Recovering the Lost World - Part 19: The day of Kan

Recovering the Lost World,
A Saturnian Cosmology --Jno Cook
Part 19: The Day of Kan and
the Course of the May.

[Table of Contents]
$Revision: 21.41 $
Contents of this chapter: [The Day of Kan] [2349 BC] [1492 BC] [747 BC] [3114 BC] [685 BC] [The Course of the May] [San Lorenzo] [Monto Alto] [Tres Zapotes] [La Venta] [The Third Conquest] [Monte Alban] [Teotihuacan] [Tula] [Cholula] [Summary] [Endnotes]
This continues the investigation into the Mesoamerican site alignments started in a previous chapter. My main purpose originally was to check site alignments to mountains and volcanos among early Olmec sites and locations in the Valley of Mexico. The data showed conclusively that the change in the inclination of the Earth's axis could be verified from site alignments before and after 685 BC.
What I will do in the following is to provide a basis for what looks like region-wide concerns about some dates in antiquity which were 'determined' by the Olmecs and the people of the Valley of Mexico, with special attention to Monte Alban. Additionally I will attempt to integrate the large sculptures (like the massive heads) into the outline of history provided at the end of the previous chapter.
Finding the Day of Kan

Two things stand out, first the notion that the new creations of Earth fell on the 'day of Kan,' and secondly that this happened in a Katun 9-Ahau. Both of these ideas apparently dated from remote antiquity, from the time of the "third creation" of 2349 BC (which I will show below), and were verified (so to speak) by data of other catastrophic events of the past.
Whatever wasn't known could be retrocalculated once the Long Count was established. And it looks like that this may certainly have been done for the "second creation" of 3147 BC, which, however, calculated to 3114 BC.
The timing of the event of 685 BC -- and thus the calendar days -- involved some amazing numerical coincidences. The nova event of Venus ended (completed) on July 25th (Gregorian), 52 days after June 6th, which was the summer solstice before 685 BC. When the concluding event of 685 BC (on July 25th) was later adopted as a date to celebrate, it could be found as 52 days after the summer solstice (as Malmstrom has pointed out), but now counting from June 21, falling on August 12 or 13. This 52 day interval may have seemed important, for '52' is four rotations of the 13 days of the Tzolkin calendar. Interestingly, it is also true that the horizon location of the setting Sun for August 12 before 685 BC and July 25 after 685 BC are nearly identical, but in reverse order from what we would find helpful.
I am bringing this up because it is really strange how soon the year 3114 BC was derived, or, actually, the date of August 12 or 13. Some stelae also announce the Long Count date of 13.0.0.0.0 -- which is recognized by us as 3114 BC. It assumes that the Olmecs performed the same retrocalculation based on a year of 375.24 days per year. More on the 3114 BC date further below. First we need to review what was obvious and well known to the Olmecs.
Teotihuacan celebrated both July 25 in the solar year and August 12. The giant city of Teotihuacan (200 BC to AD 700) is the primary example of the August 12 alignment. The city was built on a rectangular grid, with the main avenue aligned 15.5 degrees east of north. (Many other sites apparently also used this axial alignment, per Malmström, but I have few accurate details.)
At the center of the main avenue of Teotihuacan (called "the Street of the Dead" by the Aztecs) is the giant Pyramid of the Sun (also appropriately named by the Aztecs). The Sun sets directly opposite the Pyramid of the Sun, that is, at right angle to the Street of the Dead, on August 12.
Vincent H. Malmström suggests that the date of August 13 (the following day) celebrated the birth of the "second creation" of the world in 3114 BC. This is possible, and may be a coincidence resulting from the much later retrocalculations, perhaps after AD 400 (which I will take up further below), under the assumption that the solar year consisted of 365.24 days, not 360 days, as the Olmecs had known in 747 BC. It is more likely, however, that the selection of August 12 initially had more to do with aspects of the nova event of Venus in 685 BC, when the sky rotated and the solstice relocated.
The "day of Kan," was New Year's Day among the later Maya, celebrated July 26th, and noted by Landa in the 16th century AD, when July 26th actually coincided with a 'day of Kan' on the Tzolkin calendar. But the 'day of Kan' only fell on this day every other decade or so (twenty year intervals). It is clear that the 'day of Kan' is a generic name for the New Year Day, and not of necessity an actual Tzolkin calendar day.
Since 685 BC the day of Kan corresponding to July 26th rotated through the Tzolkin calendar, beginning to fall on July 26th only in 672 BC, Gregorian, and returning every 20 years or so.

---- event --- --year-- ----Aug 13 Long Count---- interval original date 685 BC 6.3.4.5.16 9-Yax 1-Cib first Kan date 672 BC 6.3.17.9.4 12-Yax 4-Kan 12 years first repeat 653 BC 6.4.16.14.4 17-Yax 2-Kan 19 years second repeat 630 BC 6.6.0.2.4 7-Zak 4-Kan 23 years third repeat 611 BC 6.6.19.7.4 7-Zak 2-Kan 19 years

And so it goes. As can be seen from the chart above, the primacy of the day of Kan is not easily established. The day of Cib would have done better. But "Kan" means maize (as well as "snake" and "sky"), first of all, and secondly, I suspect that, well before 685 BC, the 'day of Kan' was already established as the day a previous creation had come to an end or been renewed. [note 1]
After 685 BC attempts must also have been made to again rationalize the start of the current creation to a "day of Kan." The rationalization involved the simple suggestion that the day of Kan had fallen 12 days earlier, that is, it fell on July 14, Gregorian, 685 BC, which is 6.3.4.5.4 17-Chen 2-Kan on the August 13 Long Count.
This was perhaps misapplied science by the Olmecs, but it seems to have taken hold, for I suspect that the massive remodeling of the Monte Albán ceremonial center in ca 275 BC, which seems to have revolved around an alignment correction of 12 days, might have been one of the results stemming from this concept. Additionally, the Olmecs and the people of the Valley of Mexico start to align many of the ceremonial sites to the day of July 14th (12 days before July 25). This suggests that something significant happened. [note 2]
Of course, I am approaching conjecture here. But if I may be allowed to continue (and the following is not conjecture), I would suggest that the Olmecs kept day-books, like the Babylonians, Egyptians, and other literate people. They could look up the records of the past. The documents of the ceremonial centers in the Valley of Mexico were only destroyed when the Aztecs arrived. The Maya records survived until the Spanish arrived. Only a last-minute transcription to the "Books of the Chilam Balam" has saved, for our benefit, a summary record of the past, dating back thousands of years. The "Chilam Balam" frequently makes casual references to actual dates and time intervals, indicating details which must have existed in the source documents. The "Chilam Balam," in fact, provide five specific dates (as time intervals) for the summer of the year 685 BC.
What might have happened 12 days before July 25th when the plasmoid bolt of Jupiter ended an era? What comes to mind, of course, is that the plasmoid lightning bolt must have taken some time to travel 484 million miles. The Solar Wind leaving the Sun travels past the Earth at about 2 million miles per hour. It apparently does not speed up significantly after passing Earth. If a bolt traveling from Jupiter also averaged that speed, it would take 10 days to cross the 5.2 AU distance to the Sun. The Olmecs, by selecting the primacy of "the day of Kan," for July 14th, in effect are suggesting it took 12 days.
Jupiter probably flared up weeks before the return stroke was released. The specifics of the illustrations which were developed by the Olmecs, and which eventually became the religious iconography of the Maya, would require that Jupiter was clearly seen and recorded for a reasonably long period. From other alignments adopted after 685 BC, it would look like the date of the initial flare-up was July 9th. The "Chilam Balam" fully concurs in this selection.
At Monte Alban the rationalization of the Tzolkin calendar involved restarting the Tzolkin annually on August 14th. The fourth day of the Tzolkin, 4-Kan, would then fall on August 17th, the day when the Sun had passed overhead of Monte Alban in the era before 685 BC, when the Earth's axis was still at an inclination of 30 degrees. And the "day of Kan," everyone knew, had started the current era, as it apparently had started every change in the constitution of the heavens, or so it was thought to be.
After 600 BC the August 12 alignment was adopted at many locations -- but so were the three dates in July of 685 BC, and equally the date of September 8, which indicated the start of the "third creation" and constituted the completion of the previous world order. The dates of 1492 BC and 747 BC were known. The date of the "third creation" (2349 BC) was retrocalculated, probably by 600 BC, from the knowledge that it involved a culmination of the Pleiades Before 685 BC, that happened about September 8th, two days after the fall equinox of September 6th (15 days earlier than today). Directly after 685 the culmination occurred on about October 8th, and then started to drift later into the year with the precession of the equinox. As we know, the celebration shifted from the calendar date of October 8th to the day of the culmination of Pleiades which moved later and later into the year after 685 BC.
The "day of Kan" for 2349 BC

