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1.2.4
The Mayan Numerals
Introduction
In western culture we tend to think of Native "American" history as a late chapter in western civilization. They became relevant to western culture only once it came in contact with them in the middle of the second millennium A.D. The truth is however that our world really had at least two histories running parallel for a good ten thousand or so years before the European's came.
If it is true that modern humans came from a singular small group in Africa some 500,000 years ago, then all humans had to have migrated from this birthplace of humanity. This means there must have been a time when the continents now called the "Americas" were uninhabited by modern humans. The common theory is that during the Ice Age there was a bridge connecting Russia with Alaska, allowing some humans to cross over into the "new world". The last Ice Age ended sometime around 13,000 B.C. Presumably, after the end of the last Ice Age the "old" and "new" worlds became physically separated resulting in isolation and independent development. What was once a "new" world for the first settlers, was to become a lost world to those who remained on the Eurasian continent, and then a new world once again several millennia later.
Although it might seem bizarre, it is bares noting that everything that we consider classic history from the Babylonian's, the Egyptian's, the Greek's, and the Roman's, would by necessity have a "new world" equivalent! Yet despite the fact that this alternative history spans millennia across two massive continents involving many empires and civilizations it is all condensed into a neat little package called "Native American History". Rather than think of the Native Americans as a unified people it is much closer to the truth to recognize that there were many distinct empires in the new world, who would have considered themselves just as different from each other as the Greeks would have considered the Persians. The notion of a singular "Native American" identity is something that emerged with the conquest by the Europeans, as the people sought to unify themselves against a hostile enemy and redefine their identity. It is probably not a stretch to say that this unified identity was forced upon them by necessity by an enemy that was not interested in the distinctions.
With that being said I suggest dispensing with the terms "Indian" and "Native American" and simply recognize that there were many independent nations living in the new world for thousands of years without any contact from the other half of the globe. Although it might be argued that all the peoples of the New World came single ancestor who first crossed over during the Ice Age, it is more probable that many peoples crossed over the Ice Bridge over a period of thousands of years. We therefore shouldn't automatically assume that all the empires of the new world were closely related. They may have brought the civilizations from the old world, with their identity more or less maintained over the millennia. Or perhaps not. Historians still don't know all the details of this lost alternative history, but it's fascinating to think that there is a history of the Native Americans that would be as vast and complex as the histories of the Sumerians, Babylonians, Egyptians, Greeks, Persians, Romans, and Chinese, combined! That's the scale we have to imagine such a history on if we are to keep with the facts.
I do not intend to do justice to the full depth and breath of such a history in this article. Rather I intend to focus on only a single empire of this sprawling history: that of the ancient Mayan civilization; and I only intend on focusing on a small aspect of their culture and civilization, namely, their number system and it's connection to their calender.
The Great Mayan Civilization
The Mayan's were no strangers to Large Numbers. In their quest to understand the cycles of the heavens they came to a very long perspective of time (as we'll see shortly), especially when compared to other early traditions. This was more than idyle speculation and was connected to their sophisticated calander system which was more accurate even than those used in Europe millennia later. The Calander System was also closely connected with a very modern Number System that was probably developed in conjunction with it.
The Mayan civilization is said to have been established about 2000 B.C. They developed a civilization at least as advanced as anything in the Old World at the time. They lived in an area we refer to as Mesoamerica, the land bridge connecting North and South America.
Despite having no connection to the old world, they independently developed writing, mathematics, at least two systems of numeration, astronomy, a highly accurate calender system, religious beliefs and rituals, government, architecture to rivals the pyramids, and agriculture. In many ways the Mayans were more sophisicated than the Egyptians. Their calender was more precise, as was their astronomy.
The Mayan's are one of only two ancient peoples to devise a positional notation, the other being the Babylonians. Calculation and mathematical prowess is greatly enhanced by a convienent positional notation, and this may be part of the reason for their advanced astronomy despite their lack of high-tech instruments.
