Thursday, April 10, 2008

 

Aztec Math Decoded; Tax Woes

http://news.nationalgeographic.com/news/2008/04/080403-aztec-math.html

Aztec Math ; Tax Woes





Brian Handwerk
for National Geographic News
April 3, 2008

Today's tax codes are complicated, but the ancient Aztecs likely shared your pain.

To measure tracts of taxable land, Aztec mathematicians had to develop their own specialized arithmetic, which has only now been decoded.

By reading Aztec records from the city-state of Tepetlaoztoc, a pair of scientists recently figured out the complicated equations and fractions that officials once used to determine the size of land on which tributes were paid.

Two ancient codices, written from A.D. 1540 to 1544, survive from Tepetlaoztoc. They record each household and its number of members, the amount of land owned, and soil types such as stony, sandy, or "yellow earth."

"The ancient texts were extremely detailed and well organized, because landowners often had to pay tribute according to the value of their holdings," said co-author Maria del Carmen Jorge y Jorge at the National Autonomous University in Mexico City, Mexico.

The Aztecs recorded only the total area of each parcel and the length of the four sides of its perimeter, Jorge y Jorge explained.

Officials calculated the size of each parcel using a series of five algorithms—including one also employed by the ancient Sumerians—she added.

"Rule of Thumb" and Other Body Parts

The Aztec arithmetic included fractional symbols like hearts, hands, and arrows that seem unusual to modern eyes. But to the Aztecs they likely had a relation to the familiar—the human body.

"For example the heart," Jorge y Jorge said.

"If you stretch out your left arm, that would be the measure from your heart to the tip of your finger. If you stretch both arms, the measure of the hand would be the distance between the tips of your two fingers.

"It's just very natural. Your body you carry with you all the time and it's very easy to refer whatever you want to measure to your body."

The primary land unit was likely the distance from the ground to the tip of a finger on an adult's upraised right arm—about 8.2 feet (2.5 meters), she said.

Jorge y Jorge and co-author B.J. Williams of the University of Wisconsin-Rock County report their findings in this week's issue of the journal Science.

"I think [the study] is neat because it shows that this sort of math and science was pretty practical in orientation," said Michael Smith, an archaeologist and Aztec expert at Arizona State University.

(Read related story: "Inca Tax Records Were Tied Up in Knots, Study Says" [August 11, 2005].)

"We have the idea that ancient societies were dominated by religion. Yeah, religion was important, but they were also very practical people doing very practical things," Smith said.

"With this sort of rule-of-thumb surveyor's math, they figured out a way to get it done."

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Wednesday, April 9, 2008

 

Mayan - index

  1. Shaping the Mayan World View. This journey begins with murals from a ... Human sacrifice was part of ritual within Mayan culture that we may find offensive. ...
    mc.maricopa.edu/.../asb/anthro2003/legacy/mayan_lost_tribes/index.html - 9k - Cached
  2. ... vestiges in the world and one of the most beautiful cities of the Mayan culture. ... Series, in which the beginning of the Tulum's construction can ...
    www.cancuntravel.com/archaeology.asp - 41k - Cached
  3. Additional Categories. Archaeology (32) Calendars (8) SITE LISTINGS By ... "svalues"), and the beginning of an archive of digitally transcribed Mayan texts. ...
    dir.yahoo.com/Society_and_Culture/Cultures_and_Groups/Cultures/Mayan - 14k - Cached
  4. Popol Vuh: the Definitive Edition of the Mayan Book of the Dawn of Life and the Glories of Gods and Kings. ... of American Archaeology and Ethnology, Harvard ...
    en.wikipedia.org/wiki/Mayan_Calendar - 112k - Cached
  5. Beginning in October we will be offering two Mayan tours that will travel each ... remembered that Mayan lore is more than the ruins and forgotten culture of a ...
    www.themayantraveler.com - 35k - Cached
  6. ... apart from any other building at the beginning of the stone causeway leading to Uxmal. ... Mayan Culture: Mayan Beliefs. Mayan Ceremonial Site. Mayan Life ...
    www.yucatantoday.com/culture/eng-archaeology.htm - 29k - Cached
  7. ... Spas Festivals & Holidays Shopping & Handicrafts History & Culture Food & Drink ... the serpent descends, marking the beginning of Spring and bringing the ...
    gomexico.about.com/od/ancientsites/a/mayan_sites.htm - 25k - Cached
  8. As Maya archaeology advanced during the 20th century and nationalist and ethnic ... The K'iche' culture was at its pinnacle at the time of the Spanish conquest. ...
    en.wikipedia.org/wiki/Mayan_language - 191k - Cached
  9. Stelae with oldest inscribed date yet found in Guatemala (235 BC) marks beginning of the country's written history. Aguateca. On the shore of Lake Petexbatún in the ...
    www.mayalandia.com/activities/archaeology.php - 10k - Cached
  10. By studying modern Maya religious practices, archaeologists and anthropologists are beginning to gain critical insight into rites often depicted in ancient ...
    www.archaeology.org/9707/etc/maya.html - 30k - Cached
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http://news.nationalgeographic.com/news/2005/12/1213_051213_mural_photo.html