The obsession of Mesoamerica with the 'day of Kan' can be related directly to the cataclysmic event of 2349 BC, the "second creation," the fall of the Absu, the flood of Noah. From this, and from retrocalculations of the event of 1492 BC, it may have seemed obvious that any new era had to start on the 'day of Kan.' Two data points define an infinite set of curves, but for humans the coincidence typically is overwhelming evidence that an established relationship exists.
The "Chilam Balam" relates the 'day of Kan' to the time of the "second baptism," that is, the flood of Noah in 2349 BC. Much later recollections of the Maya of the Yucatan recall a flood which separated two eras. It is also referenced in both the "Popol Vuh" and the "Madrid Codex." But the "Chilam Balam" is the most specific, assigning it to a Katun 9-Ahau, which can be placed to the Long Count date of 2.2.0.0.4 2-Kan on the August 11 correlation, although the year is incorrect, for it was obviously retrocalculated to fit the July 26th horizon location. It is, in fact, as I have pointed out earlier, the only instance in the whole of the 6000 year Long Count calendar when the day of Kan actually fell on July 26th.
What probably came down from remote antiquity, well before 1492 BC, was information about this "third creation," the event of 2349 BC, what we know as "the flood of Noah." This had been the second "flood" and was a major marker in the histories of people throughout the world. The Israelites recognized it as "the flood of Noah;" China starts its history at this point. I have detailed this in Chapter 9, "The Career of Jupiter." For the Olmecs, one creation had ended and another one had started up, on the "day of Kan."
That was probably as much as was known from the records of the past in 747 BC, when the Long Count was developed, along with the common knowledge that this had happened on the "day of Kan." With the introduction of the Long Count, the Olmecs would, within a hundred years, have been making inquiries into the events of the past. These studies might have started well after 747 BC, however, for the results forthcoming from the inquiries only make sense if the Long Count and the Tzolkin calendar are used with the assumption of a 365.24 day year, not if based on shorter years before 747 BC. [note 3]
The Olmecs did not count in days before 747 BC, they counted and kept records in "tuns" -- a year. It did not matter if the year in previous ages had been 260, 273, or 360 days long. A tun was a tun, and the difference between the solar year of 2349 BC and the year 747 BC was 1602 tuns. The time of the flood, what the "Chilam Balam" called "the second Baptism," was thus 4 baktuns (4 measures of 400 tuns) and 2 years in the past from 6.0.0.0.0, February 28, 747 BC. The event could be placed in 1.19.18.0.0. The 'day of Kan' would be 1.19.18.0.4, always the fourth day of a Tun.
Using a 360 day year, an earlier 273 day year, and a yet earlier 260 day year, this would fall in 2349 BC, if the 'BC' years are counted as solar years. But of course we can't do this, we can only assume that it would work out like that. Using years of 365.24 days the above event of 1.19.18.0.4 would fall in 2327 BC. Additionally, the day would have been September 8th, as we know from the same Mesoamerican sources (the 2327 BC date falls erroneously on March 2). The second flood had nothing to do with July 26th. Yet this confusion existed.
Here is what was done by the Maya during the Classical Era: There was no 'day of Kan' to match a horizon location of July 26th during Baktun 1 Katun 19 Tun 18 (1.19.18.0.4). The solution was to consider the earlier return of the blazing of Jupiter and its mountain, perhaps in about 2500 BC, rather than the flood event of 2349 BC, as the start of the "third creation." The year 2500 BC falls in a Katun 9-Ahau. Taking a cue from "Katun 9-Ahau" it was found that in the following Katun 9-Ahau, on the day of 2.2.0.0.4, the 'day of Kan' fell on July 26th. This would not happen again in all of time, or at least until well after the present series of Katuns would turn over in AD 2012. The records of the past were changed accordingly, although the new date missed the flood of 2349 BC by 83 years. The "Chilam Balam" reports on the newly determined date as if it was fact. It is the only error in dating in Book 10 of the "Chilam Balam." [note 4]
And here is what most likely actually happened: First, the Tzolkin calendar was started in 2349 BC, in fact it probably started with the day the plasmoid from Venus arrived, September 6, 2349 BC. Another, separate page of the "Chilam Balam," dealing only with the "third creation," states that "then days of the year were introduced." We know that the people of Mesoamerica had been accounting in 'Tun' years since 8347 BC. It is also obvious that after 3147 BC a 240 day calendar consisting of 12 rotations of 20 named days was in use.
With the calamity of 2349 BC (and the first appearance of the Moon) an accounting of numbered days was added -- "days of the year were introduced." Thus to the established calendar of 20 named days were added a count of 13 numbers, representing a half period of the Moon. This resulted in 260 uniquely named and numbered days. The length of the year had just changed to 260 days. This is the Tzolkin, which fits the year exactly.
The Tzolkin that we are familiar with started on September 6, 2349 BC. On the third day of the new calendar Jupiter flared up ("returned from the dead"). By this time the smaller plasmoids from Venus had passed, and the turmoil in the sky might have subsided. Thus the third day (September 8th) actually marked the "third creation," and the next day would be "New Year's Day" of the "third creation" of the world. This fourth day was the "day of Kan," as it always is for the first Tun of a new Katun.
The fact that a Katun and Tun had just started on September 6 (the fall equinox before 685 BC) may be coincidence or it may be purposefull. It can be suggested that a new year normally started at the fall equinox. Since the previous calendar of 240 days rotated through the 20 day names 12 times, a new year would always start on day-name Imix. The fourth day would be Kan.
Since the Olmecs already had a year-count in use of named Katuns (20 year periods) and Baktuns (400 year periods), it is possible that this was actually the start of a Katun 9-Ahau. Otherwise the notion that the "third creation" started in a Katun 9-Ahau might have followed from what had happened in 747 BC, when the Long Count was started at the beginning of a Katun 9-Ahau.
The "day of Kan" for 1492 BC

For 1492 BC, I thought initially that perhaps I could just roll back the Tzolkin calendar from February 28th, 747 BC, compensating for the fact that the year was of a different length, and do a search for when in the remote past -- somewhere around 1492 BC -- a Gregorian equivalent day of April 19th would have coincided with a day named "Kan." But this yielded no sensible results. I subsequently considered that perhaps the Olmecs or the people of the Valley of Mexico might already have made the calculations using the Tzolkin and a record of events from antiquity.
I thus checked the Gregorian date of April 19, 1493 BC (-1492 in astronomical nomenclature). It turns out to fall on 4.2.4.5.4 6-Kan (August 11 correlation). The day of April 19 will not again fall on the 'day of Kan' for many years before or after 1492 BC (22 years earlier, 25 years later).
Those applying the Long Count obviously had forgotten that the year had lengthened in 747 BC, or it did not matter for a calendar which rotated through the year, and the retrocalculations were performed as if the solar year had always been 365.24 days long. This would suggest that the retrocalculations were made some time after 650 BC.
Consider how important 'era-ending' dates were for the Zapotecs, who made the investment of remodeling Monte Alban by completely leveling off a mountain top and reconstructing all the buildings (except one building away from the main structures) to face a different direction, so that the end of an era could be pointed to. The 'day of Kan' was held as a sacred truth; it was the name of the day each era had ended. [note 5]
Of course, the remodeling of Monte Alban does not prove that by 275 BC the 360 day year had already been forgotten. Nor does the introduction by the Zapotecs of an annual version of the Tzolkin calendar, restarting each year on August 14th, so that the 4th day, 4-Kan, would fall on the Gregorian equivalent day when, 400 years earlier, the Sun had passed directly over Monte Alban on August 17th. But being able to use the day number and a day name of Kan to coincide with a zenithal Sun at their sacred location, was important enough to the Zapotecs to break faith with all the other tribes in Mesoamerica and refashion the sacred Tzolkin to their own needs. No other tribe ever did that.
Note that, as with the date of July 26th, 2349 BC, above, this works out on the August 11 correlation, not the August 13 correlation. The 'day of Kan' of 1492 BC was derived by use of the original Long Count. It also suggests that the notion of a 'day of Kan' came from much older sources. This can be seen, as I have shown, also from the 1492 BC alignments which show up at the oldest site, San Lorenzo. [note 6]
The "day of Kan" for 747 BC

Working backwards with the Long Count notation, no 'day of Kan' can be found at 6.0.0.0.0 for 747 BC, except that a 'day of Kan' follows four days later (6.0.0.0.4) as it always does at the beginning of a Katun. But what the event of 747 supplies, is the start of an era in a Katun 9-Ahau. It hardly seems that the occurence of this in 747 BC would have been assigned so much importance as to determine the rewriting of the books of recorded history as synopsized in the "Chilan Balam." It should also be noted that the "Chilam Balam" places the events which follow directly after 3114 BC (or 3147 BC) in a Katun 9-Ahau -- despite the fact that the Long Count date of 0.0.0.0.0 starts a Katun 4-Ahau.
Despite the lack of a 'day of Kan' for 747 BC, the era-ending is celebrated with alignments to volcanoes and mountains at La Venta (also with a site axis alignment), Tres Zapotes, Cerro de la Mesas, Remojades, Zempoala, Tlatilco, Cuicuilco, and Tlapacoya, 8 of the 13 sites I investigated.
The Earth shock of 747 BC was not understood to be the end of a creation. The destructive close passes of Mars continued for another 60 years (as they also had preceded 747 BC by 60 years). There is virtually no mention of this event in the "Chilam Balam" and none in the "Popol Vuh." Instead, it was the events of 685 BC which are brought forward as the relief from an impending end of creation -- or as another recreation of the world.
The "day of Kan" for 3114 BC

For 3114 BC no actual 'day of Kan' can be found. (I have to use 3114 BC here, rather than 3147 BC.) Of course the fourth day of the new era, 13.0.0.0.4, is 4-Kan.
The suggestion by Vincent Malmström, that the various and frequent site orientations to (about) 15.5 degrees north of west all represent the celebration of the start of the current epoch, on August 13, 3114 BC, would has credence. In an article written in 1981 Malmström lists some 20 sites with axial alignments at 15.5 degrees north of west and thus pointing to a sunset on August 12. [note 7]
Of the 13 sites I investigated, 8 have alignments reflecting some aspect of the August 12 or 13 date, La Venta, Tres Zapotes, Cerro de la Mesas, Teotihuacan, Tlatilco, Tizatlan, Cuicuilco, and Tlapacoya. At Tres Zapotes, which may have preceded La Venta, the zenithal sun passes over the site on August 13 before 685 BC.
At La Venta there are two alignments representing April 19 (15.22 and 15.32 degrees north of west) before 685 BC. These were not corrected after 685 BC, but likely became the markers for an August 12 sunset. It is also likely that the zenithal passage of the sun on August 14, before 685 BC, reflected in sunsets at 19.35 degrees (n of w) and 19.50 degrees (s of w), might have been meant to represent the date of August 13, but as the day after (thus a New Year's Day).
Only at Tres Zapotes or at La Venta could the calculations have been made, after the institution of the Long Count, to find the day of the "second creation." To find the August 13 date, shortly after 747 BC, as was certainly done at Tres Zapotes, is rather stunning. First, because it assumes that the Olmecs wasted no time in the research potential of the Long Count, and, second that in a very short span of time the original length of the year, 360 days (whose measure was incorporated in the Long Count), had been forgotten.
The "day of Kan" for 685 BC

