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#426691 - 01/04/12 09:07 AM Mayas Never Predicted December 2012 Apocalypse
Marty Offline

One of history’s most famous and foreboding doomsday predictions might never have been made, according to a German researcher. His new interpretation of a 1,300-year-old tablet affirms that the ancient Maya regarded December 21, 2012, as a moment of great importance—but not, as some believe, because they foresaw an apocalypse on that date.


Centered in the tropical lowlands of what is now Guatemala, the powerful Maya empire reached the peak of its influence around the sixth century A.D. and collapsed several hundred years later. Along with impressive stone monuments and elaborate cities, the lost Mesoamerican civilization left behind traces of its sophisticated calendar, which scholars have spent decades struggling to decipher. In recent years, popular culture has latched on to theories that the close of the calendar’s current cycle—set to occur around December 21, 2012—corresponds to the end of the world in the Maya belief system.

The first Maya calendar, known as the Calendar Round, appears to have been based on two overlapping annual cycles: a 260-day sacred year and a 365-day secular year that named 18 months with 20 days each. Under this system, each day was assigned four pieces of identifying information: a day number and day name in the sacred calendar and a day number and month name in the secular calendar. Every 52 years counted as a single interval, or Calendar Round, and after each interval the calendar would reset itself like a clock.


A panel depicting ceremonies of the Mayan kings. (Credit: LeClair/Reuters/Corbis)

But because the Calendar Round measured time in an endless loop, ancient Mayas couldn’t use it to establish chronologies or relate events with wide spans of time between them. Around 300 B.C., priests apparently solved this problem by devising a new method known as the Long Count, which identified each day by counting forward from a base point calculated to fall on August 11, 3114 B.C. It grouped days into several sets: baktun (144,000 days), k’atun (7,200 days), tun (360 days), uinal or winal (20 days) and kin (one day). A single cycle of the Long Count calendar lasts 13 baktuns, or roughly 5,126 solar years, meaning that it is slated to end on a date correlating to December 21, 2012.

What exactly happens when the Long Count winds down? For some theorists, hieroglyphs on a 1,300-year-old stone tablet from the Tortuguero archaeological site in Mexico might hold the answer. Worn with age and riddled with cracks, it includes a hazy prediction of an event involving Bolon Yokte, the Maya god of creation and war, at the end of the 13th baktun. One hotly disputed hypothesis holds that the passage describes a cataclysmic end to the world as we know it.

Various Maya scholars have attempted to debunk this reading, including Sven Gronemeyer of Australia’s La Trobe University, who has studied the Tortugero tablet in great detail. On Wednesday he presented his decoding of the inscription, suggesting that Bolon Yokte’s prophesied appearance on December 21, 2012, represents the start of a new era and not the end of days. Proponents of the apocalyptic interpretation have misunderstood the poorly preserved hieroglyphs, he said.

Gronemeyer outlined his findings a week after Mexico’s National Institute of Anthropology and History announced that another inscription with a possible mention of December 2012 was found at the Maya ruins of Comalcalco, located not far from Tortuguero. The institute has long maintained that the Maya calendar does not foretell the world’s destruction a year from now.

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#426697 - 01/04/12 09:27 AM Re: Mayas Never Predicted December 2012 Apocalypse [Re: Marty]
Marty Offline

2012: Beginning of the End or Why the World Won't End?

Scenes from the upcoming film 2012. Courtesy Columbia Pictures.
Scenes from the motion picture "2012." Courtesy Columbia Pictures.
Remember the Y2K scare? It came and went without much of a whimper because of adequate planning and analysis of the situation. Impressive movie special effects aside, Dec. 21, 2012, won't be the end of the world as we know. It will, however, be another winter solstice.

Much like Y2K, 2012 has been analyzed and the science of the end of the Earth thoroughly studied. Contrary to some of the common beliefs out there, the science behind the end of the world quickly unravels when pinned down to the 2012 timeline. Below, NASA Scientists answer several questions that we're frequently asked regarding 2012.

Question (Q): Are there any threats to the Earth in 2012? Many Internet websites say the world will end in December 2012.
Answer (A): Nothing bad will happen to the Earth in 2012. Our planet has been getting along just fine for more than 4 billion years, and credible scientists worldwide know of no threat associated with 2012.

