Mayan

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Hernán Cortés, excited by stories of the lands which Columbus had recently discovered, sailed from Spain in 1505 landing in Hispaniola which is now Santo Domingo. After farming there for some years he sailed with Velázquez to conquer Cuba in 1511. He was twice elected major of Santiago then, on 18 February 1519, he sailed for the coast of Yucatán with a force of 11 ships, 508 soldiers, 100 sailors, and 16 horses. He landed at Tabasco on the northern coast of the Yucatán peninsular. He met with little resistance from the local population and they presented him with presents including twenty girls. He married Malinche, one of these girls.

The people of the Yucatán peninsular were descendants of the ancient Mayan civilization which had been in decline from about 900 AD. It is the mathematical achievements of this civilization which we are concerned with in this article. However, before describing these, we should note that Cortés went on to conquer the Aztec peoples of Mexico. He captured Tenochtitlán before the end of 1519 (the city was rebuilt as Mexico City in 1521) and the Aztec empire fell to Cortés before the end of 1521. Malinche, who acted as interpreter for Cortés, played an important role in his ventures.

In order to understand how knowledge of the Mayan people has reached us we must consider another Spanish character in this story, namely Diego de Landa. He joined the Franciscan Order in 1541 when about 17 years old and requested that he be sent to the New World as a missionary. Landa helped the Mayan peoples in the Yucatán peninsular and generally tried his best to protect them from their new Spanish masters. He visited the ruins of the great cities of the Mayan civilization and learnt from the people about their customs and history.

However, despite being sympathetic to the Mayan people, Landa abhorred their religious practices. To the devote Christian that Landa was, the Mayan religion with its icons and the Mayan texts written in hieroglyphics appeared like the work of the devil. He ordered all Mayan idols be destroyed and all Mayan books be burned. Landa seems to have been surprised at the distress this caused the Mayans.

Nobody can quite understand Landa's feelings but perhaps he regretted his actions or perhaps he tried to justify them. Certainly what he then did was to write a book Relación de las cosas de Yucatán (1566) which describes the hieroglyphics, customs, temples, religious practices and history of the Mayans which his own actions had done so much to eradicate. The book was lost for many years but rediscovered in Madrid three hundred years later in 1869.

A small number of Mayan documents survived destruction by Landa. The most important are: the Dresden Codex now kept in the Sächsische Landesbibliothek Dresden; the Madrid Codex now kept in the American Museum in Madrid; and the Paris Codex now in the Bibliothèque nationale in Paris. The Dresden Codex is a treatise on astronomy, thought to have been copied in the eleventh century AD from an original document dating from the seventh or eighth centuries AD.

The Dresden codex:

Knowledge of the Mayan civilization has been greatly increased in the last thirty years (see for example [3] and [8]). Modern techniques such as high resolution radar _images, aerial photography and satellite _images have changed conceptions of the Maya civilization. We are interested in the Classic Period of the Maya which spans the period 250 AD to 900 AD, but this classic period was built on top of a civilization which had lived in the region from about 2000 BC.

The Maya of the Classic Period built large cities, around fifteen have been identified in the Yucatán peninsular, with recent estimates of the population of the city of Tikal in the Southern Lowlands being around 50000 at its peak. Tikal is probably the largest of the cities and recent studies have identified about 3000 separate constructions including temples, palaces, shrines, wood and thatch houses, terraces, causeways, plazas and huge reservoirs for storing rainwater. The rulers were astronomer priests who lived in the cities who controlled the people with their religious instructions. Farming with sophisticated raised fields and irrigation systems provided the food to support the population.

The Maya number system was a base twenty system.

Here are the Mayan numerals.

Almost certainly the reason for base 20 arose from ancient people who counted on both their fingers and their toes. Although it was a base 20 system, called a vigesimal system, one can see how five plays a major role, again clearly relating to five fingers and toes. In fact it is worth noting that although the system is base 20 it only has three number symbols (perhaps the unit symbol arising from a pebble and the line symbol from a stick used in counting). Often people say how impossible it would be to have a number system to a large base since it would involve remembering so many special symbols. This shows how people are conditioned by the system they use and can only see variants of the number system in close analogy with the one with which they are familiar. Surprising and advanced features of the Mayan number system are the zero, denoted by a shell for reasons we cannot explain, and the positional nature of the system. However, the system was not a truly positional system as we shall now explain.