Having found, or verified, the 'day of Kan' for three past creations, the scribes and day-keepers seemed to have been satisfied, for these two dates were never again corrected or accessed. A more important problem came forward: What was the day of the current creation, the events which were witnessed in 685 BC? For this everyone had accurate records, to the day, and certainly for the sunrise and sunset horizon locations.
We could imagine a conference of scribes, recorders, and day-keepers from surrounding cities and ceremonial centers convened at Teotihuacan some time during these centuries for the purpose of hammering out the theological difficulties. Most sites already had alignments established long ago, selected from four dates in 685 BC, and a large number which recalled earlier era-endings.
The solution seems to have been to move the Long Count up by two days, by dropping what is known as the August 11 correlation for the competing August 13 correlation. This made it clear that the day Jupiter released its plasmoid thunderbolt, July 14, 685 BC, fell on the day of Kan -- 6.3.4.5.4 2-Kan, on the August 13 correlation.
I should note that, considering the sacredness of the Tzolkin, it would seem impossible that the Tzolkin could have been moved by two days. More likely the August 13 version arose from an early misunderstanding in its adoption by some tribes, although it would have to be at a time when the Tzolkin and Haab were already widely distributed. Possibly this happened in 747 BC, when some tribes did not acknowledge the two days which were missing because the sun had not risen as the Earth's axis went through a spin. The Long Count, where it was adopted, was added in each instance of its adoptation to an on-going tally of the local Tzolkin calendar. The days of the Tzolkin (and the Haab) are the same sequence in both versions of the Long Count.
The Zapotecs of Monte Alban must have worked under the same prohibition of interrupting the calendar. Thus when they switched over to an annual calendar which would restart every year on August 14th, this must have been done when the day 1-Imix, the first day of the 260 day Tzolkin, corresponded to our calendar day of August 14th. This happened only three times in a span of about 2400 years, in 439 BC, 523 BC, and 607 BC. Of these three, the last date listed corresponds to the first archaeological dating of the site of Monte Alban.
The Course of the 'May'

"One preplexed writer suggested that the Mesoamerican Olmecs aligned their structures with the Big Dipper. When neither the north-south axis nor the solar behavior nor a constellation fits the orientation, then it is that the ancients could not tell directions well, or that the matter in any case was not important to the builders."
"What is absent from such reasoning? First, there is a failure to appreciate that the desire to orient to the skies was an obsession, a compulsion, an inescapable tradition, a sacred obligation, a proud duty. Second, the ancients, as far back as we can discover their humanity, could calculate readily and exactly the course of heavenly bodies and orient themselves thereto. Many examples of this are presented in G. de Santillana and H. von Dechend's book, 'Hamlet's Mill.'"
-- Alfred de Grazia, "The Lately Tortured Earth" (1983)

We can thank the Olmecs for recording for us, in the site selections for ceremonial centers, the alignments of the heavens before and after the 7th century BC, and Vincent H. Malmström for pointing these out to us. In the following few paragraphs I will review the changes already noted above, and in the previous chapter, but in a broader historical perspective.
The sequence will be based on the fact that the interval between approaches of Venus was known by the people of Mesoamerica to be 52 years, at least, in an earlier era. The actual 'Venus interval' at various times is detailed in Appendix B, "The Celestial Mechanics."
Munro S. Edmonson, in an essay "Some Postclassic Questions About The Classic Maya," proposes that, at least for Post Classical and Colonial times, some Maya ceremonial center were designated as a type of central capital city, for a term of 20 years, that is, the duration of a Katun. He writes..
"The Books [the "Chilam Balam" books] explicitly say they did. In the Postclassic and later the cycle seat ('may cu') was the primate city of a region. It was not a capital in any normal sense, but rather a holy city, recognized by the title Born of Heaven ('ziyan can, can sih'), and notable for its sacred ceiba tree ('yax che'), its sacred grove ('tzucub te'), its sacred well ('ch'en'), and its plaza, which was the crossroads ('hol can be') and navel of the world." [note 8]

Edmonson claims that there was a larger cycle consisting of 13 Katuns, an interval of about 256 years, and would suggest that this could be extended back in time. He notes that the period of primacy (the 'may') always ends at Katun 8-Ahau. About the abandonments, he writes..
"The Postclassic Maya destroyed the primate city and its road at the end of the 'may.' There are indications that this 'destruction' may have been largely ritual and symbolic, and that the 'abandonment' of the city was an evacuation by the ruling dynasty rather than total depopulation." [note 9]

I do not think we can hold that the later Katun endings used by the Maya could be extended backwards in time to San Lorenzo. But the concept of primacy of a single location seems to have existed. However, we have to use a different cycle, not the rotation of 13 Katuns. Most appropriate, in the era when Venus was the main threat, this might have been an interval of periods of 52 years. As it turns out, a period of ten 52 year periods seems to have been in use -- 520 years -- which equals two cycles of 13 Katuns.
It has been estimated that San Lorenzo was destroyed and abandoned in about 900 BC. The first Baktun and Katun ending in 8-Ahau before about 900 BC is 868 BC. Additionally, San Lorenzo was only in use after 1440 BC. If we use the first Baktun and Katun ending in 8-Ahau after 1440 BC, which is 4.9.0.0.0, 1367 BC, then the span of time to 868 BC is two cycles of 13 Katuns -- 520 years. In fact, this cycle of 520 years can be readily traced forward (and backward) in time, to include, for example, the well dated site of Teotihuacan. This 520 year period also hints at the fact that the previous era might have been of the same measure. I will address this further below. Thus the primacy of San Lorenzo was from 1367 BC through 868 BC, when it was destroyed and abandoned. [note 10]
Because with the establishment of the Haab calendar (of 360 days) after 1492 BC or 1440 BC, the people of Mesoamerica recognized a 'world ending' date, when the same day name and number on the Haab and Tzolkin calendars recurred -- a period of 52 years (initially of 360 days). This interval became high science for the Olmecs, as well as all the later people of Mesoamerica, for it had a certain numerological beauty. If fact, I suspect that the whole of calendaric history after 1440 BC, when the Haab calendar was established, lies suspended between math and magic. As I have pointed out in an endnote to Chapter 14, "Language and Subjective Consciousness," Colonial native documents which propose to reveal the history of the region in deep antiquity, as for example, the "Annals of Cuahitlan," make claims to ages of the world which are uniformly reported as products of 52 and 13 years and their differences.
We have no evidence that Venus might have aligned with Earth at regular 52 year intervals after 2193 BC. I have shown, in fact, that the period would have dropped to 47 years after 2193 BC, and was 50 years between 1492 BC and 1442 BC. (See Appendix B, "Celestial Mechanics.") Yet the expected end of the world was still celebrated at the time of the Spanish invasion in the 16th century AD, even though by this time the dates of the '52 year round' had not coincided with alignments of Venus for over 2000 years. Since some time after 747 BC, Earth and Venus had settled into regular and mostly circular orbits, and Venus would be seen rising at the same horizon location every 52 Haab years (and in fact, every 8 years).
I dislike numerological analysis of ancient history, but, considering the seriousness with which the Mesoamerican people seems to have approached the same subject -- to the point where most of the Maya monuments deal almost exclusively with time periods and Katun endings -- it might in this instance be appropriate. I'll follow Edmonson's suggestion of the existence of the 'may,' but I will not use a single cycle of 13 Katuns (260 years), but a period of 2 cycles of 13 Katuns, 520 years (2 * 13 * 20 = 520 years). This is also 10 cycles of 52 years, and this is probably what defined the 'may' in remote antiquity. I'll start with the second 'may' in order to settle some dates and practices.
The Second 'may' at San Lorenzo, 1367 BC to 847 BC

In Veracruz the oldest Olmec site, San Lorenzo, dating from around 1440 BC, shows two alignments with the mountains El Chichon and Zempoaltepec, for a date of an April 19 or 20 sunrise and sunset, recalling the start of the era after 1492 BC. An additional alignment with Popocatepetl signals the day (sunset) that the Sun passes directly overhead, on August 15.
I would suggest that the site of San Lorenzo was significant to the Olmecs in preventing the repetition of attacks on Earth by the planet Venus after 1492 BC, or, more likely, after 1440 BC (or 1442 BC). The giant heads excavated at the site would then represent Venus. A new head would be carved every 52 years as Venus was expected to approach the Earth again, to be used in some preventive ceremonies, and buried when the crisis had passed. Starting after 1367 BC and extending to about 900 BC, some 10 or 11 giant heads would have been carved and disposed of. Dates can be selected as multiples of 52 years, starting from 1492 BC. Even if the dates are not correct, dividing the 520 year span of time of the 'may' by 52 yields an estimate of 10 heads. Ten heads have been found.
The actual 'Venus cycle' after 1440 BC was probably 50 years -- if it existed at all. But the 360 day Haab had been devised, and the Olmecs were thoroughly convinced that the appearances of the celestial Gods followed their calendar. It may be that the two contacts of 1492 BC and 1442 BC were actually 52 years apart, since we know almost nothing of the orbits of Venus and Earth between these two dates. We also have no evidence that Venus was ever again involved in a catastrophic approach to Earth after 1442 BC.
What I am suggesting is that the celebration of the '52 year interval' was most likely entirely ritualistic and based only on calendarical considerations. Thus, although the actual Venus cycle varies from 47 to 52 years, I have used a Venus cycle interval of 52 years throughout most of the chart presented below. For the period of 2193 BC to 1492 BC I have used an interval of 47 years. This would be suggested from the fact that there was no Haab calendar, and the intervals might represent actual sightings of Venus and would be counted in Tun years, representing solar years of whatever length.
About the heads, I would further suggest that they were indeed intended to resemble ball players (after all, Venus bumped the Earth like a ball player in 1492 BC), and are additionally wearing flayed human faces as a mask, which last would account for the swollen lips and flattened nose. There is no question that the Olmecs played games with a rubber ball. That has been archaeologically established. The mask designates the depiction as representing a God, as is clear from contemporaneous and later iconography. That flayed human faces were depicted is clear from an inspection of smaller sculptures, shown with eyes in deep outlined sockets, incised lines along the left and right sides of the faces, flattened noses, and rolled back lips. A mask, or wearing a mask, was, since the Olmec era, the disguise of a God. [note 11]
After 520 years of preventing disaster, the site of San Lorenzo became irrelevant, and in about 900 BC the ceremonial center was destroyed and abandoned. I would suggest the year of 847 BC, the end of the 'may.'
The First 'may' at Monte Alto, 1887 BC -- 1367 BC