Q: What is the origin of the prediction that the world will end in 2012?
A: The story started with claims that Nibiru, a supposed planet discovered by the Sumerians, is headed toward Earth. This catastrophe was initially predicted for May 2003, but when nothing happened the doomsday date was moved forward to December 2012. Then these two fables were linked to the end of one of the cycles in the ancient Mayan calendar at the winter solstice in 2012 -- hence the predicted doomsday date of December 21, 2012.

Q: Does the Mayan calendar end in December 2012?
A: Just as the calendar you have on your kitchen wall does not cease to exist after December 31, the Mayan calendar does not cease to exist on December 21, 2012. This date is the end of the Mayan long-count period but then -- just as your calendar begins again on January 1 -- another long-count period begins for the Mayan calendar.

Q: Could phenomena occur where planets align in a way that impacts Earth?
A: There are no planetary alignments in the next few decades, Earth will not cross the galactic plane in 2012, and even if these alignments were to occur, their effects on the Earth would be negligible. Each December the Earth and sun align with the approximate center of the Milky Way Galaxy but that is an annual event of no consequence.
› More about alignment

"There apparently is a great deal of interest in celestial bodies, and their locations and trajectories at the end of the calendar year 2012. Now, I for one love a good book or movie as much as the next guy. But the stuff flying around through cyberspace, TV and the movies is not based on science. There is even a fake NASA news release out there..."
- Don Yeomans, NASA senior research scientist
Q: Is there a planet or brown dwarf called Nibiru or Planet X or Eris that is approaching the Earth and threatening our planet with widespread destruction?
A: Nibiru and other stories about wayward planets are an Internet hoax. There is no factual basis for these claims. If Nibiru or Planet X were real and headed for an encounter with the Earth in 2012, astronomers would have been tracking it for at least the past decade, and it would be visible by now to the naked eye. Obviously, it does not exist. Eris is real, but it is a dwarf planet similar to Pluto that will remain in the outer solar system; the closest it can come to Earth is about 4 billion miles.

Q: What is the polar shift theory? Is it true that the earth’s crust does a 180-degree rotation around the core in a matter of days if not hours?
A: A reversal in the rotation of Earth is impossible. There are slow movements of the continents (for example Antarctica was near the equator hundreds of millions of years ago), but that is irrelevant to claims of reversal of the rotational poles. However, many of the disaster websites pull a bait-and-shift to fool people. They claim a relationship between the rotation and the magnetic polarity of Earth, which does change irregularly, with a magnetic reversal taking place every 400,000 years on average. As far as we know, such a magnetic reversal doesn’t cause any harm to life on Earth. A magnetic reversal is very unlikely to happen in the next few millennia, anyway.
› More about polar shift

Scenes from the upcoming film 2012. Courtesy Columbia Pictures.
Earth, as seen in the Blue Marble: Next Generation collection of images, showing the color of the planet's surface in high resolution. This image shows South America from September 2004.
Q: Is the Earth in danger of being hit by a meteor in 2012?
A: The Earth has always been subject to impacts by comets and asteroids, although big hits are very rare. The last big impact was 65 million years ago, and that led to the extinction of the dinosaurs. Today NASA astronomers are carrying out a survey called the Spaceguard Survey to find any large near-Earth asteroids long before they hit. We have already determined that there are no threatening asteroids as large as the one that killed the dinosaurs. All this work is done openly with the discoveries posted every day on the NASA NEO Program Office website, so you can see for yourself that nothing is predicted to hit in 2012.

Q: How do NASA scientists feel about claims of pending doomsday?
A: For any claims of disaster or dramatic changes in 2012, where is the science? Where is the evidence? There is none, and for all the fictional assertions, whether they are made in books, movies, documentaries or over the Internet, we cannot change that simple fact. There is no credible evidence for any of the assertions made in support of unusual events taking place in December 2012.
› Why you need not fear a supernova
› About super volcanoes

Q: Is there a danger from giant solar storms predicted for 2012?
A: Solar activity has a regular cycle, with peaks approximately every 11 years. Near these activity peaks, solar flares can cause some interruption of satellite communications, although engineers are learning how to build electronics that are protected against most solar storms. But there is no special risk associated with 2012. The next solar maximum will occur in the 2012-2014 time frame and is predicted to be an average solar cycle, no different than previous cycles throughout history.
› More about solar storms

Addition information concerning 2012 is available on the Web, at:

NASA


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#427141 - 01/08/12 09:04 AM Re: Mayas Never Predicted December 2012 Apocalypse [Re: Marty]
Marty Offline

It’s 2012, which means another doomsday may be upon us

On Dec. 21, 2012, the Mayan calendar reaches the end of its 5,126 epoch. That’s a cause of consternation among some end-times adherents, and amusement among some descendants of the Maya.