In a true base twenty system the first number would denote the number of units up to 19, the next would denote the number of 20's up to 19, the next the number of 400's up to 19, etc. However although the Maya number system starts this way with the units up to 19 and the 20's up to 19, it changes in the third place and this denotes the number of 360's up to 19 instead of the number of 400's. After this the system reverts to multiples of 20 so the fourth place is the number of 18 20², the next the number of 18 20³ and so on. For example [8;14;3;1;12] represents

12 + 1 20 + 3 18 20 + 14 18 20² + 8 18 20³ = 1253912.

As a second example [9;8;9;13;0] represents

0 + 13 20 + 9 18 20 + 8 18 20² + 9 18 20³ =1357100.

Both these examples are found in the ruins of Mayan towns and we shall explain their significance below.

Now the system we have just described is used in the Dresden Codex and it is the only system for which we have any written evidence. In [4] Ifrah argues that the number system we have just introduced was the system of the Mayan priests and astronomers which they used for astronomical and calendar calculations. This is undoubtedly the case and that it was used in this way explains some of the irregularities in the system as we shall see below. It was the system used for calendars. However Ifrah also argues for a second truly base 20 system which would have been used by the merchants and was the number system which would also have been used in speech. This, he claims had a circle or dot (coming from a cocoa bean currency according to some, or a pebble used for counting according to others) as its unity, a horizontal bar for 5 and special symbols for 20, 400, 8000 etc. Ifrah writes [4]:-

Even though no trace of it remains, we can reasonably assume that the Maya had a number system of this kind, and that intermediate numbers were figured by repeating the signs as many times as was needed.

Let us say a little about the Maya calendar before returning to their number systems, for the calendar was behind the structure of the number system. Of course, there was also an influence in the other direction, and the base of the number system 20 played a major role in the structure of the calendar.

The Maya had two calendars. One of these was a ritual calendar, known as the Tzolkin, composed of 260 days. It contained 13 "months" of 20 days each, the months being named after 13 gods while the twenty days were numbered from 0 to 19. The second calendar was a 365-day civil calendar called the Haab. This calendar consisted of 18 months, named after agricultural or religious events, each with 20 days (again numbered 0 to 19) and a short "month" of only 5 days that was called the Wayeb. The Wayeb was considered an unlucky period and Landa wrote in his classic text that the Maya did not wash, comb their hair or do any hard work during these five days. Anyone born during these days would have bad luck and remain poor and unhappy all their lives.

Why then was the ritual calendar based on 260 days? This is a question to which we have no satisfactory answer. One suggestion is that since the Maya lived in the tropics the sun was directly overhead twice every year. Perhaps they measured 260 days and 105 days as the successive periods between the sun being directly overhead (the fact that this is true for the Yucatán peninsular cannot be taken to prove this theory). A second theory is that the Maya had 13 gods of the "upper world", and 20 was the number of a man, so giving each god a 20 day month gave a ritual calendar of 260 days.

At any rate having two calendars, one with 260 days and the other with 365 days, meant that the two would calendars would return to the same cycle after lcm(260, 365) = 18980 days. Now this is after 52 civil years (or 73 ritual years) and indeed the Maya had a sacred cycle consisting of 52 years. Another major player in the calendar was the planet Venus. The Mayan astronomers calculated its synodic period (after which it has returned to the same position) as 584 days. Now after only two of the 52 years cycles Venus will have made 65 revolutions and also be back to the same position. This remarkable coincidence would have meant great celebrations by the Maya every 104 years.

Now there was a third way that the Mayan people had of measuring time which was not strictly a calendar. It was an absolute timescale which was based on a creation date and time was measured forward from this. What date was the Mayan creation date? The date most often taken is 12 August 3113 BC but we should say straightaway that not all historians agree that this was the zero of this so-called "Long Count". Now one might expect that this measurement of time would either give the number of ritual calendar years since creation or the number of civil calendar years since creation. However it does neither.

The Long Count is based on a year of 360 days, or perhaps it is more accurate to say that it is just a count of days with then numbers represented in the Mayan number system. Now we see the probable reason for the departure of the number system from a true base 20 system. It was so that the system approximately represented years. Many inscriptions are found in the Mayan towns which give the date of erection in terms of this long count. Consider the two examples of Mayan numbers given above. The first

[8;14;3;1;12]

is the date given on a plate which came from the town of Tikal. It translates to

12 + 1 20 + 3 18 20 + 14 18 20² + 8 18 20³

which is 1253912 days from the creation date of 12 August 3113 BC so the plate was carved in 320 AD.