The Mayan's were one of the great civilizations of Pre-columbian Mesoamerica, along with the Olmec, Toltec, Aztec, Zapotec, and Teotihuacanos. They built great pyramids as for the purpose of gathering spiritual energy. These were built a few centuries before those built by the Egyptians! The Mayan Pyramid in Cuicuilco Mexico was built in 2750 B.C., while the great Pyramid in Egypt was built in 2560 B.C. It is often assumed the other way around, but again this is part of a western bias of seeing "Native American Civilization" as an Appendix to early American history. These Mayan Pyramids were some of the largest structures ever built in ancient times!
The Mayan's believed in a Universe that was eternal, or at least mind-bogglingly ancient, and was cyclical rather than linear. This view probably developed from centeries of careful observation of the sky. They came to recognize very long cycles of astronomic time that had escaped astronomers of other civilizations. Part of the Mayan's claim to fame in recent years is their calender and it's connection to a predicted end of the world on December 21st 2012 (A date only a few months away as of this writing). This has fueled much interest for the Mayan civilization. However the Mayan's are much more remarkable for their accomplishments than for making a "doomsday prediction". In fact, it is quite possible that our interpretation of Mayan beliefs is baised by our western tradition of a catalysmic apocalypse. The Mayan's more likely would interpret the date as not simply an "end of the world" but rather a period of purging and rebirth.
The Mayan's were artists as well as scientists, and Mayan art is considered the most sophisicated in Mesoamerica at the time.
They were some of the earliest people to have developed writing in the New World. The Olmec predated them, but there isn't much similiarity between their form of writing and that of the Mayan's so it is believed that the Mayan's developed their writing independently. Mayan writing took the form of hieroglyphs, just as it had in Egypt. Hieroglyphic writing is a particular type of writing that uses pictograms (pictures) to represent whole "words" or "concepts". This is in contrast to phonetic writing where the individual glyphs (letters) are abstract in form and represent vocal sounds rather than ideas, and must be combined to form words.
Although the Mayan's were did not have the most military prowess in Mesoamerica, the Toltec being much more militeristically minded, they still managed to hold their own and create a thriving and long lasting civilization. The achieved the height of sophistication from about 250 A.D. to 900 A.D. By the time the Spanish arrived from the Old World in the 1500's the Mayan's were already in decline and the Spanish found the great Mayan cities eeriely vacant. No body seems to know quite why they left their civilization, though historians have plenty of theories. The most likely explainations is environmental: the soil and simply become unfertile due to overuse. The Mayan's thrived and had quite a large population at their peak with some cities estimated with populations up to 50,000. Although the Mayans faded into obscurity they never completely vanished. They were still living in the surrounding area when the Spanish arrived, and were assimulated into the spanish culture. There are still individuals who can trace their lineage back to the Mayan, although there are few pure blooded Mayan's left. Most of them still practice a form of their beliefs, but in conjunction with Catholic believes they adopted when they assimulated with the Spanish conquerors.
The Maya were not simply another tribe of Native Americans. They were an advanced ancient civilization whose legacy can still be seen today in the great Mayan ruins in Mexico.
The Mayan Calender
Now that we have some idea who the Mayan's were let's discuss their calendar system, which formed the basis of their view of the universe. Two reasons why this is of interest to us here is that their calendar involved some large numbers, larger than those expressed by other ancient people around the same time period. Another reason is because their calender and their number system were closely related.
As stated earlier, their view of time was cyclical, and this is reflected in their calender. Rather than establish a starting date and simply count up indefinitely, as we do with our modern calendar, the "years" of the Mayan calender cycle through a pattern made up of different cycles with different ratios. The Mayan Calendar was actually a composite of many calenders, each of a different length, and as these smaller calendars (referred to as rounds) fell in and out of sync with each other it formed the basis of their sense of time. Every day's spiritual quality was related directly to the combinations of dates from each of the calendar rounds. When all these rounds were combined, a cycle was created with very long periods between repeats. Although this might at first seem bizarre, it is not without some logical basis. The Mayan calender reflects the genuine cycles of the solar system itself. The moon, the sun, the seasons, and the phases of Venus are all at odd ratios to each other. Each one of these phenomenon are like individual rounds. Over long periods of time this rounds fall in and out of sync with each other, just as the Mayan Calender does.
