (400 Tuns or 20 x 20 Tuns). Including the Bak’tun the numbers above the K’atun (20 Tuns) number 20. The Mayan numerical system was 20 based so 20 numbers for a “century” and above as a certain numerical logic. However added to this is the fact that the Maya like the other people of Mesoamerica had a sacred calendar, (The Tzolkin), of 260 days. It consisted of the numbers 1-13 and 20 day names. After 260 days the names repeated. The origin and source of the sacred calendar are not clear but it appears to exist because it is a close approximation to the period of human gestation of c. 9 months.6

Given that the number 13 is important along with the number 20 the result is each unit of the actual long count goes to 13 of the unit and then reverts to 1 which then goes to 20 of the that unit. Thus each unit of the long count actually goes through 33 of the units and not 20 before it affects the unit above in magnitude. This is so that the numbers 13 and 20 which the Mayans use in their calendar system are used in calculating time intervals.

What is also of interest is that in each of the units above a Bak’tun in the Mayan numerical system the unit number 13. So that an actual full date would be in the long count.

Now here is where it gets a little stranger. The date of the start of the long count is, which is August 11, 3114 B.C.E. After that date the Bak’tuns started again at 0 and they will go on until there are 20 of them. So that for example is November 13, 2720 B.C.E. however the date of repeats and that date ( is December 21 2012 C.E. (A.D.)7

So note that the Mayans did not date the end of the world to December 21, 2012 and neither did they date the beginning to August 11, 3114 B.C.E. That date was simply the end of the current cycle of first 13 Bak’tuns out of 33 which then reverted back to 0 and then start the period of 20 Bak’tuns as part of the current cycle of 33 Bak’tuns (13+20). Bak’tuns. Undoubtedly they ascribed importance to the date December 21 2012 ( given that it is a reoccurrence of the date of the end of the first 13 Bak’tuns, August 11, 3114 B.C.E. ( However because this is the second part (20 units), of the current cycle of Bak’tuns the after the 13 Bak’tun they do not revert to 0 but instead go to the number 14 Bak’tun thus the date March 26, 2407 is It is also interesting to note that the Mayans began their short form of the long count with the 20 highest units of the long count (Bak’tun and above), all 20 set on 13. Thus using both 20 and 13 important in their astronomy and mathematics / time keeping to set the start of their calender.8

Since all the numbers above the Bak’tun are at 13 they have yet to be reset so to speak to 0 and then go through an additional 20 units making 33 altogether. The results in terms of numbers are huge. We can calculate that the number of days that past before August 11, 3114 B.C.E., in this system and that works out to 10,331,233,010,526,315,789,473,684,122,000 days or 28,285,978,483,664,581,446,157,328,238.631 years!

For calculating future time i.e., all the time since August 11, 3114 B.C.E. that works out to 15,894,204,631,578,947,368,421,052,480,000 days or 43,517,152,096,098,311,708,523,306,538 years!

Thus the total length of the actual long count is 26,225,437,642,105,263,157,894,736,592,000 days or
71,803,130,579,762,893,154,680,634,776 years!9

Let us compare the above number to other numbers.

The total number years let alone days in the actual Mayan long count is gigantic! The Mayan Universe has conceived by them came into being unimaginable eons ago and would in their minds endure for unimaginable eons to come. Given that this is the case the whole fuss over 2012 is absurd. The Maya did not expect the world to end on December 21, 2012; what they expected to happen was that the 13 Bak’tun would end and the 14th Bak’tun begin.

As it is the huge calendaric numbers of the Maya indicate a striking confidence in using and manipulating huge numbers. It is such a pity that modern people looking for new thrills and woo missed that the conventional long count dates on Mayan monuments etc., were abbreviations of a much longer and deeper conceptions of time.

1. See The Mayan Calendar, Xibalba Here and Mayan Math, Xibalba Here.

2. Stuart, David, The Order of Days, Harmony Books, New York, 2011, p. 239. The date the Mayan long count begins is debated some give the date August 13, 3114 B.C.E, see Montgomery, John, How to Read Maya Hieroglyphs, Hippocrene Books Inc, New York, 2002. See also Coe, Michael D., The Maya, Eight Edition, Thames and Hudson, London, 2011, p. 62-69, Wren, Linnea H, & Spencer-Ahrens, Kaylee, Arithmetic, Astronomy, and The Calendar, in Foster, Lynn V., Handbook to Life in the Ancient Maya World, Oxford University Press, Oxford, 2002, pp. 245-263, at 255-259, Sharer, Robert J., & Traxler, Loa P., The Ancient Maya, Sixth Edition, Stanford University Press, Stanford CA, 2006, pp. 110-115.

3. Stuart, pp. 239, 245-251.

4. IBID, p. 231-232, 237. See also Sharer, p. 102.

5. IBID, p. 237. An example of a rare complete long count date is Stela One located in Coba, Yucatan, Mexico, which has all 24 units! See Stuart, pp. 232-236.

6. Wren, pp. 251-260, Sharer, pp. 102-115, Coe, pp. 62-69, Montgomery, pp. 71-88.

7. Stuart, pp. 241-242.

8. IBID, pp. 239-242.

9. IBID, pp. 238-241.

10. How many Grains of Sand on Earth?, Answers Com Here. How Many Galaxies?, NASA HereHow Many Stars in the Milky way, Curious About Astronomy Here. The Estimated Number of Stars in the Universe just Trebled, 80 Beats, Discover Magazine Here.

Pierre Cloutier

1 comment:

  1. Above is a drawing of Stela 20 from the archaeological site of Coba in Quintana Roo, Mexico (Yucatan). The stela portrays I believe the accession of a ruler, wearing an elaborate feathered headdress crowned with the Fleur-de-lis emblem, that bears the image of the Maya god K'awil (God K). The ruler I believe is portrayed at his death, based on the ollin iconography (meaning movement) encoded into the royal ceremonial bar that bears the images of the Maya god Chac, who I propose represents an aspect of Venus as the Evening Star and the god of underworld decapitation. The Maya ruler also depicts blood stained spots that appear in groups of three, which is iconography associated with death, along with the ollin symbol (twisted X icon) which alludes to the ruler's accession at death, and that the grouping of three blood stained dots are code for a trinity of deities known to scholars as GI, GII, and GIII, or the "three hearth stones of creation". I argue that the Fleur-de-lis emblem depicted above symbolizing divine rulership and a trinity of creator gods has the same exact meaning in both Mesoamerica and the Old World .