Photo in the News: Oldest Known Maya Mural Reveals Royal Tale

Photo: Maya mural of San Bartolo




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December 13, 2005—Archaeologists today revealed the final section of the earliest known Maya mural ever found, saying that the find upends everything they thought they knew about the origins of Maya art, writing, and rule.

The painting was the last wall of a room-size mural to be excavated. The site was discovered in 2001 at the ancient Maya city of San Bartolo in the lowlands of northeastern Guatemala.

"It is really breathtaking how beautiful this is," said William Saturno, an archaeologist with the University of New Hampshire and the Harvard Peabody Museum of Archaeology and Ethnology.

The mural tells the story of creation, the mythology of kingship, and the divine right of a king, according to Saturno, who made the find and leads the excavation.

The painting dates to 100 B.C., proving that stories of creation and kings—and the use of elaborate art and writing to tell them—were well established more than 2,000 years ago, 700 years earlier than previously believed.

"In that way it really is like you didn't know the Renaissance ever happened—you have no knowledge that anyone ever painted anything in Florence in the 16th century, then all of sudden you see a Michelangelo," Saturno said.

John Roach


Photograph by Kenneth Garrett © 2006 National Geographic
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http://news.nationalgeographic.com/news/2005/11/1117_051117_maya_massacre.html
Mass Graves Reveal Massacre of Maya Royalty

Mass Graves Reveal Massacre of Maya Royalty

Stefan Lovgren
for National Geographic News
November 17, 2005

Archaeologists have discovered what they believe was the gruesome scene of a royal massacre in the ancient city of Cancuén, once one of the richest cities in the Maya empire.

The bones of 31 executed and dismembered Maya nobles were found in a sacred reservoir at the entrance to the royal palace in Cancuén in the Petén rain forest of Guatemala.

Researchers also found a shallow grave nearby containing the skeletons of two people they believe were the king and queen.

The bones of more than a dozen executed upper-class Maya were found at a third burial site north of the royal palace.

The apparent executions—along with the discovery of unfinished defensive walls and houses—suggest that the city was wiped out by an invading force around A.D. 800, a critical moment at the beginning of the mysterious collapse of the great Maya empire.

Arthur Demarest, who led the research team that made the discovery, has studied the collapse of the Maya civilization for 20 years. He says the massacre site is "by far the most important thing" he has ever found.

"It's like a photograph of a single, very critical moment in time," Demarest, an anthropology professor at Vanderbilt University in Nashville, Tennessee, said by phone from Guatemala.

The Cancuén excavation was partly funded by the National Geographic Society. The discovery is the subject of Explorer: Last Days of the Maya, which airs on the National Geographic Channel on Sunday, November 27 at 8 p.m. ET/PT.

Ancient CSI

The wealthy Cancuén kingdom was strategically located at the start of the Pasión River, the greatest trade route of the ancient Maya world. Its royal palace covered an area equal to more than five football fields.

Demarest began exploring the site in 1996 and has been excavating there since 1999.

In May this year the researchers were studying the area's water system when they made their gruesome discovery: a 90-square-yard (75-square-meter) reservoir near the entrance to the royal palace filled with thousands of human bones and precious artifacts.

Because of the scale of the discovery, the archaeology team enlisted the help of the Forensic Anthropological Foundation of Guatemala.

The scientists found bones of 31 bodies in the grave. Forensic analysis determined that victims had been killed with spears and axes. Many of the bodies had been dismembered. The bones were dated to A.D. 800.

"The deposit was sealed in wet mud, and the preservation is extraordinary," Demarest said. "These are the best-looking bones I have ever seen. We could tell that these were not war wounds but that the people had been executed."

Precious jewelry found in the grave—including jades, jaguar fang necklaces, and coast shells—indicates that the victims were nobles, possibly from the royal palace.

In a shallow grave 80 yards (73 meters) away, the researchers made another spectacular discovery: two people who appear to be the king and queen of Cancuén buried in full regalia.

Demarest says a necklace found on the king has an inscription that says in part, "Kan Maax. Holy Lord of Cancuén."

Failed Defense

In the years preceding the massacre, warfare had spread across the western region of the ancient Maya world. The unrest seems to have reached Cancuén in A.D. 800.

Unfinished construction around the city, including a system of hastily built stone and wooden palisade walls, suggests that the residents may have known that they were going to come under attack.