One of the rounds is closely connected to our notion of a "year". This round lasts 365 days exactly, and is referred to as the Haab. Early historians thought that the Mayan Calendar was not very sophicated, and that the Mayans were unaware that the true length of the year is more precisely, about 365.2422 days.
Although our modern calendar also has a year of exactly 365 days, we intersperse leap years of 366 days every 4 years. This keeps the seasons in line with the calendar dates to within a day for a hundred years. When the error accumulates to a full day we simply skip a leap year on a century year (ie. 1700, 1800, 1900, etc.). This also leaves a minute error we correct every 400 years by instating a leap year on a century year divisible by 4 (ie. 1600, 2000, 2400, etc.). This will keep our modern calendar accurate to within a day for the next 3200 years. This is what is known as the Gregorian Calendar. In the Gregorian Calender the average length of a year over a 400 year "cycle" is 365.2425, which is Still not the correct value!
The Mayans instituted no modifications to the length of the Haab cycle. It was 365 days every round. This meant that the Haab date would gradually slide across the seasons from Haab cycle to Haab cycle. The Mayans however were well aware of this, but could easily determine the seasons by the path of the sun through the sky on any given day. Furthermore, they could determine how the Haab date was sliding and thereby correct for the length of the year. They could then determine on what Haab date a solistice or equinox would fall on any given Haab cycle, without interspersing leap days. It's simple once you accept that dates don't neccessarily have to remain fixed relative to the seasons. Afterall the earths rotation doesn't remain fixed to its orbit around the sun, so instead of "correcting for it", wouldn't it be more natural to simply take this into account. Any point in time could then be recognized as a unique combination of the earth's rotational orientation and position from the sun.
The next important round in the Mayan Calendar was that of the Tzolk'in cycle. This round lasted exactly 260 days. Actually the Tzolk'in cycle was composed of two smaller rounds which would fall in and out of sync with each other. After 260 days they would finally line up again. The length of the two smaller rounds was 13 and 20 days, and 260 is the least common multiple of 13 and 20.
The Tzolk'in and the Haab would gradually shift about each other like intermeshed gears with different numbers of teeth. After 18,980 days the Haab and Tzolk'in would again reach the beginning of their rounds on the same date. This took 52 Haab cyles or 73 Tzolk'in cycles. Thus the Haab and Tzolk'in realigned roughly every 52 years.
The Mayan's were also greatly interested in the phases of Venus. The developed a 584 day round to keep track of Venus. When the Venus cycle was combined with the Haab and the Tzolk'in a 37,960 day "grand cycle" was created, that represented 104 Haab cycles, or 146 Tzolk'in cycles, or 65 Venus cycles. Thus the Haab, Tzolk'in and Venus cycle realigned roughly every 104 years.
These 3 rounds formed the basis of their civil calendar, and since a full cycle was 104 years, almost everyone would never see a repeat combined date of the three rounds within their lifetime. This however proved insufficient for the recording of history, so a longer count was needed for historical records, hence the institution of the "Long Count Calendar". This is where the numbers start to get pretty big.
The Long Count Calendar used a 360-day Haab year composed of 18 20-day "months" (we'll see how this is directly related to their numbering system). This was known as a "Tun". Larger cycles were created through multiples of this basic unit:
A Katun was the length of 20 Tuns, or 7200 days (roughly 19.7 solar years)
A Baktun was the length of 20 Katuns, or 400 Tuns, or 144,000 days (roughly 394 solar years)
The next unit of time was the "Great Cycle" which was 13 Baktuns, or 260 Katuns, or 5200 Tuns, or 1,872,000 days (roughly 5,125 years). Consider that this is a time period long enough to represent a good portion of written history.
Finally we reach the "Grand Cycle" which was 5 "Great Cycles", or 65 Baktuns, or 1300 Katuns, or 26,000 Tuns, or 9,360,000 days (roughly 25,627 solar years). The Grand Cycle represents a completion of something known as the "Procession of the Equinoxes". You may recall that the Earth axis of rotation is not completely perpendicular to the plane of its orbit. Rather it is tilted back about 23.5 degrees. It turns out however that this is not a fixed value and that the earth infact wobbles very slowly so that this tilting angle actually changes, resulting in a shift in how the seasons proceed. The time it takes to return back to it's original tilt is a cycle of 25,627 years.