If San Lorenzo then held its period of primacy for "10 periods" of 52 years on the basis that some previous site had also held its primacy for an identical period of time (and was destroyed), what site was this? We do not really know. It would have to be a site with an occupation dating back to about 2000 BC.
A likely site might be located in the Soconusco region of Guatemala, along the Pacific coast and in a tropical region similar to Mexico's Veracruz. This includes Izapa, El Jobo, Abaj Takalil, Chocola, Chukumuk, Kaminaljuyu, El Baul, and Monte Alto, all of which are located along a 120 mile coastal strip. All the sites share the same art style, and share this with Tres Zapotes in Veracruz. Some sites are dated to have had their start in the period of 1850 BC to 1650 BC, thus 200 to 400 years before the establishment of San Lorenzo. But dates to 2000 BC have also been suggested.

Image: Stone head ("Monument 1") from Monte Alto, Guatemala. After Michael Coe, "The Maya" (2005)

What is of interest is that 11 large undated carved heads or rotund bodies with heads ("fat boys") have been found in a cornfield near Monte Alto, the southmost site. Malmström describes them as..
" .. large rounded boulders, often 1.5 m (5 ft) or more in diameter, were selected as the medium upon which either the rudimentary features of a head or a body were etched out in bas-relief. Only a minimal amount of carving was done, so in all cases the faces have a decidedly bloated appearance and the bodies are corpulent."
"The heads that were depicted tended to have a fairly similar, generic appearance. If they were intended to highlight any individual differences, their sculptors appear to have been singularly unsuccessful, although a few of the heads do have some strikingly unique characteristics."
"The bodies, on the other hand, almost invariably have the arms wrapped around them so the fingers of the hands nearly come together over the fullness of their abdomens, and the legs and feet often do a similar encircling act near the base of the sculpture."

There are other large sculptures in stone in the Soconusco region, including heads, turtles, and reclining jaguars. But the collection at Monte Alto is amazing and unusual. The oldest of these are estimated to date to 2000 BC.
The collection of 'fat boys' suggest that, like at the later San Lorenzo these might represent efforts at staving of the destructions which might have resulted from the passages of Venus at 52 year intervals. The sculptures would have been created over the course of 520 years, the term of the primacy of the site.
In Appendix B, "The Celestial Mechanics" I developed that during a yet earlier era, 2349 BC to 2193 BC, Venus indeed made contact with Earth, or crossed Earth's orbit at 52 (solar) year intervals. During the next period, 2193 BC to 1492 BC, I would suggest that the '52 year period' was reduced to 47 years. If during some 520 year period ending in 1492 BC or 1442 BC the fat boy bodies were carved to coincide with the 47 year intervals, then we could divide 520 years by 47 to find that 11 sculptures would have been carved. Eleven heads and bodies have been found.
Assuming that the primacy of Monte Alto indeed extended to 520 years, then it seems that the efforts at the prevention of disasters seem to have carried right through the Pacific contact by Venus of 1492 BC, and the later 1442 BC event. We cannot neglect the Earth shock experienced in 1492 BC in the Pacific. It sent tsunamis across the Pacific, reaching to China, and certainly the whole of coastal South Anerica and Central America. This may have been the event which made the shamans of Monte Alto conclude that the effectiveness of their services had come to an end.
Another solution, in line with later practices, would be to suggest that the nearest '8-Ahau' closing date after 1492 BC or 1442 BC would apply, which would be 1367 BC, the year 4.9.0.0.0 8-Ahau. Baktun 4 and Katun 9 were known, as was the fact that the last day of the Tun was 8-Ahau. It had been shown, the old records would reveal, that a site could only hold its mandate until 8-Ahau was reached, and ten cycles of 52 tun years had lapsed.
Following the event of 1492 BC, the Haab was established, and now a rotation through the two calendars would repeat any Tzolkin and the Haab day name-number every 52 tun years. The knowledge that, 700 years earlier the potential end of creation had indeed occurred at 52 year intervals, now became the method of choice in warding off the end of creation at San Lorenzo. Venus, however, never again crossed Earth's orbit after 1492 BC or 1442 BC, and the interval between approaches after 1492 BC was not 52 years, but 50 years. Actuality. it seemed not to have mattered, what the calendars predicted was important.
The Third 'may' at Tres Zapotes, 847 BC to 747 BC.

It is easier to identify a site which take on primacy after San Lorenzo. The most likely choice seems to be Tres Zapotes. The site is located so that a zenithal passage of the Sun happened on August 13 during the time before 685 BC (and rises out of Vulcan San Martin Tuxtla). There is also an alignment for February 28, also conformed to the era before 685 BC. There are additional alignments, also for before 685 BC, for July 25 (two) and July 9.
San Lorenzo had performed their last preventive ceremonies in 892 BC. Thereafter, or soon thereafter, primacy passed to Tres Zapotes who proceeded to carve the large stone heads for the next expected approach of Venus, first in 816 BC, and again in 764 BC -- two heads. Two heads have been found at Tres Zapotes. The third expected approach of 712 BC never materialized, for before that date, in 747 BC, Mars shocked Earth, Tres Zapotes was destroyed by a celestial catastrophe, and after that everything changed. [note 12]

Image: Rancho La Cobata stone head ("Monument 1"), 11 feet high.

It might be suggested that an unusual head ("Monument I"), found at Rancho La Cobata, near the site of Tres Zapotes, was originally destined for delivery to Tres Zapotes for a ceremony after 747 BC (but perhaps after 685 BC), but was never delivered. Rancho La Cobata is thought to be a stone workshop for Tres Zapotes. The head found at Rancho La Cobata, and the two found at Tres Zapotes, are local and similar in style, differing from those found at San Lorenzo or La Venta.
The head at Rancho La Cobata is absolutely enormous. It stands over 11 feet high, whereas the heads found at San Lorenzo vary from over 5 feet to 9.5 feet tall and the heads at La Venta vary in height from 5.5 feet to 8 feet. But what is most unusual is that, unlike all the other heads, it was carved with closed eyelids and with a down-turned mouth similar to the "snarling" down-turned mouths found on the later "were-Jaguar" sculptures at La Venta. It is the face of a dead person.
This giant 11 foot high boulder may have represented the death of Venus or Mars. The bolt from Jupiter in 685 BC was clearly understood to end the brilliant display of Venus, although others understood it as representing the end of threats by Mars. The plasmoid prevented another destruction of the world, and removed Venus from the vicinity of Earth (as it also did for Mars).
The Third 'may' passes to La Venta after 747 BC

After 747 BC La Venta became the next center for the prevention of celestial disasters. The change in primacy was unexpectedly soon, certainly not the 520 years that San Lorenzo had been in use. Even if Tres Zapotes retained primacy until 712 BC, three periods of 52 years, 156 years, this represented less than 8 Katuns. This may have been the event which changed the period of primacy as defined by Edmonson. I think, however, that the 52 year counts continued. More on this below.
La Venta became a primary ceremonial center after 747 BC, and certainly a likely founding date for La Venta, as a ceremonial center, would be 747 BC. The site was selected to have alignments for April 19, 1492 BC but also for February 28th, 747 BC. The alignments were conformed to an axial inclination of 30 degrees.
There would have been five opportunities to carve a head representing Mars and prevent disasters after 747 BC, if the date of 747 BC is included. Certainly Mars was prevented, through whatever ceremonies, from becoming "the God of hell" (as the "Chilam Balam" calls the attempts by Mars at ending creation). Either four (or five) heads might have been carved before Bolon-ti-ku, Jupiter, called it off in 685 BC. Four heads have been found at La Venta. Five "elaborate tombs" have been found at the site, and five large caches of serpentine blocks. (The tombs will be reflected in the five houses used by the Gods of the underworld to keep the "Popol Vuh" twins Hunahpu and Xbalanque, overnight, in attempts to kill them.)
Seven basalt 'altars' have also been found, six feet high, and 12 feet wide, whose purpose is "still unclear" to archaeologists. The altars are reminiscent of the 'creation' altars built by Maya shamans today. If the Olmec altars celebrated recreations of the world at 52 year intervals, the sculptures would extend to 400 BC. This matches the archaeological date of abandonment of La Venta. If started in 712 BC, the 7th altar would date to 400 BC. At a height of six feet, these are not altars, or kingly thrones (as some archaeologists hold), but models of the raised sky. [note 13]
The theology of the Olmecs changed after 685 BC at La Venta as everywhere else in the world. The emphasis changed from warding off Mars to celebrating Jupiter as the God of deliverance. This resolved at Teotihuacan, some 400 years later, to considering Quetzalcoatl, Venus, as the saviour God through his self-sacrifice. The understanding reached in Mesoamerica of the events of 685 BC were in essence no different from the understanding achieved in the eastern Mediterranean region. The missionaries who followed the Spanish invasion after AD 1500, quickly understood the philosophical underpinnings of the Indian 'idol worship,' and at first considered that Christ had perhaps appeared to the Mexica and the Maya independent of his appearance in Israel.
When the inclination of the Earth's axis changed to 23.5 degrees after 685 BC, La Venta was remodeled (or the first monumental construction was started), aligning the long axis of the site to be at a right angle to the new horizon location for the date of February 28, 747 BC. The zenithal Sun still set in the volcano San Martin Tuxtla. The giant heads and the "number 9 Jaguar" mosaics, all of which were created after 747 BC, were retained or relocated.
The monumental construction at La Venta clearly recalls the events of 685 BC. This is shown in the iconography of stela and engraved ceremonial objects, and, in fact, by the creation of the first pyramid in Mesoamerica. The pyramid, a "red house," is the image of the lower plasma expulsion of Jupiter in 685 BC.
After having prevented the ending of creation in the era after 747 BC, and no doubt continuing with other functions for an additional 200 or 300 years, the religious utility of La Venta eventually also came to an end. The 'may' came to an end. There was no reason to carve additional stone heads. The shamans knew, too, that the site was not aligned with what was now considered the newest location of the end of the previous creation. There were no alignments to the dates of 685 BC at La Venta.
When was La Venta abandoned for another location? Archaeology suggests 400 to 300 BC. That suggests 7 periods of 52 years after 764 BC, when it most likely took over the mandate from Tres Zapotes. If we carry the 520 year period forward from the ending year of 868 BC at San Lorenzo, the end of the 'may' would fall in 334 BC for La Venta.
The Third Conquest