Fresh from having survived one end-of-the-world prediction — a two-stage affair covering 2011’s drop-dead dates of May 21 and Oct. 21 — we now plunge into the countdown for End Times 2012.

Should you be inclined, you can use your smart phone to check how many days are remaining before a date that was carved into rock by a pre-Columbian civilization.

You can blame — or credit — the Maya for the commotion. Or, more likely, their New Age adherents.

Sure, the ancient Mayan calendar does technically end at Dec. 21, 2012.

But Mayan experts say it’s simply a case of one long Mayan epoch — of 5,126 years — coming to an end, in much the same way the 1900s came to an end.

“I don’t think the Mayan put a picture of Porky Pig at the end of their calendar and said, ‘That’s all, folks,’” said Jefferson Harman, a Pompton Lakes, N.J., “intuitive,” or dream-interpreter, who runs a workshop called “Beyond 2012.”

All this calendar talk is news to Firmo Choc, a 39-year-old Mayan farmer who lives in a rural village in Belize. The first he heard of the New Age crowd’s fuss over his culture’s ancient calendar was recently, when his American employer told him about it.

Not only was Choc taken aback to hear the end of the world prediction attributed to his people, he was surprised outsiders are even familiar with the calendar. He, his family, his friends and neighbors all use the standard Western calendar.

“The Mayan who surround me have no idea that some calendar their ancestors created indicates that a great change is to occur in 2012. They are just hoping their corn and cacao crops will be plentiful so their family won’t starve in 2012,” said Choc’s employer, Anne-Michelle Marsden — a Rutgers University professor who lives in Belize.

About a decade ago, Marsden spent her sabbatical year in Belize producing a documentary called “The Living Maya.” Choc travels to the coast by bus along unpaved roads twice a week to work as her groundskeeper.

He has eight children; the oldest boy had to stop his schooling to help on the family cacao farm. He’s Catholic, but participates in the Mayan Deer Dance ceremony when it is celebrated in his village.

Choc is not concerned about the world ending any time soon. He’s mostly concerned about supporting his family. School fees are very expensive, wages are low and job prospects for non-farmers poor.

Mayans in parts of Guatemala and Mexico still refer to the ancient Mayan calendar, consulting it in part because of the belief that certain glyphs, or pictures that accompany the days, influence events in much the way astrological signs are said to hold sway.

The Maya wouldn’t be the first civilization to come up with an increasingly complicated system for tracking time. The most obvious way to mark time is by using the moon’s cycle. However, this doesn’t match up neatly with the solar year, or the time the Earth takes to circle the sun. So every culture’s calendar has had to insert little amendments along the way to account for those burps and hiccups of time.

Christians tinkered with the length of the months, dumped the Julian calendar (for the most part) and threw in Leap Year. Jews insert a lunar month every now and then. Muslims simply decided against trying to have each month fall during the same season every year.

The Mayans just kept adding to their equation of time, creating a dizzying combination of Round and Long Form calendars, peppered by little symbols, or glyphs. Some interpret the calendar to include 13 “tones,” or characteristics that affect the day.

Over the years, this has proved to be a veritable cottage industry for archeologists, anthropologists and numerologists, who have been throwing out theories of interpretation since the turn of the (previous) century.

With very little in the way of written documentation from the calendar’s originators, the theories are hard to prove — or disprove.

The “end times” proposition has been floating around for 30 years or so by New Age spiritualists like the late Terence McKenna, who claimed it signaled the start of a period of broader human consciousness.

Denise Saracco, a self-described shaman and massage therapist who runs a workshop called “Demystifying the Mayan Calendar” out of the Peaceful Paths store in Butler, N.J., learned about the calendar as part of her two-year shaman apprenticeship.

Between the calendar’s 20 glyphs and 13 tones, “it can get crazy complex,” she said. Saracco feels 2012 is a key date — although she stops short of predicting what will happen.