On December 21st, 2012, we will be reaching the end of a Grand Cycle and the beginning of a new one. This is the source of the "2012" end of the world phenomenon. There is an important myth connected with the long count calendar that is closely related to the prediction of this doomsday. Each of the 5 "Great Cycles" represented 5 ages of man (similar to the Greek concept). At the beginning of each Great Cycle, a race of man was created, and at the end of each, they were destroyed. Unlike the Greek 5 ages of man, in which man began as a Golden race, that gradually degenerated with each successive age, the Mayans had it in reverse. The earlier races of man were inferior to the later ones, and in fact this is the reasons the Gods destroyed them. This is suppose to be the end of the 5th age of man, and presumably he in turn will also be destroyed ... and then what? Are we the last race, and does the Grand Cycle represent all of time to the Maya? No. Remember that the Maya viewed time as cyclical. It is a Judeo-christian tradition to view time as linear with a definite beginning and definite end. The Grand Cycle does not represent the whole of history. The Mayans had a much more expansive view of time and the universe than other ancient cultures. The Grand Cycle which is soon to end, is but one in a long procession of Grand Cycles. One reason that the 2012 date is believed to represent the "end of time" for the Mayans is that their calendar supposedly ends on this date. Firstly, even if this was so, the Mayan's would have simply reset their calendar to day one of their long count. Secondly, even though the long count official did not contain any larger rounds, it would be a simple matter to add another one and another as the need arose. In other words they could have simply added longer and longer rounds as needed. This is substantiated by the fact that the Mayan's had even longer units of time beyond the Grand Cycle!
After the Baktun, four additional units of time were designated by the Mayans:
A Pictun was equal to 20 Baktuns, or 400 Katuns, or 8000 Tuns, or 2,880,000 days (roughly 7885 solar years). A Pictun was longer than a Great Cycle which is only 13 Baktuns.
A Calabtun was equal to 20 Pictuns, or 400 Baktuns, or 8000 Katuns, or 160,000 Tuns, or 57,600,000 days (roughly 157,704 solar years). A Calbtun was roughly 5 times that of a Grand Cycle! And we still have two more units of time to go ...
A Kinchiltun was equal to 20 Calabtuns, or 400 Pictuns, or 8000 Baktuns, or 160,000 Katuns, or 3,200,000 Tuns, or 1,152,000,000 days (roughly 3,154,971 solar years). Wow! Just think about it, going back 1 Kinchiltun would bring us all the way back to early human evolution!
A Alautun was equal to 20 Kinchiltuns, or 400 Calabtuns, or 8000 Pictuns, or 160,000 Baktuns, or 3,200,000 Katuns, or 64,000,000 Tuns, or 23,040,000,000 days (roughly 63,081,429 Solar years). Going back 1 Alautun would bring us all the way to the extinction of the dinosaurs!!
And there is some evidence that the Mayan's went even further, imagining even longer time frames. What's interesting is that this time frames already begin to rival those used in modern science! Why were the Mayan's so interested in such remote time frames. These long time periods were far vaster than even the procession of the equinoxes, so they didn't have any celestial significance that we know of. What significance could events millions of years in the past or future have to indigenous people? Did the Mayan's really think the world was that old, or would last that long?
Let's now examine the Mayan Numeration system. Once we understand their numbering system we will return to a more complete discussion of Large Numbers in the Mayan Culture.