What is interesting, with respect to the status of La Venta, is an obscure reference to the ending of the second and third 52-year period at La Venta from inscriptions at the Maya site of Yaxchilan, 1300 or 1400 years later.
At a number of Maya ceremonial sites, ball courts are named as "First Conquest," "Second Conquest," and the "Third Conquest," and more frequently just as "Third Conquest." At the Maya site of Yaxchilan, three ballcourts are inscribing with a dedication date of October 21, AD 744. My first guess was that the date of AD 744 might have represented a multiple of 520 year intervals ('may' cycles) since some important date in antiquity, especially since dates were appended to indicate the first manifestation of the event significant to each of three ballcourt. The appended dates all point to the seventh century BC. As a matter of fact, AD 744 is 3 times 520 years (1560 years) since the first manifestation of the first collosal head at Tres Zapotes, in 816 BC.
"Conquest," as Schele and Freidel note, in "Maya Cosmos" (1993), was originally translated as "Creation" -- creation of the world -- which is probably more correct in the context I have presented here. Schele and Friedel note that "manifest" might also have been intended. I have estimated that a first, second, and third "Creation Altars" were built at La Venta in 712 BC, 660 BC, and 608 BC. These might have been recorded in ancient records as the "first," "second," and "third anniversary" of "creation." Information on these ventures was available to other sites through copies of "The Council Book" which, since 747 BC had recorded events at La Venta by Long Count dates.
The distance numbers of the Long Count dates of the three ballcourts are incomplete, so that at best Schele and Friedel could only suggest "1400 years before" the dedication date of the ball courts in AD 744. That places the dates of the original "First Creation," "Second Creation," and the "Third Creation" in the era when La Venta was the center of religious activity. As Schele and Friedel point out, the calculations based on distance numbers do not match the Tzolkin and Haab day names and numbers of the inscriptions. The three Tzolkin/Haab dates are 13-Manik 5-Pax, 9-Kan 12-Xul, and 1-Ahau 13-Xul.
Using only the (two) distance numbers referenced by Schele and Friedel in a footnote, Long Count dates can be derived from a dedication date of 9.15.13.6.9 by subtracting the two recorded distance numbers of 3.8.10.14.11 and (3).5.19.0.7, resulting in 6.9.14.6.2 (September 19, 557 BC) for the "Second Creation" and 6.7.2.9.18 (September 2, 608 BC) for the "Third Creation." These match the dates of the fourth altar (for the "Second Creation") and third altar (for the "Third Creation") at La Venta, in 556 BC and 608 BC. (I do not know why the cardinal numbers are chronologically reversed.)
The date for the "Third Creation" is correct at 698 BC. This is (or should be) the date of the third altar in a series that was carved at La Venta. It would seem from this that a "Third Creation" was thus correctly pinpointed by Yaxchilan even though it was not the "third creation" they were looking for.
The problem with the distance numbers of the three ballcourts (of which I only have two) is that the Calendar Round day names for the remote dates do not match what would be expected from a retrocalculation of the Long Count. We could, however, search the 8th and 7th century BC for significant dates based on the day names. Calendar Round day names repeat every 52 years in the 520 year period (the 'may') from Baktun Katun 5.15 to 7.1. There are quite a few dates to check. With some exceptions, none of them make much sense.
The "First Creation" date of 13-Manik 5-Pax first occurs on 5.17.6.0.7 (802 BC), and every 52 years after. The second instance (5.19.18.13.7) happens in 750 BC. This is three years further in the past than the first appearance of Mars in 747 BC. The date of 750 BC might qualify as an equivalent astronomical date for a Gregorian calendar date, except that I would expect a difference of four years, not three years.
The "Second Creation" date of 9-Kan 12-Xul first occurs on 5.16.19.7.4 (808 BC), and also repeats every 52 years. The third instance (6.2.4.15.4) happens in 704 BC, two years after 702 BC, the fourth appearance of Mars.
It is very possible that the ceremonies involving the appearances of Mars were delayed by months or years, so that we simply have no way of knowing what the actual date was for the carving and burial of a stone head.
This is not true of ceremonies involving the "Creation Altars" which were governed by the calendar rather than some cataclysmic event. Thus it is interesting that one of the dates for the "third creation" day names of 1-Ahau 13-Xul falls on 6.7.1.3.0, which is 609 BC, and only 498 days different from the Long Count date found from the distance numbers.
A difference of 1.3 years between the calendar date derived from the Long Count and the calendar date derived from the Calendar Round suggests that perhaps we are looking at records which were altered, that is, 'corrected,' by Monte Alban. It was in 607 BC, as I have pointed out above, that Monte Alban dropped the repeating Tzolkin calendar for a system where the Tzolkin would be restarted in the 365 day year after the first round, and then cut short after the 105th day. The Long Count was continued, but after the first year of the new calendar, the Tzolkin was displaced by 155 days, by 310 days after two years, and by 465 days after the third year.
I think the scribes at Yaxchilan made a serious mistake. They were looking for dates of the "first creation," the "second creation," and the "third creation," which would have been dates in the years 8347 BC, 3147 BC, and 2349 BC. These are the recognized "first creation," "second creation," and "third creation" as we know from other Maya source documents. The scribes checked their records, the same records which had been recorded at La Venta and transcribes by others, eventually to be confused as the complete history of humanity. Some of the books, without giving dates, indeed did record events dating back thousands of years, but the references to the first, second, and third creation were recorded in detail from ceremonies at La Venta in the 7th century BC. The dates were transcribed without thought about the actual scope of history.
More importantly to compound the error, the records had been 'corrected' by the scribes at Monte Alban to conform to their particular calendar. For dates close to 607 BC, like 608 BC, the corrections amounted to a displacement of a few hundered days, as recounted above. For other dates further in the past from 607 BC, the slippage of the Tzolkin calendar became an incomprehensible tangle.
The Fourth 'may' at Monte Alban, 334 BC to AD 179

Let's follow this trail in the manner told in the Guatemalan "Popol Vuh." I would assume that the scribes at Yaxchilan derived their information from books obtained from Monte Alban, but these books described information originally obtained by Monte Alban from La Venta. Those same books might have been repeatedly recopied before reaching Yaxchilan, but they were held as sacred and true. The books told of how the leaders (of Monte Alban) traveled east to the city by the sea (La Venta) to obtain their insignias of leadership. Received from La Venta were the "Council Book," and books called "The Light that Came from Besides the Sea," "Our Place in the Shadows," and "The Dawn of Life."
The books revealed the most ancient of history, the experience of darkness, the migrations of the tribes, the genesis of the Gods, the founding of the calendar, the "third creation" -- but all from records derived from La Venta. The books were probably not transmitted until hundreds of years had passed, and with time the stories they told were taken as the history of those who received copies.
The dates match. Monte Alban was active before La Venta was abandoned. It was Monte Alban also where a script was developed. The Tzolkin and Haab calendar was not received from Monte Alban, for everyone already had the calendar, as hinted at by the fact that the August 11 version was in use in both the southern Veracruz region (as at La Venta) and in part of Guatemala, whereas the Valley of Mexico and the Guatemalan Peten and the Yucatan region used the August 13 version.
The 'may' ended in AD 179. Monte Alban was not destroyed after AD 179, but held on to maybe AD 700 to AD 1000, after which it was mostly abandoned. By the 16th century AD there was still a priestly college in the Oaxaca region, which seemed to have remained unmolested by the Aztecs.
Interestingly, Monte Alban did not go into a decline until AD 700, suggesting that perhaps it held the 'may' for two periods, from 334 BC to AD 179, and from AD 179 to AD 692. This last is the same period where Teotihuacan obviously held primacy. Perhaps this is an instance of the regionalization of the 'may' since Monte Alban was a considerable distance from the Valley of Mexico. Edmonson has suggested that the 'may' might have passed to Tres Zapotes in about 78 BC for a 256 year span.
The Fifth 'may' at Teotihuacan, AD 179 to AD 692