She foresees a shift in collective priorities, away from materialism to a simpler life of more mutual respect and less divisiveness.

“Is it the end of the world? No,” she said. “It’s the end of the world as we know it.”

(Kathleen O’Brien writes for The Star-Ledger in Newark, N.J)

Copyright: For copyright information, please check with the distributor of this item, Universal Uclick.

Washington Post


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#427540 - 01/12/12 08:08 AM Re: Mayas Never Predicted December 2012 Apocalypse [Re: Marty]
Marty Offline

SSB: The Day After The CEO’s Fall

Today was anything but business as usual at Social Security Headquarters in Belmopan as the boss had been sent home - suspended, or nicely put, placed on "administrative leave" after the board launched an investigation into "insider trading", reportedly by more than 10 staffers.

Chairman Lois Young called it insider trading because she claims those persons used their inside knowledge that government was preparing a mortgage forgiveness programme to get their balances under the fifty thousand dollar threshold.

Solid information says that CEO Merlene Bailey Martinez did this - as early as November - and others followed. So Bailey-Martinez has been suspended along with the internal auditor Denise Mahler. We could not confirm if Mahler participated - or simply failed to report the irregularity, or both.

Chairman Lois Young says they will remain on suspension for two weeks or until an independent investigation is completed. In the meantime, we understand there has been a mood of stunned disbelief at Social Security as Bailey-Martinez is known to be strict and scrupulous, but has now fallen from grace with a mighty thud - with the tremors resonating all through the organization. A terse communiqué sent to staff this morning from the executive secretary simply informs them that Leticia Vega - the head of the office of Strategic Management is holding over as the Chief Executive Officer and Carol Moss is holding over as Manager of the Internal Audit department until further notice.

Staffers have not been told about the when the independent audit will commence or - for those who tried to get into the mortgage forgiveness programme - what will happen to their outstanding balances, or the money paid in. Chairman Lois Young did not respond to our questions about the investigation today.

Whatever the case, the Ministry of Finance's list has been finalized and tomorrow the house is expected to approve the write-off of 6.9 million dollars in mortgages - which is the present value of the 17 million in mortgages 0- many of which are impaired.

Channel 7

2012: What Does It Really Mean?

And while that young business owner is banking on future growth - followers of the 2012 Apocalypse narrative wonder if there will be a future.

It's no joke, many take December 23, 2012 as a very serious date - that marks the end of the Mayan Calendar, a b'ak'tun, as it is called.

And while the end of the world types will be preparing for the worst, Belize's Tourism industry will be preparing for the very best of times - that's because visitor interest in the Mundo Maya world will be at an all-time high.

BTB and NICH have teamed up for a full Calendar of activities for 2012 - starting with a lecture by a visiting professor tonight at the Bliss Center.

Director of the Institute of Archaeology, Dr. Jaime Awe told us what the ancient Maya actually said about 2012:

Dr. Jaime Awe - Director, Institute of Archaelogy
"There's been a lot of "hoopla" about 2012. In fact, for many people, they see 2012 as the end of this eventful occasion in the Maya calendar, when the calendar ends; so ends the world. But in fact - and there is a lot of publications that are going around, in fact I brought one with me, that's being done by the Institute of American Archaeology. And as you can see, there's the "hoopla" that also looks at it as a myth, some event that we really can't explain the year in the Ancient Maya calendar because it marks the completion of this great cycle of time called "The 13th B'ak'tun", but what happens is that a lot of folks said, 'We like things very apocalyptic, and we like these kinds of events that makes the headlines'. But what indeed was December 21, 2012 to the Maya? Well, it doesn't seem to have been as negative a deal as we modern Western philosophers believe. In fact, what we know is that there is actually only one reference in Ancient Maya records that make reference to 2012. Only on one monument that's found in at a site in Mexico called "Tortuguero" is the date 2012 mentioned. And what do they mention about it? Well, they say that on that date, this deity, who's not even a very well-known important god, that he comes down to Earth and gets dressed. What does that mean? Nobody really knows, but does it mean that it's going to be apocalyptic, that the world will come to an end? We don't believe so. Why? Well because there are also at least one, if not more, monument that talk about dates even beyond 2012. There's an inscription on a monument at Palenque that says that something is also going to happen at the end of the 20th B'ak'tun, in about something like 5072 A.D. So obviously, to the Maya, they knew that the world wasn't going to come to an end."