"The defense obviously failed," Demarest said.

While commoners may have run away or been taken captive, nobles—men, women, and children—were lined up and executed. The bodies were then deposited with some ceremony in the sacred cistern at the palace entrance, the researchers speculate.

There is no evidence that the city was conquered. Instead the assailants seem to have abandoned it after their attack.

"The massacre is an exceptionally dramatic example of the violence marking the end of royal court life and divine kingship in classic Maya civilzation," said David Freidel, a Maya expert at Southern Methodist University in Dallas, Texas.

At least one Maya expert declined to comment on the discovery, citing that the findings had not yet been published in an academic journal and had not been peer reviewed.

Experts have fiercely debated the cause of the quick demise of Maya society, which once ranged from Mexico's Yucatán peninsula to Honduras.

Some of the theories about the collapse include such factors as overpopulation, drought, political conflict, and loss of the royal court.

While the massacre discovery seems to suggest that warfare played an important role, Demarest believes there is no one "silver bullet" to explain the decline of the Maya culture.

"What we are seeing [with massacres like these] is the beginning of the end," he said. "That doesn't mean they caused the collapse. We're moving away from this idea that it had to be this one dramatic reason for the collapse."

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http://news.nationalgeographic.com/news/2002/09/0917_020919_pilas.html

Maya Hieroglyphs Recount "Giant War"

D.L. Parsell
for National Geographic News
September 19, 2002

Newly translated inscriptions at an ancient pyramid in Guatemala suggest that the Maya civilization, at its peak, was dominated by two powerful city-states that engaged in a protracted "superpower" struggle.

The evidence comes from hieroglyphs on a building at Dos Pilas, a relatively small but strategically important Maya kingdom now partly obscured in dense rain forest.

The inscriptions, which appear on the staircase of a Maya pyramid dating from the seventh century, are one of the most extensive Maya texts ever found.

The texts show that Dos Pilas played a major role in fierce and bloody warfare that raged back and forth between the major Maya cities of Tikal and Calakmul for a century, until Tikal finally prevailed in about A.D. 695.

The inscriptions offer strong evidence supporting a theory proposed a decade ago by two Maya experts who challenged the prevailing belief that conflicts in the region were mainly local clashes between independent city-states. In their alternative interpretation, Simon Martin and Nikolai Grube proposed that these campaigns reflected a larger struggle between major powers.

Arthur Demarest, a professor of anthropology at Vanderbilt University in Tennessee who organized the translation of the newly revealed glyphs, said their content has convinced him, after years of skepticism, that Martin and Grube were right.

"Rather than being an independent actor, as previously thought, it now appears that Dos Pilas was a pawn in a much bigger battle," said Demarest. "In today's terms, Dos Pilas was the Somalia or Vietnam of the Maya world, used in a war that was actually between two superpowers."

Some of the inscriptions at Dos Pilas first came to light years ago. The glyphs describe repeated clashes between Dos Pilas and Tikal, a successful attack on Tikal by Calakmul, and eventually a great defeat for the king of Tikal.

Information about these events was fragmentary, however, and many questions were left unanswered. Two years ago, a storm blew through Dos Pilas, knocking down a tree and exposing ten more steps, which have provided a much more complete picture of events.

Federico Fahsen, a Guatemalan expert on Maya glyphs, headed a team that traveled to Dos Pilas last year to excavate the steps and document the inscriptions. "The hundreds of new glyphs fill in a vital 60-year gap of unknown Maya history and clarify many of the political and military relationships of this critical period," said Fahsen, an adjunct professor at Vanderbilt.

Demarest added, "It's rare that you find a new monument and it fills in such a large blank spot about the history of a region."

Puppet State

One of the biggest mysteries the inscriptions answered was the nature of Dos Pilas's relations with Tikal and Calakmul.

Tikal (known at that time as Mutul) was located in what is now northern Guatemala; Calakmul was about 60 miles (97 kilometers) further north, in Mexico. Dos Pilas is about 70 miles (113 kilometers) southwest of Tikal.

Many scholars have thought that any alliances between Maya kingdoms were weak associations between entities that were essentially autonomous. Thus, the researchers were surprised to discover from the new inscriptions that Dos Pilas was conquered by Calakmul and became its puppet state for many years.

"When I read those glyphs, I had to blink to make sure I was reading it correctly," said Fahsen. "I had never heard of Calakmul actually invading and defeating the king of Dos Pilas. We thought that, at most, they may have had a weak alliance of some type."

The text also forced researchers to revise earlier assumptions about the conflict between Dos Pilas and Tikal. "This had previously been known as only a domestic quarrel between two brothers. Now we know it was part of a more global conflict between Tikal and Calakmul, in which Dos Pilas played a part," said Fahsen.