The second example

[9;8;9;13;0]

is the completion date on a building in Palenque in Tabasco, near the landing site of Cortés. It translates to

0 + 13 20 + 9 18 20 + 8 18 20² + 9 18 20³

which is 1357100 days from the creation date of 12 August 3113 BC so the building was completed in 603 AD.

We should note some properties (or more strictly non-properties) of the Mayan number system. The Mayans appear to have had no concept of a fraction but, as we shall see below, they were still able to make remarkably accurate astronomical measurements. Also since the Mayan numbers were not a true positional base 20 system, it fails to have the nice mathematical properties that we expect of a positional system. For example

[9;8;9;13;0] = 0 + 13 20 + 9 18 20 + 8 18 20² + 9 18 20³ = 1357100

yet

[9;8;9;13] = 13 + 9 20 + 8 18 20 + 9 18 20² = 67873.

Moving all the numbers one place left would multiply the number by 20 in a true base 20 positional system yet 20 67873 = 1357460 which is not equal to 1357100. For when we multiple [9;8;9;13] by 20 we get 9 400 where in [9;8;9;13;0] we have 9 360.

We should also note that the Mayans almost certainly did not have methods of multiplication for their numbers and definitely did not use division of numbers. Yet the Mayan number system is certainly capable of being used for the operations of multiplication and division as the authors of [15] demonstrate.

Finally we should say a little about the Mayan advances in astronomy. Rodriguez writes in [19]:-

The Mayan concern for understanding the cycles of celestial bodies, particularly the Sun, the Moon and Venus, led them to accumulate a large set of highly accurate observations. An important aspect of their cosmology was the search for major cycles, in which the position of several objects repeated.

The Mayans carried out astronomical measurements with remarkable accuracy yet they had no instruments other than sticks. They used two sticks in the form of a cross, viewing astronomical objects through the right angle formed by the sticks. The Caracol building in Chichén Itza is thought by many to be a Mayan observatory. Many of the windows of the building are positioned to line up with significant lines of sight such as that of the setting sun on the spring equinox of 21 March and also certain lines of sight relating to the moon.

The Caracol building in Chichén Itza:

With such crude instruments the Maya were able to calculate the length of the year to be 365.242 days (the modern value is 365.242198 days). Two further remarkable calculations are of the length of the lunar month. At Copán (now on the border between Honduras and Guatemala) the Mayan astronomers found that 149 lunar months lasted 4400 days. This gives 29.5302 days as the length of the lunar month. At Palenque in Tabasco they calculated that 81 lunar months lasted 2392 days. This gives 29.5308 days as the length of the lunar month. The modern value is 29.53059 days. Was this not a remarkable achievement?

There are, however, very few other mathematical achievements of the Maya. Groemer [14] describes seven types of frieze ornaments occurring on Mayan buildings from the period 600 AD to 900 AD in the Puuc region of the Yucatán. This area includes the ruins at Kabah and Labna. Groemer gives twenty-five illustrations of friezes which show Mayan inventiveness and geometric intuition in such architectural decorations.

Article by: J J O'Connor and E F Robertson

Maya
a. A member of a Mesoamerican Indian people inhabiting southeast Mexico, Guatemala, and Belize, whose civilization reached its height around A.D. 300-900. The Maya are noted for their architecture and city planning, their mathematics and calendar, and their hieroglyphic writing system. b. A modern-day descendant of this people.
2. Any of the Mayan languages, especially Quiché and Yucatec.

Excerpted from The American Heritage Dictionary of the English Language, Third Edition Copyright © 1992 by Houghton Mifflin Company. Electronic version licensed from Lernout & Hauspie Speech Products N.V., further reproduction and distribution restricted in accordance with the Copyright Law of the United States. All rights reserved.

maya (mä'ye) noun
Hinduism.

1. The power of a god or demon to transform a concept into an element of the sensible world.
2. The transitory, manifold appearance of the sensible world, which obscures the undifferentiated spiritual reality from which it originates; the illusory appearance of the sensible world.

http://www.michielb.nl/maya/astro.html

The Aztec Calendar http://www.xs4all.nl/~voorburg/aztec.html
This privately maintained site provides a tool to convert Julian and Gregorian dates into Aztec dates as well as information about the Aztec calendar itself.