The Belize 2012 Mayan calendar was launched at 6:00 at the Bliss Center and right now - starting at 7:30 a lecture will be given by expert professor Dr. Mark Van Stone on what the ancient Mayan actually said about 2012.

Channel 7


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#428411 - 01/19/12 10:34 AM Re: Mayas Never Predicted December 2012 Apocalypse [Re: Marty]
Marty Offline
The Living Maya

The following information was released by the Presbyterian Church (U.S.A.):

On Dec. 21, 2012, the Mayan calendar reaches the end of its 5,126 epoch. Thats a cause of consternation among some end-times adherents, and amusement among some descendants of the Maya.

Fresh from having survived one end-of-the-world prediction " a two-stage affair covering 2011s drop-dead dates of May 21 and Oct. 21 " we now plunge into the countdown for End Times 2012.

Should you be inclined, you can use your smart phone to check how many days are remaining before a date that was carved into rock by a pre-Columbian civilization.

You can blame " or credit " the Maya for the commotion. Or, more likely, their New Age adherents.

Sure, the ancient Mayan calendar does technically end at Dec. 21, 2012. But Mayan experts say its simply a case of one long Mayan epoch " of 5,126 years " coming to an end, in much the same way the 1900s came to an end.

I dont think the Mayan put a picture of Porky Pig at the end of their calendar and said, Thats all, folks, said Jefferson Harman, a Pompton Lakes, N.J., intuitive, or dream-interpreter, who runs a workshop called Beyond 2012.

All this calendar talk is news to Firmo Choc, a 39-year-old Mayan farmer who lives in a rural village in Belize. The first he heard of the New Age crowds fuss over his cultures ancient calendar was recently, when his American employer told him about it.

Not only was Choc taken aback to hear the end of the world prediction attributed to his people, he was surprised outsiders are even familiar with the calendar. He, his family, his friends and neighbors all use the standard Western calendar.

The Mayan who surround me have no idea that some calendar their ancestors created indicates that a great change is to occur in 2012. They are just hoping their corn and cacao crops will be plentiful so their family won't starve in 2012, said Chocs employer, Anne-Michelle Marsden " a Rutgers University professor who lives in Belize.

About a decade ago, Marsden spent her sabbatical year in Belize producing a documentary called The Living Maya. Choc travels to the coast by bus along unpaved roads twice a week to work as her groundskeeper.

He has eight children; the oldest boy had to stop his schooling to help on the family cacao farm. Hes Catholic, but participates in the Mayan Deer Dance ceremony when it is celebrated in his village.

Choc is not concerned about the world ending any time soon. Hes mostly concerned about supporting his family. School fees are very expensive, wages are low and job prospects for non-farmers poor.

Mayans in parts of Guatemala and Mexico still refer to the ancient Mayan calendar, consulting it in part because of the belief that certain glyphs, or pictures that accompany the days, influence events in much the way astrological signs are said to hold sway.

The Maya wouldn't be the first civilization to come up with an increasingly complicated system for tracking time. The most obvious way to mark time is by using the moons cycle. However, this doesnt match up neatly with the solar year, or the time the Earth takes to circle the sun. So every cultures calendar has had to insert little amendments along the way to account for those burps and hiccups of time.

Christians tinkered with the length of the months, dumped the Julian calendar (for the most part) and threw in Leap Year. Jews insert a lunar month every now and then. Muslims simply decided against trying to have each month fall during the same season every year.

The Mayans just kept adding to their equation of time, creating a dizzying combination of Round and Long Form calendars, peppered by little symbols, or glyphs. Some interpret the calendar to include 13 tones, or characteristics that affect the day.

Over the years, this has proved to be a veritable cottage industry for archeologists, anthropologists and numerologists, who have been throwing out theories of interpretation since the turn of the (previous) century.

With very little in the way of written documentation from the calendars originators, the theories are hard to prove " or disprove.

The end times proposition has been floating around for 30 years or so by New Age spiritualists like the late Terence McKenna, who claimed it signaled the start of a period of broader human consciousness.

Denise Saracco, a self-described shaman and massage therapist who runs a workshop called Demystifying the Mayan Calendar out of the Peaceful Paths store in Butler, N.J., learned about the calendar as part of her two-year shaman apprenticeship.