Clearly it was Teotihuacan which held the 'may' from AD 179, to be abandoned, "conquered," in AD 692. As I have noted, Teotihuacan was one of the largest city in the world. Teotihuacan established a widespread trade network across Mesoamerica. There was a population of Monte Alban craftsmen in one of the precincts of Teotihuacan
Following the Post-Classical usage by the Maya, it would seem that by "conquest" is meant the destruction and abandonment of a ceremonial site after some period of use, as Edmonson has suggested. This has been seen in the case of San Lorenzo and La Venta, and has recently been suggested for the destruction of Teotihuacan in about AD 700, which at an earlier time had been attributed to the Toltecs who invaded the Valley of Mexico. Today it is attributed to the priests of Teotihuacan. Assuming that the cycle of primacy is indeed 520 years, it could be suggested that Teotihuacan took on primacy shortly after AD 172. This agrees, in fact, with the archaeology of Teotihuacan.
At the beginning of this period, outside of the Valley of Mexico, in Honduras and the Peten of Gautemala, the Maya seriously start up their ceremonial centers, and start up the celebrations of Kutun endings, and any number of other dates which were perceived as important in sustaining the world. These are discussed by Edmonson. The Maya seem to have disregarded the 'may' as it was defined in the Valley of Mexico, but retained the concept of a primary regional site. In this respect the Toltecs of Tula may have done the same. [note 15]
The Sixth 'may' at Tula, AD 692 -- AD 1219

In the Valley of Mexico it was an invading tribe, the Toltecs, who built and occupied the city which is today known as Tula or Tollan who seem to have held primacy after Teotihuacan, although Tula was not built until after AD 900 and destroyed some time around AD 1170, after which the primary city of the Toltecs was reestablished elsewhere. Their calendar, however, dates from AD 726. During this period the Toltecs dominated much of central Mexico. Around AD 900, Tula was the largest city in Mexico. [note 16]
When Teotihuacan was abandoned in about AD 700, the Pleiades passed directly over the city at culmination. When Tula was constructed 200 years later and at a half degree further north in latitude, the Pleiades passed directly overhead of the new ceremonial center.
The word "Tula" or "Tollan" means "place of the reeds" or "place of the rushes." It had been applied to Teotihuacan also, and the later Aztecs applied it to their city of Tenochtitlan (today Mexico City) as well. Not much is known of Tula since the Aztecs plundered it for building material and sculptures.
Nine intervals of 52 years had passed since Teotihuacan was abandoned, when Tula was conquered by invading tribes. The architecture of Tula shows up at the Maya site of Chichen Itza.
The Seventh 'may' at Cholula, from AD 1219

Cholula was a very large city southeast of the Aztec city of Tenochtitlan, and only a little smaller in the 16th century AD. Dating from about 200 BC, it lasted to the time of the Spanish invasion. "Cholula remained a regional center of importance, enough so that, at the time of the fall of the Aztec empire, Aztec princes were still formally anointed by a Cholulan priest" (Wikipedia)
Cholula probably had a population of near 100,000. The center included the largest pyramid in the world. Cortes reported counting 430 temples (there were only 365). When Cortes arrived, he massacred 3000 nobles and priests of Cholula in two hours, to demonstrate the invincibility of the Spanish to the neighboring cities.
The 'may' among the Maya

The Maya may have redefined the 'may' to a reduced periods, as little as a single twenty year Katun, rotating primacy among 13 prominent sites, although there also was a much longer period. Among the Maya the long 520 year period of the 'may' seems to have been defined from the time of the fall of Tula.
Edmonson identifies Mayapan of the (Maya) Itza as holding primacy from AD 1243 to 1752, a 509 year period, starting in a year 6-Ahau (20 years after 8-Ahau) and ending in a year 8-Ahau (and thus one Katun short of 520 Tun years), even though Mayapan was deserted during the last 300 years. The Toltecs in the Yucatan (remembered later as the Itza) used the start of the 11th Baktun (11.0.0.0.0) as the start of a 'may.' Edmonson further shows both the startup and the collapse or abandonment of numerous sites coincided with Katuns ending of 8-Ahau.
It could be suggested that the Classical era Maya sites in the Peten fully expected to last to the end of the next 520 year interval after the 'conquest' of Teotihuacan, that is, to AD 1212. None of the highland Maya sites did. They all floundered and were abandoned by about AD 900.
Summary

What will be seen in the list of ceremonial centers and cities, is a sequence of events which promotes each city in turn to the status of a major center of activity and extended hegimony for a period of somewhat under 520 years, after which it disappears from view. As a primary center, they are consistently the largest and most populous sites, they conduct trade over nearly all of Mesoamerica, and are widely influencial in promoting their architecture and their iconography, and -- we would presume -- their religious ideas.
In almost all instances the archaeological dating matches the expectations of the sequence of the 'may' over a period of 3000 years, although it is not always clear cut. Some sites are already established at the start of a 'may,' but others, like Teotihuacan and Tula spring into existence as new ventures. Probably more important is that San Lorenzo, La Venta, and Teotihuacan clearly were destroyed by the residents or the leadership of the centers. The destruction of Tula, although at about the right time for a 'may' ending, is today attributed to other invading tribes.
As time progressed, hegimony over the region is expressed more and more with force, culminating the extreme militarism of Tula which extended its control into Guatemala and even into the Yucatan region of the Maya. The later Aztecs take up the concept of military control after the fall of Tula, and claim themselves as their descendents. Cholula seems to have avoided militarism, since it existed in the shadow of the Aztec empire.
Abandoning a site after a set span of time is a concept entirely foreign to our way of thinking. It is a disruptive, self defeating, and senseless gesture, and can only be understood if seen as a religious necessity. The nations of Europe often act the same way, but somehow their religiously based actions make more sense to us.
The following table lists Katuns ending in 8-Ahua and anniversaries of the 52 year Venus cycles, in addition to a few other events. The 52 year intervals, shown below, are based on 'Venus cycles' in solar years before San Lorenzo, and on 52 calendar years afterwards.
The 'years BC' for the 8-Ahau Katuns listed below are corrected by assuming, as would be the case before 747 BC, that the Baktuns and Katuns represented actual years, that is, solar years. This matches dates from the eastern Mediterranean, where the 'BC' notation is also in solar years. The 52 Tun-year anniversaries of Venus are shown in BC/AD notation, and are thus approximate. Since the final celebration in the Valley of Mexico happened in AD 1507, my series of 52-year anniversaries, which ends in AD 1472, is off by 35 years near the end. I have added Malmstrom's derived dates for the period after Teotihuacan.

Baktun/Katun corrected date Venus 52 year cycles marked (*), 8-Ahau ending (see note 1) and other notes (see text) ------------- -------------- -------------------------------- 1.17 2407 BC possible start of an earlier 'may' 2349 BC (*) The 'flood of Noah' 2297 BC (*) 2nd appearance of Venus 2245 BC (*) 3rd appearance of Venus 2193 BC (*) The fall of Akkad (2197 BC # same as 2193 BC) 2150 BC # (*) (see note 3) 2.10 2147 BC 2103 BC # (*) 2056 BC # (*) 2009 BC # (*) 1962 BC # (*) 1915 BC # (*) 3.3 1887 BC the 'may' at Monte Alto 1868 BC # (*) 1st fat boy, Monte Alto 1821 BC # (*) 2nd fat boy, Monte Alto 1774 BC # (*) 3rd fat boy, Monte Alto 1727 BC # (*) 4th fat boy, Monte Alto 1680 BC # (*) 5th fat boy, Monte Alto 1633 BC # (*) 6th fat boy, Monte Alto 3.16 1627 BC 1586 BC # (*) 7th fat boy, Monte Alto 1539 BC # (*) 8th fat boy, Monte Alto 1492 BC (*) 9th fat boy, Monte Alto The Exodus of Moses; note 4 1440 BC (*) 10th fat boy, Monte Alto End of Middle Kingdom 1388 BC (*) 11th fat boy, Monte Alto 4.9 1367 BC end of the 'may' the 'may' at San Lorenzo 1336 BC (*) 1st Venus head, San Lorenzo 1284 BC (*) 2nd Venus head, San Lorenzo 1232 BC (*) 3rd Venus head, San Lorenzo 1180 BC (*) 4th Venus head, San Lorenzo 1128 BC (*) 5th Venus head, San Lorenzo 5.2 1107 BC 1076 BC (*) 6th Venus head, San Lorenzo 1024 BC (*) 7th Venus head, San Lorenzo 972 BC (*) 8th Venus head, San Lorenzo 920 BC (*) 9th Venus head, San Lorenzo 868 BC (*) 10th Venus head, San Lorenzo 5.15 847 BC end of the 'may' San Lorenzo destroyed ca 900 BC the 'may' at Tres Zapotes 816 BC (*) 1st Venus head, Tres Zapotes 764 BC (*) 2nd Venus head, Tres Zapotes the 'may' passed to La Venta 747 BC Earth's orbit changes 747 BC 1st Mars head, La Venta 732 BC 2nd Mars head, La Venta 717 BC 3rd Mars head, La Venta 712 BC (*) 1st altar. La Venta 702 BC 4th Mars head, La Venta 686 BC Mercury Earth shock 685 BC Nova event and plasmoid of Jupiter 660 BC (*) 2nd altar, La Venta 608 BC (*) 3rd altar, La Venta 6.8 591 BC 556 BC (*) 4th altar, La Venta 504 BC (*) 5th altar, La Venta 452 BC (*) 6th altar, La Venta 400 BC (*) 7th altar, La Venta 7.1 334 BC end of the 'may' La Venta destroyed, 400 -- 300 BC (it is uncertain where primacy passed next, may have passed to Monte Alban) 348 BC (*) 296 BC (*) 244 BC (*) 192 BC (*) 140 BC (*) 88 BC (*) 7.14 78 BC (Edmonson: perhaps the 'may' at Tres Zapotes) 36 BC (*) AD 16 (*) AD 68 (*) AD 120 (*) AD 172 (*) 8.7 AD 179 end of the 'may' the 'may' at Teotihuacan AD 224 (*) AD 276 (*) AD 328 (*) AD 380 (*) AD 432 (*) 9.0 AD 435 AD 484 (*) AD 536 (*) AD 588 (*) AD 640 (*) AD 692 (*) 9.13 AD 692 end of the 'may' Teotihuacan destroyed, ca AD 700 the 'may' at Tula Malmstrom dates AD 744 (*) 779 AD 796 (*) 831 AD 848 (*) 883 AD 900 (*) 935 AD 952 (*) 987 10.6 AD 948 AD 1004 (*) 1039 AD 1056 (*) 1091 AD 1108 (*) 1143 AD 1160 (*) 1195 Tula destroyed ca AD 1170 AD 1212 (*) 1247 10.19 AD 1204 end of the 'may' the 'may' at Cholula (?) AD 1264 (*) 1299 AD 1316 (*) 1351 AD 1368 (*) 1403 AD 1420 (*) 1455 11.12 AD 1460 AD 1472 (*) last Venus anniversary (AD 1507) AD 1519 Cortez massacred 6,000 Cholulans Note 1: 'corrected dates' are Baktuns and Katuns as solar years. Note 2: Prior to 2193 the 'Venus cycle' consisted of 52 solar years. Note 3: For the period of 2193 BC to 1492 BC, the 'Venus cycle' is based on an interval of 47 solar years, marked #. Note 4: After 1492 BC I have used a 52 year 'Venus cycle.'