"Like U.S.-Russian fighting by proxy," he added, "this introduces the whole concept of a sort of global fighting in the Maya civilization."

Dos Pilas was first established in A.D. 629 as a military stronghold of Tikal. Dos Pilas was important to Tikal and later to Calakmul because it strengthened their clout at the southern edge of the Maya lowlands, which was a major gateway for trade. Precious goods such as jade, obsidian, quetzal feathers, and shells from the Caribbean flowed between the highlands and lowlands via the region"s Pasón River.

When Dos Pilas was founded, the ruler of Tikal installed his four-year-old brother on the throne. The glyphs include a detailed account of significant events in the life of this first king, Balaj Chan K'awiil, who lived to be about 60.

The inscriptions show that Balaj Chan K'awiil became a young warrior and remained loyal to his brother and other members of the royal family at Tikal for years. But when he was in his 20s, Calakmul conquered Dos Pilas and the young king was forced to shift his alliances.

Under the banner of Calakmul, K'awiil waged war against Tikal for a decade and eventually sacked the city-state, carrying its ruler—his brother—and other members of the nobility back to Dos Pilas to be killed.

The text at Dos Pilas describes the bloodshed and the celebration that followed. "The west section of the steps was very graphic," said Fahsen. "It says, 'Blood was pooled and the skulls of the people of the central place of Tikal were piled up.' The final glyphs describe the king of Dos Pilas doing a victory dance."

After the victory over Tikal, Dos Pilas embarked on a campaign of conquest with Calakmul's backing and became a major regional power until it collapsed in A.D. 760.

Changing Views

Ideas about the Maya civilization and its political organization have changed steadily over the past several decades as scholars have acquired new evidence from archeological discoveries and translations of Maya texts. And the "Maya superpowers" theory, like all scholarship, will remain subject to debate and revision.

Simon Martin of the Institute of Archaeology at University College, London, said that in the 1960's, most scholars viewed Maya cities as components of a small number of "regional states."

Then, as translations of Maya texts became available beginning in the 1980s, these cities were shown to be capitals of smaller kingdoms that were almost constantly in conflict with one another, but failed to create bigger and more stable states by conquest. To explain such a fragmented political landscape, many researchers assumed that Maya kingdoms were inherently weak.

Martin said he and Grube regarded the prevailing ideas as "implausible."

For one thing, although there were a great number of small Maya states, the capitals of some were vastly larger and more populous than others. More important, Maya inscriptions indicated that some kings were "owned" by other kings from bigger and more successful cities or were crowned under the "supervision" of rulers from dominant kingdoms who evidently had established themselves as regional hegemons.

Martin said that when he and Grube compared this evidence with records of warfare in the region, there was a strong correlation between militarily successful cities and those sanctioning and installing other rulers.

"We took these structures and charted them, building a database that suggested there was some kind of greater shape in the ways that Maya kingdoms were organized," he said.

Scholars don't know how much the constant warfare between city-states may have contributed to the eventual collapse of the Maya civilization by A.D. 900, although most agree that it was probably a significant factor.

Demarest thinks the warfare described in the Dos Pilas inscriptions may reflect a period when the Maya civilization was on the verge of moving to a higher level of organization and consolidating into a single empire. "However, this didn't happen," he said.

"Instead, the giant war went back and forth," he explained. "After Tikal was sacked, it eventually roared back and crushed Calakmul. And then the Maya world broke up into regional powers, setting the stage for a period of intensive, petty warfare that finally led to the collapse of the Maya."

David Stuart, a Maya hieroglyph expert at Harvard University, said the conflicts recorded in the seventh-century inscriptions at Dos Pilas did not lead directly to the abandonment of Maya cities, which happened much later. "But it's true," he said, "that warfare is a big issue in Maya history, right up to the time of abandonment, although I think something catastrophic, whether environmental or what, played a major part."

The information on the staircase at Dos Pilas is important, said Stuart, because it "gives us an idea of how bad things were—of the warfare and intrigue that was going on. It shows that these couldn't have been very happy times."

The discovery of the glyphs at Dos Pilas is reported in the October 2002 issue of National Geographic magazine, and aired on the National Geographic U.S. cable television program National Geographic Today. National Geographic supported this work along with Vanderbilt University, the Foundation for the Advancement of Mesoamerican Studies, and Guatemala's Ministry of Culture.

For Additional National Geographic News Stories and Web Sites

Copan Update: Maya Tomb Ransacked
National Geographic Kids Secret of the Maya Glyphs
Excavations Challenge Views of Maya Development in Yucatán
Maya Murals May Depict Murder of Royal Scribes
Oldest Intact Maya Mural Found in Guatemala



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