Between the calendars 20 glyphs and 13 tones, it can get crazy complex, she said. Saracco feels 2012 is a key date " although she stops short of predicting what will happen.

She foresees a shift in collective priorities, away from materialism to a simpler life of more mutual respect and less divisiveness.

Is it the end of the world? No, she said. Its the end of the world as we know it.

Kathleen O'Brien writes for The Star-Ledger in Newark, N.J.

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#431159 - 02/23/12 08:29 AM Re: Mayas Never Predicted December 2012 Apocalypse [Re: Marty]
Marty Offline

Why did the Maya go through all the trouble to calculate events and dates so far in the past and into the future?

Last month we hosted renowned Mayanist Dr Mark Van Stone, author of the recently released book, 2012 – Science and Prophecy of the Ancient Maya as part of our 2012 year-long series of Maya presentations, special tours and events.

We asked Dr. Mark Van Stone a number of questions on the Maya and the year 2012 and we have decided to share the questions and answers with our readers.

The first question we asked him was:

Why did the Maya go through all the trouble to calculate events and dates so far in the past and into the future?

His response:

Because they could. Most of our familiar ancient civilizations had relatively primitive numerical systems. Egypt and China, for example, and particularly the nations which used letters for numbers. These systems are cumbersome to calculate with.Try multiplying Roman numerals; LXXIX times DCCLXIV, for example.
Greeks and Canaanites wrote 1, 2, 3, … as alpha, beta, gamma (aleph, beth, gimel). The next ten letters stood for 10, 20, 30, and so on, and the next letters stood for 100, 200, 300, and pretty soon they ran out of letters. The reason that Noah and Adam lived to 950 years, and Methusaleh to 969, was because the Old Testament Hebrews had no easy way to write 1000 (or 2011, or 186,284).

The Maya, on the other hand, had a numeral system like ours, with place-value and zero. (Our system, first introduced from India some 2000 years ago, allows us to write very large numbers very precisely, like 1,346,708,093.) The Maya system works the same way, though they count by twenties. We count on our ten fingers, and the tropical Maya went barefoot and counted on their toes, too.

This facility with numbers enthralled Maya priests. They must have seen this power over quantities as a kind of reflection of godly power, because their Mathematics was pretty much the servant of Numerology. At least so far as we know. We actually know very little about the Maya, really, and we do our best to fill in the gaps. By far, most of what we know about their mathematics is deduced from the huge calculations they made counting days: They made a point of connecting events in time with specific intervals of days (we call them “distance numbers”), just as Abraham Lincoln connected the Battle of Gettysburg with the Declaration of Independence, with, “Four score and seven years ago…”
A Maya historical inscription would say, for example: “The birth of Lord Such-and-Such occurred on Thursday, August 7th. Five days, three months, and six years later, it was Tuesday, November 10th, and Lord Such-and-Such was designated heir. Ten days, two months, and 22 years later, it was Tuesday, January 20th, and he was crowned king….”

Apparently Maya priests considered an event’s placement in the cycles of time to be of paramount importance. Presumably this has to do with the auguries of the days: A particular day’s horoscope had a lot to do with the activities scheduled for that day. And this horoscope was extraordinarily sophisticated and complex. All four of the surviving books we have from the Maya were guides for Calendar-priests, mostly complex augury/horoscope tables.

For ordinary events divided by short intervals, time distances were pretty random. But the Maya also liked to connect their rulers’ lives and reigns with similar events in the noble past —especially those performed by gods—, and sometimes into the future. These connections were more than an intellectual game, they were a guide, a justification, for the rulers’ choices. The king might choose to inaugurate a ceremony on a certain day because an ancient god did the same on the same day in the distant past. This practice turns these events into a kind of anniversary celebration.

More commonly, the intervals were not, say, the 100th anniversary of an event, but rather more complex. For example, in a Palenque inscription on the Tablet of the Cross, two similar events were separated by 1,359,540 days (more than 3722 years). Floyd Lounsbury discovered that this number was not accidental: It was a carefully-calculated multiple of several Maya magic numbers: 4 x 5 x 7 x 9 x 13 x 83. The numerological power of each of these factors combined to sanctify the later event. This kind of justification-by-multiplication became a feature of Classic Maya religion; many of their inscriptions devote fully half the space to the mathematics.

SOURCE


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