The Mayan Numerals
The Mayan Number System was elegantly simple and powerful, employing only 3 symbols to form numerals. It was positional in nature, just like our modern decimal notation. These symbols were the "dot", the "bar", and the "shell". The "dot" represented the count of one, the "bar" represented the count of five, and the "shell" represented an empty position, or zero. The system was primarily vigesimal (base 20) in nature. The numbers 0 through 19 were written as follows:
As you can see the numbers 1 through 19 were simple additive combinations of the bars and dots. Dots were written in rows, with no more than 4 appearing in any row. Horizontal bars were stacked vertically with the dots placed on top. These first 20 numbers can be thought as the 20 digits of the Mayan Number System. Just as in our decimal system, several digits may be combined in sequence to form larger numbers. The Mayan's wrote their numbers vertically however, with the highest place value on the top. The bottom most position was the Ones place. The next position up represented units of 20. Thus the numbers would continue as follows:
The single dot on top would represent a count of 20, since it is in the "2nd position" from the bottom (I will order the positions from bottom to top for convenience). You would naturally assume that the next position up, the 3rd, would be units 20 times that of the 2nd, or units of 400. The Mayans however used the 3rd position to represent units 18 times that of the 2nd, or units of 360. This at first seems bizarre, but recall that their long count calendar used 360-day years. This effectively meant that their numerals could be used to represent dates as well as numbers. Subsequent positions always represented units 20 times that of the previous position. Because of this little hitch the Mayan's didn't use a pure vigesimal system, but a mixed-radix system. It is speculated that the Mayan's used the modified vigesimal system for their dates, and a pure vigesimal system for their numbers. The problem is there is no evidence to substantiate this. All the numerals that have been found so far have used the mixed-radix system. I suspect there was no pure vigesimal system. It is possible that their number system originated from their calendar and was later adopted as their number system. If this is true it would be awkward to switch to a pure vigesimal system once the Mayans had gotten used to their mixed-radix system. The only reason we seem to think this is awkward, and probably why a pure vigesimal system is hypothesized despite the lack of evidence, is because we are used to a pure-radix system.
Here are some example numbers. I've shown how to convert them into modern notation:
As you can see the Mayans were well equipped to express Large Numbers. Because their base was larger than ours in fact, they could express large numbers slightly more compactly. The 5-digit Mayan number on the right expresses a 7-digit decimal expression in modern notation. The Mayan system can be seen to be vastly superior to the Egyptian Numerals. Not only did it express numbers more compactly, but it was far more extendable. Furthermore while the Egyptian numerals required 7 symbols, the Mayan numerals only required 3.
Now that we know how the Mayan Numerals work let's return to the subject of the Mayan Calendar and Large Numbers.
Large Numbers of the Mayan
With the Mayans we find that dates in the Long Count Calendar and numbers are virtually synonymous with every day potentially being associated with a number. Typically the Long Count date was written as a 5-digit numeral. The 1st position would represent the day, the 2nd position the month (each of 20 days), the 3rd position the year, the 4th position the Katun, and the 5th position the Baktun. This was sufficient to keep track of dates within the Great Cycle, since a Great Cycle is 13 Baktuns. In fact, the 5 place values could actually be used to cover a time period of 20 Baktuns, or roughly 7885 solar years. This effectively meant that the Mayans would never have to use the same date twice in their long count calendar and it could be used to cover all of Mayan History. Here is an example date:
For convience we can adopt a modernized notation for mayan numerals. Each "mayan digit" can be written as a number from 0 to 19 as in ordinary decimal notation, and the mayan digits can be separated by periods. The above number/date can then be written as 9.9.2.4.8. As a date this corresponds to July 27th 615 A.D. This date marks the accession of K'inich Janaab' Pakal to the throne of the Mayan Empire [1]. As a number this corresponds to 1,361,608. This number is more than a mere nominal designation providing a "name" for the day. It can also literally be thought of as the count of days from the traditional creation date of the Mayans. When the Mayans created their long count calendar they did not begin at zero, as you might expect. Instead they designated a distant date in the past as the day of creation. This date corresponds to August 11th 3114 B.C. in our modern proleptic gregorian calendar. This can quite literally be thought of as "day zero" for the Mayan's. You might assume that the Mayan's would record this as 0.0.0.0.0. However they designated this date as 13.0.0.0.0 as it represented both the end and beginning of one great cycle. For every succeeded day the Mayans could assign a date which was also the precise number of days after the date of creation. For example 0.0.0.0.1 would correspond to "day one" or August 12th 3114 B.C. So Pakal assended to the thrown exactly 1,361,608 days after the zero-day.