From this table it would be clear that primacy of a site is concluded after the 10th anniversary of the 52 year Venus cycle (whether the cycle existed in reality or not). This assumes a missing primacy between La Venta and Teotihuacan, for which I have suggested Monte Alban, although Tres Zapotes was also revived.
Considering the role played by San Lorenzo and La Venta in the maintenance of creation and prevention of the destruction of the world for over 1000 years, it becomes obvious that these two sites were very important and influencial, and would have set the religious agenda for Mesoamerica for the following 2000 years.
As I have noted earlier, most of the other Olmec sites, and most of the sites in the Valley of Mexico, show the same concern with 'era-ending' alignments similar to what was incorporated in the choices for the location of San Lorenzo, Tres Zapotes, and La Venta. The alignments established at San Lorenzo and La Venta became the minimum required alignments. After 600 BC new 'era-ending' alignments are added, reflection dates from the year 685 BC.
It could be suggested that the older horizon locations (like for April 19, 1492 BC, or February 28, 747 BC) were simply copied from the older sites, except that we start to see these older alignments being conformed to the new axial inclination of 23.5 degrees, just as we also see some of the newer 'era-ending' dates configured to horizon locations conformed to the old axial inclination of 30 degrees. This is a truly strange procedure, and it is almost beyond the imagination to attempt to understand how the alignments for the previous era could have been found geometrically. But it is clear that it happened. We also have absolutely no idea what was so important about establishing these site alignments.
Orientation of the major axis of a site would be the easiest method of forcing the 'proper' layout of a ceremonial center, one which did not require triangulation with two mountains. There might have been many more than the two I have noted. Unfortunately I am lacking axial locations of site orientations except for a few well-studied sites and I may be missing horizon alignments because of this.
The alignments to be used to signal the new creation were not immediately obvious after 685 BC. Which date to use, and how it reflected new developing theologies, remained a question. Using two revolving calendars which did not match the solar year did not help to resolve this initially. There were many understanding of what had happened, and many solutions. Probably the alignments implemented by Teotihuacan were adopted by the Maya in the Peten and on the Guatemalan coast, due to the hegemony Teotihuacan exerted over much of Mesoamerica. Again, I have also not followed up on site alignments in the Yucatan or Guatemala. The alignments found for Veracruz and the Valley of Mexico were, I felt, sufficient to establish the importance of site alignments.
The events of 685 BC were of course written down. There would have been day books, records of events by years and by days. Narrative versions probably came much later, and likely encompassed all of sacred history, from the first creation onward. The understanding of what transpired in 685 BC probably took many forms. But everything that was told in the narrative could be verified.
What does all this mean? It means that we are dealing here with able historians, excellent geographers, superb observational astronomers, and astute mathematicians. Before the Spanish destroyed all their records, these stone age people had the longest continuous historical records in the world, the only accurate record of past celestial events, and the closest observations of the Sun. We only need to get past their quirky concepts of geography, and their strange notions of cyclical time and disregard of the historical length of the year, in order to extract information which other nations of the world have failed to record or make sense of.

Endnotes

Note 1 --
Which creation ended on the day of Kan? Both 2349 BC or 1492 BC might be suggested, but it is impossible to run the Tzolkin calendar backwards to determine if either year coincided with a "day of Kan," for we do not know the exact year of these two changes, in addition to the fact that we do not know the exact length of the year during these periods, and especially in the period between 2349 BC and 2193 BC. In this case I have to go on legend and hearsay as recorded in the "Chilam Balam" and in the obvious efforts in assigning site alignments.
"Kan" means both "snake" and "sky" because the night sky is define by the object which acts in the sky, the snake-like equatorial belt, Apep of the Egyptians. The snake in the sky had a head and a tail. The head and tail showed up in the sky as the vernal and autumnal equinoxes were approached. Considering the frequent use of the Saint Andrew's Cross in the iconography of the Classical Maya to denote the sky, the sun-lit equatorial band probably lasted into the first millenium AD.
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Note 2 --
The misapplied science involves the use of the August 13 correlation. It is the only one where the day-names hold up. It differs from the August 11 correlation, which was certainly in use in 747 BC.
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Note 3 --
The Olmecs, and certainly the later Maya, were perfectly capable of dealing with the 0.24 fractional day. So says Michael Coe. The Maya used ratios to approach the values of numbers less than one, similar to the Egyptian use of additive fractions in doing division.
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Note 4 --
The association of the 'day of Kan' with the flood of Noah (the fall of the Absu) is not entirely certain from a reading of the "Chilam Balam." Katun 9-Ahau is clearly identified, however, and this is immediately followed by, "Kan was the day when its burden was bound to it," after which follows, "Then the water descended, it came from the heart of the sky for the baptism of the House of Nine Bushes." It is quite possible that the (supposed) sentence about the 'day of Kan' belongs elsewhere in the text. (All sentence punctuation is missing from the "Chilam Balam" and the order is systematically jumbled.) The fact that the opening day of Kan falls in Katun 9-Ahau, 2.2.0.0.4, would argue against this, however.
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Note 5 --
All people do this, find similarities, and assume a connection. We frequently make these connections on a very slim basis. The Olmecs had assumed that a flood would separate recreations of the world, based on the flood of 3147 BC and the celestial food of 2349 BC, which last also caused incessant rains and storms. The "Chilam Balam" still acknowledges this connection, offering events surrounding 2349 BC as the "Third Reign." But the Earth shock of 1492 BC had not involved flooding of the scope of the previous era-endings, and with the shock of 747 BC the flood was also missing, except, of course for the hurricanes due to the electrical arc from a passing planet.
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Note 6 --
The use of the August 11 correlation used to find these two day names in remote antiquity is another sign of the disagreements in Mesoamerica about the actual ending date of the era before 747 BC.
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Note 7 --
Malmström in "Architecture, Astronomy, and Calendrics" ("Pre Columbian Mesoamerica Archaeoastronomy in the Americas" Ray A. Williamson, ed. (1981)), writes..
"From field measurements begun in 1971, Aveni was able to confirm that 50 of 56 sites which he examined were indeed oriented east of north, and that a 17 degree 'family' of alignments did in fact seem to exist (Aveni 1975) [Antoni Aveni, ed. "Archaeoastronomy in Pre-Columbian America" (1975)]. Aveni also concluded that this particular pattern of orientation seemed to be most prevalent in the Valley of Mexico and he specifically mentioned Tenayuca, Tepozteco, and Tula as sites where this alignment was encountered. (It should be pointed out that Aveni's '17 degree family' of alignments includes orientations as far off as 15.5 degrees, [azimuth of 285.5 degrees, less 270 degrees] for he includes Teotihuacán in this 'group'.)"

I have reproduced a chart of results by Malmström further below. Because Malmström specifically notes that some of these values have been corrected by him, I do not have complete confidence in the chart. Malmström notes that..
"Aveni has had to dismiss all later sites built on the Mexican plateau having similar orientations to Teotihuacan (such as Tenayuca, Tepozteco, and Tula) as being simply 'non-functional imitations' of the great Mesoamerican metropolis (Aveni 1975)."

Aveni's alignments are reproduced in "Skywatchers of Ancient Mexico" (1980).