Other Views and writings on the Mayans

Map of the Mayans

The Dresden codex:

A common culture, calendar, and mythology held the civilization together and astronomy played an important part in the religion which underlay the whole life of the people. Of course astronomy and calendar calculations require mathematics and indeed the Maya constructed a very sophisticated number system. We do not know the date of these mathematical achievements but it seems certain that when the system was devised it contained features which were more advanced than any other in the world at the time. The Maya number system was a base twenty system.

Here are the Mayan numerals.

A very interesting twist on the place values after 360 is that they are multiples of 18. The first place value is 1; the second, 20, the third 18*20, the fourth is 18*202; the fourth 18*203, and so forth. Thus the Mayan numerical system would translate into ours as follows:

Mayan head numerals
Here are the head numerals for 0 through 19.

They also used a head symbol representing the moon for 20. Here is a representation of the 31st day in their calendar. You will notice that the head symbol is combined with the "normal" numerical system.

12 + 1 20 + 3 18 20 + 14 18 20² + 8 18 20³ = 1253912.

As a second example [9;8;9;13;0] represents

0 + 13 20 + 9 18 20 + 8 18 20² + 9 18 20³ =1357100.

Both these examples are found in the ruins of Mayan towns and we shall explain their significance below.

Even though no trace of it remains, we can reasonably assume that the Maya had a number system of this kind, and that intermediate numbers were figured by repeating the signs as many times as was needed.

At any rate having two calendars, one with 260 days and the other with 365 days, meant that the two would calendars would return to the same cycle after lcm (260, 365) = 18980 days. Now this is after 52 civil years (or 73 ritual years) and indeed the Maya had a sacred cycle consisting of 52 years. Another major player in the calendar was the planet Venus. The Mayan astronomers calculated its synodic period (after which it has returned to the same position) as 584 days. Now after only two of the 52 years cycles Venus will have made 65 revolutions and also be back to the same position. This remarkable coincidence would have meant great celebrations by the Maya every 104 years.

Now there was a third way that the Mayan people had of measuring time which was not strictly a calendar. It was an absolute timescale which was based on a creation date and time was measured forward from this. What date was the Mayan creation date? The date most often taken is 12 August 3113 BC but we should say straight-away that not all historians agree that this was the zero of this so-called "Long Count". Now one might expect that this measurement of time would either give the number of ritual calendar years since creation or the number of civil calendar years since creation. However it does neither.

[8;14;3;1;12]

is the date given on a plate which came from the town of Tikal. It translates to

12 + 1 20 + 3 18 20 + 14 18 20² + 8 18 20³

which is 1253912 days from the creation date of 12 August 3113 BC so the plate was carved in 320 AD.

The second example

[9;8;9;13;0]

is the completion date on a building in Palenque in Tabasco, near the landing site of Cortés. It translates to

0 + 13 20 + 9 18 20 + 8 18 20² + 9 18 20³

which is 1357100 days from the creation date of 12 August 3113 BC so the building was completed in 603 AD.

[9;8;9;13;0] = 0 + 13 20 + 9 18 20 + 8 18 20² + 9 18 20³ = 1357100

yet

[9;8;9;13] = 13 + 9 20 + 8 18 20 + 9 18 20² = 67873.

Finally we should say a little about the Mayan advances in astronomy. Rodriguez writes in [19]:-

The Mayan concern for understanding the cycles of celestial bodies, particularly the Sun, the Moon and Venus, led them to accumulate a large set of highly accurate observations. An important aspect of their cosmology was the search for major cycles, in which the position of several objects repeated.

The Caracol building in Chichén Itza:

Top of Page

Relationships with the Egyptians, placement of pyramids are similar to Ceops and/or Kufu

Construction is similar to Greece and Rome and the Egyptians.

How can this be you ask?

The Continuum, in the collectiveness of Man.