The whole reason we are able to relate gregorian dates to Mayan dates is because there was an event described in both Mayan records and spanish records that establishes the folowing correspondence:
11.16.0.0.0 = November 2nd 1539 A.D.
(11.16.0.0.0 corresponds to the number 1,699,200)
This is all closely related to the so called "2012 phenomenon" as December 21st 2012 would be the date 13.0.0.0.0 in the Mayan Calendar, ... the same date they used to mark their day of creation. It is for this reason that theories started to circulate that this marked the "end" of the Mayan Calendar and consequently why the Mayan's proportedly prophesied that this would mark the "end of the world". However there is good reason to believe that the Mayans would have simply reset the long count at 0.0.0.0.1 for December 22nd 2012 and begun another great cycle. Not that the reset would have been a non-event for them. Just as the western world became excited with the approach of the year 2000, and considered it the "end of an era and the beginning of a new one", so too the coming to the completion of a cycle was cause for great celebration and reflection about the coming age. The truth is that there are indications that the Mayan's were envisioning even further times into the future, and that they intended to extend their long count with even greater cycles ... possibly ad infinidum. These are details that are often glossed over or omitted by those who've promoted the "2012 myth" if I may call it that. I would go so far as to say that the western researchers were only seeing the kind of apocalypses typical of western traditions: one that either involves total annhilation, or total judgement, or at least represents an end of the world as we know it, usually for the worse. The Mayan's however we're not looking for some kind of cosmic conclusion or book end. They were seeking the eternal return, and looking for every sign in the heavens that their world would never change. Their vision of the future and the past was expansive, especially in constrast to other ancient cultures. Perhaps they longed for a cosmic guarantee that their civilization would never pass away.
Now that we have some handle on how numbers and long count calendar dates work in conjunction, let's look at just how far the Mayan vision of time extended. We'll begin with the smallest unit of time of the Mayans: the day. The day was called a K'in. It was, even more so than in our culture, the fundamental unit of time. Every other time unit was a whole multiple of this basic unit. Each unit of time recieved a special symbol. The K'in was symbolized as [2]:
Symbolically we can think of a K'in as synonymous with "One", and treat it in someways like a number. It can be represented numerically in the Long Count as 0.0.0.0.1.
20 K'ins made up a Mayan month known as a Winal. It was symbolized as:
What exactly this is, is anyone's guess. In any case we can say that a Winal can also double as the number 20. It can be represented numerically in the Long Count as 0.0.0.1.0.
Next would be the Tun, which was 18 Winals or 360 K'ins. The Tun is very close to our concept of a year. The Tun was symbolized as:
The Tun can be thought of as the number 360. It can be represented numerically as 0.0.1.0.0. The Next unit was the K'atun which represented a period of 20 Tuns (basically the equivalent of 20 years). The K'atun was symbolized as:
The K'atun represented the passage of 7200 days, or we can think of it's symbol as representing the number 7200. It can be represented as 0.1.0.0.0.
Lastly for the Long Count Calendar we have the Baktun, a period of 20 K'atuns or 400 Tuns (basically 394 solar years). The Baktun was symbolized as:
A Baktun was the passage of 144,000 days, and so we can think of it's symbol as representing the number 144,000. It can be represented as 1.0.0.0.0. 13 Baktuns would make up a great cycle and 65 Baktuns would make up a grand cycle.
For reasons that we can only speculate the Mayans wanted to go even further. Sir J. Eric Thompson has theorized that originally the Mayans had used a 13 Baktun cycle, but when they wished to continue beyond this point they created a 20 Baktun cycle instead, to fit in better with their numeration system [3]. Thus the Mayans created 4 more units beyond the Baktun, each 20 times greater than the previous one. We do not know the original names of these units but Mayanists have traditionally used the terms Piktun, Kalabtun, K'inchiltun, and Alawtun, with some variations in spelling (For convience I'll use these terms as well). There are some inscriptions that suggest that the Mayans went even further than this, though there are no official terms for units past the Alawtun, though the term Hablatun has been used for the unit just above the Alawtun.