STRUCTURES ORIENTED TO ~285 degrees General Region Orientation Measurement Site Time-Frame Structure face degrees source -------------- ---------- ------------------ ------ ------- ----- -- Mexican plateau -- Teotihuacan A.D. 0-650 Pyramid of the Sun Front *285.5 (M) Tula A.D. 950-1150 Temple B Side 287.1 (A) Tenango A.D. 650 Principal Structure Side 283.7 (A) Xochicalco A.D. 650 Temple of Plumed Serpent Front 286.8 (A) -- Yucatan -- Edzna 150 B.C.-A.D. 850 Cinco Pisos Front *285.5 (M-D) Sayil A.D. 600 (?) Main Palace Side 282.4 (A) Labna A.D. 600 Temple of Columns: Mirador Side 282.1 (A) Kabah A.D. 600 Codz Pop Front 283.6 (A) Mayapan A.D. 900-1300 Observatory: (152) Front 282.8 (A) Temple of Sacrifices (151) Side 282.8 (A) Izamal A.D. 600 (?) Platform, Pyramid of Kinich-Kakmo Side 287.2 (A) Chichen Itza A.D. 700-1300 Chicchan Chob Front 285.0 (M-D) House of the Deer Side 285.0 (M-D) Caracol (mid-line -Window) Front *284.9-285.7(A) Coba A.D. 600 XV, XVI Side 285.0 (M-D) Kohunlich A.D. 600 Ball-court (Main axis) 285.0 (M-D) Chicanna A.D. 450 Groups C and E Side 283.0 (M-D) Becan A.D. 450 East Group (I, IV) Side 283.0 (M-D) II, III Front 283.0 (M-D) -- Belize-Peten -- Altun Ha A.D. 600 (?) Structure A-5 Front 285.0 (M-D) Tikal A.D. 200-900 Alignment of Temple I to Temple IV Front *285.0 (M-D) Alignment of Temple I to Temple V (RightAngle) 15.0 (M-D) -- Oaxaca -- Monte Alban 600 B.C.-1100 A.D. Mound Y Front 285.0 (M-D) Huamelulpan 300 B.C.- ? Main Pyramid Front 285.0 (M-D) -- Gulf Coast -- La Venta 1000-600 B.C. Stirling "Acropolis" & "Plaza" Side *285.0 (B) note a (*) -- The present author [Malmström] has chosen to re-define Aveni's "17 degree family" of alignments as the "15.5 degree family" inasmuch as the principal structures in the major sites of Mesoamerica appear to center on this value; see asterisked items above. note b -- Sources of measurements: A: Aveni; B: Bernal; M: Millon; M-D: Malmström and Dunn. Inasmuch as the author and his assistant carried out their measurements with a surveyor's compass, wherever data obtained by more precise instrumentation are available, they are cited instead--rounded to a tenth of a degree.

The problem I have with the arbitrary assignment of Aveni's "17 degree family" to the "15.5 degree family" is that the 17 degree alignments are likely to represent the setting of the Pleiades in about AD 200 or AD 400, as set by Teotihuacan. (See the text for this.) But otherwise, Malmström suggests (correctly) that the 15.5 degree east of north alignments represent a sunset on "August 12-13," and writes..
"Of these two possibilities, the latter is definitely the more interesting to students of Mesoamerican calendrics. This is because the Maya -- the most highly advanced of all Mesoamerican peoples in the realm of astronomy -- believed that the present era of the world began on August 13, 3114 B.C., according to the Goodman-Martinez-Thompson correlation between the Maya and Christian calendars."
"... recurrent building alignments throughout Mesoamerica appear to commemorate a date which can only have had astronomical (i.e., solar) origins or, at the very least, could only have been established by astronomical means -- i.e., by counting the number of days from some fixed point in time. (In the latter regard it should be pointed out that the August 13 sunset position could easily have been defined simply by counting 52 days from the summer solstice.) In the light of the evidence at hand, one can conclude that far from being just one more in a series of 'coincidences,' the correspondence of building alignment azimuths throughout Mesoamerica and the beginning date of the Goodman-Martínez-Thompson correlation should more realistically be considered as additional proof of the validity of the latter."

For the location where I have certain alignments, I arrive at a date of August 12, not 13. August 13 is the day after, and thus after the 'completion' of the previous era. It is also not an easy matter to count 52 days into the future when the solstice cannot be found with any certainty. It would be easier by far to count 40 days back from the fall equinox (to August 12).
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Note 8 --
Munro S. Edmonson, "Some Postclassic Questions About The Classic Maya" (Fifth Palenque Round Table, 1978).
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Note 9 --
See http://www.mesoweb.com/pari/publications/RT04/Edmonson.pdf (1978). Edmonson also notes..
"The seat of the katun ('hetz' katun) was the real capital of the region in Postclassic and Colonial times. Though it only served for 20 tuns at a time, each city competed vigorously for the honor, since it conferred tribute rights and the right to confirm titles to land and public office throughout the region. While these rights must have belonged to ruling lords of major centers, there may nonetheless have been some ritual rotation of subsidiary responsibilities among the cities of the second rank."
"Councils of sages and prophets were held at Mayapan and Chichen Itza in 13 Ahau (1539) and at Merida in 7 Ahau (1579). Such councils were apparently called in times of crisis to resolve calendrical and religious issues, and one such may well have been responsible for the founding of the League of Mayapan in 2 Ahau (1263). They appear to have resembled the Vatican Councils in function, and they commanded enormous respect, representing in Colonial times the highest moral authority in the country. Such a body might for example have had a role in the investiture of the rulers in Classic times as well as later."
"The ritual importance of the katuns is fully attested by katun ending monuments. Perhaps some of these contain texts with the curious blend of prophecy and history presented in the 'Books of Chilam Balam.'"
"[A] table has been drawn up as a documentation and speculation in relation to the recurrence of the 'may' cycle ending on 8 Ahau katuns and its possible relevance to the chronology of Maya history. As is summarized in Table I in the text, it is possible to consider eleven such cycles within the framework of Middle American prehistory, from the ninth century B.C. to the twentieth century A.D. The eleventh such cycle would be completed in 2016 A.D., according to the most recent Maya calendar reform, that of Valladolid."
"It is of some interest that the first three of these cycles come within three katuns of accepted dates for the beginnings of the Olmec period, the Middle Formative and the Late Formative respectively, and that the earliest long-count dates of the next two cycles fall outside of Maya country as usually defined (Tres Zapotes, El Baul and Tuxtla)."

[Table not reproduced]
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Note 10 --
The interval in solar years will match the count recorded by the Olmecs in "Tuns," since a Tun is a year. Their records would thus match the chronology of the eastern Mediterranean region. After 1492 BC the year went to 360 days, and a Tun was still a solar year. After 747 BC, when the Long Count was established, the Tun of the Long Count was retained at 360 days.
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Note 11 --
At Teotihuacan warriors start using the flayed human face as a shield, and introduce this to the Maya during the Classical Period.
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Note 12 --
William Mullen in "Catastrophism and the Compulsion to Meaning" (Kronos, Vol. 6:1) (?) wrote, "Much of the Early Tres Zapotes level was sealed with volcanic ash." He also notes the deposition of bitumen or asphalt. There were two occupations of Tres Zapotes. Bitumen was also found at San Lorenzo (Coe).
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Note 13 --

Image: Olmec stone altar from Potrero
In the chart presented in the text it is shown that La Venta probably celebrated seven of the 52-year Venus anniversaries since 712 BC. Thus the massive stone altars might have served ceremonial purposes at these celebrations. Note that the other three celebrations were held at Tres Zapotes.
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Note 15 --
Ralph L. Roys, in an appendix to "The Book Of Chilam Balam Of Chumayel" lists a "Chronological Summary" of founding and abandonments of sites in the Yucatan, with respect to Katun 8-Ahau and Katun 6-Ahau, as follows. The Christian (AD) dates used by Roys represent the 'Morley-Spinden' correlation, off by three years from the 'Goodman-Martinez-Thompson' correlation. I have shown the 'GMT' dates to match the data of the table in the text, and added the Baktun and Katun.

Baktun.Katun AD date event 9.0 8-Ahau 435 a half interval 6-Ahau 455 Chichen Itza discovered 11-Ahau 534 Chichen Itza occupied (estimated) 9.13 8-Ahau 692 Chichen Itza abandoned Teotihuacan destroyed 4-Ahau 731 Chakanputun seized 10.6 8-Ahau 948 Chakanputun abandoned 4-Ahau 988 Chichen Itza occupied 10.19 8-Ahau 1204 Chichen Itza conquered Tula destroyed ca AD 1170, 4-Ahau 1244 Mayapan seized 11.12 8-Ahau 1461 Mayapan destroyed

Notice that the primary city is destroyed during each instance of Katun 8-Ahau, but that the interval, as a result, is 256 years (as Edmonson noted), not the 520 years I have found for Olmec sites and locations in the Valley of Mexico.
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Note 16 --
As mentioned by Malmstrom, Walter Krickeberg, in "Mitos y leyendas de los Aztecas, Incas, Mayas, y Muiscas" (1980), states that the Nahua (Aztecs) believed that the present "world" came into being in the equivalent of our year 726. Malmstrom calculates the Toltec Haab calendar as starting in AD 778 (52 years later). Krickeberg also dates the actual founding of the city of Tula to the year AD 856. The Toltecs apparently took up their earliest residence at a location south of Mexico City. The native history of Ixtlilxochitl claims the founding of Tula to AD 566.
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Calculations are in Unix bc notation, where ^ denotes exponentiation; the functions (a)rctangent, (s)ine, and (c)osine use radians; angle conversions to radians or degrees by the divisors rad=.017+ and deg=57.2+; other functions are shown as f( );
units: million == 1,000,000; billion == 1,000,000,000;
one AU == 93,000,000 miles.

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Recovering the Lost World, A Saturnian Cosmology --Jno Cook Part 19: The Day of Kan and the Course of the May.

Finding the Day of Kan

The "day of Kan" for 2349 BC

The "day of Kan" for 1492 BC

The "day of Kan" for 747 BC

The "day of Kan" for 3114 BC

The "day of Kan" for 685 BC

The Course of the 'May'

The Second 'may' at San Lorenzo, 1367 BC to 847 BC

The First 'may' at Monte Alto, 1887 BC -- 1367 BC

The Third 'may' at Tres Zapotes, 847 BC to 747 BC.

The Third 'may' passes to La Venta after 747 BC

The Third Conquest

The Fourth 'may' at Monte Alban, 334 BC to AD 179

The Fifth 'may' at Teotihuacan, AD 179 to AD 692

The Sixth 'may' at Tula, AD 692 -- AD 1219

The Seventh 'may' at Cholula, from AD 1219

The 'may' among the Maya

Summary

Endnotes

Recovering the Lost World,
A Saturnian Cosmology --Jno Cook
Part 19: The Day of Kan and
the Course of the May.