The completion of the first Piktun after creation will occur on 1.0.0.0.0.0 or October 13th 4772 A.D. Perhaps when the notion of a Piktun cycle becomes more popular this will be the new "end of the world" date people look for. Although this is only 7 Baktun's from 2012, this is still pretty far in the future, but the Mayans looked even further into the future and past than this.
The Mayans saw the number 13 as sacride. They believed that there were 13 major joints of the human body corresponding to 13 major points in the heavens, and that one effected the other. It is also possible that 13 represented "completion" to them. The number 13 can be seen to pop up alot of their dates, especially dates projected far into the future or past.
For example on "Quirigua Stela 4" there is an inscription which records the date of 13.13.0.0.0.0.0.0.0. In this case this represents a date in the far future ... about 800 million years from now! As a number this represents a count of exactly 314,496,000,000 days after creation (approx. 861,061,509 solar years). Don't wait up for the Mayan apocalypse ... it might be awhile.
The Largest Number/date that has been found involves some 20 positions past the Baktun[4]:
13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.0.0.0.0
As a number this is:
10,331,233,010,526,315,789,473,684,112,000 [2]
Although the purpose of this date is unclear there is evidence that this was a symbolic extension of the creation date. In essense it suggests that there was been countless cycles that lead up to the "Mayan Creation date", and the world has been created many many times. Because the Mayans believed time was cyclical this could just as easily represent a time in the distant future. If so it would represent a time approximately 28,285,978,483,700,000,000,000,000,000 years in our future. This is a time frame roughly 2,064,000,000,000,000,000 times the current age of the universe! And there is no reason not to think that the Mayans might have gone further still, if not in the written record than in their minds eye. Doesn't the above date suggest that the Mayans believed the universe was eternal. If a date of 13.0.0.0.0, could be expanded out to 13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.0.0.0.0, why couldn't it be expanded to ... ... ... ... ... ... ... ... 13.13.13.13.13.13.13.13.0.0.0.0 with any number of 13s, any number of completed cycles of ever increasing size! The Mayan view of time was that it was far more ancient than even they could imagine, it would seem. Constrast with the rather small world view of the hebrew people who believed that the world was only a few thousand years old, and whose creation was a once in eternity event never to be repeated. In working with such hypothetical dates the Mayans were using numbers much much larger than those used elsewhere during the same time period. The Egyptians numeration system didn't have denominations above 1,000,000, and they used such a denomination so infrequently that the glyph for it was synonymous with the ancient worlds version of infinity (countless). But for Mayans mere millions were not countless at all, and they worked with numbers not in the billions, or even trillions, ... but nonillions (we'll learn more about extending millions, billions, and trillions in chapter 2.4).
All of this begs the question: why were the Mayans so interested in extending their calendar so far? What significance could events millions of years in the past or future, let alone even longer times, have to indigenous people. Did they really think the universe was that ancient? And even if they did, why did they bother inscribing it. Perhaps they thought the universe was eternal. If so why even bother with times outside of your own civilization. Isn't it enough to know that the past and future extend indefinitely without troubling yourself with the details? There can only be one answer : they were fascinated by a universe that was both vast and ancient, and they sought to grasp both it's size and age through their numbers and their calendar. Human beings seem drawn to the vast, even while it frightens them and makes them feel impossibly small. I don't think what drove the Mayans to consider such vast amounts of time was all that different than what drives people interested in Large Numbers to study them. It's but one small step of abstraction to pass beyond a fascination with the vastness of the world around us to a fascination with vastness itself. For me it's one and the same. Perhaps the Mayans would agree...
Written Sources:
The Complete Idiot's Guide to 2012 : An Ancient Look at a Critical Time, by Synthia Andrews and Colin Andrews
A History of Pi , by Petr Beckmann, pgs 33-35.
Internet Sources:
[1] http://en.wikipedia.org/wiki/Mesoamerican_Long_Count_calendar
[2] http://www.pauahtun.org/Calendar/calglyph.html
[3] http://mayan-calendar.com/ancient_longcount.html
[4] http://en.wikipedia.org/wiki/2012_phenomenon
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