Article by: J J O'Connor and E F Robertson

The URL of this page is:
http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Mayan_mathematics.html

References (26 books/articles)
Other Web sites:

Rhonda Robinson (Mayan numbers)
Mayan World Study Center (Mayan Mathematics)
Mayan World Study Center (The Mayan calendar)
Michiel Berger (Mayan Astronomy)
B and V Böhm(The Dresden codex)

Mayan Invention

I.
INTRODUCTION
Maya Civilization, an ancient Native American culture that represented one of the most advanced civilizations in the western hemisphere before the arrival of Europeans. The people known as the Maya lived in the region that is now eastern and southern Mexico, Guatemala, Belize, El Salvador, and western Honduras. The Maya culture reached its highest development from about AD 300 to 900. The Maya built massive stone pyramids, temples, and sculpture and accomplished complex achievements in mathematics and astronomy, which were recorded in hieroglyphs (a pictorial form of writing). After 900 the Maya mysteriously declined in the southern lowlands of Guatemala. They later revived in the north on the Yucatán Peninsula and continued to dominate the area until the Spanish conquest in the 16th century. Descendants of the Maya still form a large part of the population of the region. Although many have adopted Spanish ways, a significant number of modern Maya maintain traditional cultural practices.
II
PRE-CLASSIC PERIOD Many aspects of Maya civilization developed slowly through a long Pre-classic period, from about 2000 BC to AD 300. By the beginning of that period, Mayan-speaking Native Americans were settled in three adjacent regions of eastern and southern Mexico and Central America: the dry, limestone country along the north coast of Mexico's Yucatán Peninsula; the inland tropical jungle in the Petén region of northern Guatemala; and an area of volcanic highlands and mountain peaks in southern Guatemala near the Pacific Ocean.
The earliest Maya were farmers who lived in small, scattered villages of pole and thatch houses. They cultivated their fields as a community, planting seeds in holes made with a pointed wood stick. Later in the Pre-classic period, they adopted intensive farming techniques such as continuous cultivation involving crop rotation and fertilizers, household gardens, and terraces. In some areas, they built raised fields in seasonal swamps. Their main crops included maize (corn), beans, squash, avocados, chili peppers, pineapples, papayas, and cacao, which was made into a chocolate drink with water and hot chilies. The women ground corn on specially shaped grinding stones and mixed the ground meal with water to make a drink known as atole or to cook as tortillas (flat cakes) on flat pottery griddles. The Maya also drank balche made from fermented honey mixed with the bark of the balche tree. Rabbits, deer, and turkeys were hunted for making stews. Fishing also supplied part of their diet. Turkeys, ducks, and dogs were kept as domesticated animals.
When they were not hunting, fishing, or in the fields, Maya men made stone tools, clay figurines, jade carvings, ropes, baskets, and mats. The women made painted pottery vessels out of coiled strands of clay, and they wove ponchos, men's loincloths, and women's skirts, out of fibers made from cotton or from the leaves of the maguey plant.

s the forehead or chest) or transported them in dugout canoes along the coasts and rivers.
The early Maya probably organized themselves into kin-based settlements headed by chiefs. The chiefs were hereditary rulers who commanded a following through their political skills and their ability to communicate with supernatural powers. Along with their families, they composed an elite segment of society, enjoying the privileges of high social rank. However, these elites did not yet constitute a social class of nobles as they would in the Classic period. A council of chiefs or elders governed a group of several settlements located near one another. The council combined both political and religious functions.
Like other ancient farming peoples, the early Maya worshiped agricultural gods, such as the rain god and, later, the corn god. Eventually they developed the belief that gods controlled events in each day, month, and year, and that they had to make offerings to win the gods' favor. Maya astronomers observed the movements of the sun, moon, and planets, made astronomical calculations, and devised almanacs (calendars combined with astronomical observations). The astronomers' observations were used to divine auspicious moments for many different kinds of activity, from farming to warfare.
Rulers and nobles directed the commoners in building major settlements, such as Kaminaljuyú, in the southern highlands, and Tikal, in the central lowlands of the Petén jungle. Pyramid-shaped mounds of rubble topped with altars or thatched temples sat in the center of these settlements, and priests performed sacrifices to the gods on them. As the Preclassic period progressed, the Maya increasingly used stone in building. Both nobles and commoners lived in extended family compounds.
During the Preclassic period the basic patterns of ancient Maya life were established. However, the period was not simply a rehearsal for the Classic period but a time of spectacular achievements. For example, enormous pyramids were constructed at the site of El Mirador, in the lowlands of Guatemala. These pyramids are among the largest constructions in the ancient Maya world. By about 400 BC El Mirador was a major population center that served as the seat of a powerful chiefdom.
The highland and the lowland regions were in close contact at this time. Obsidian, a smooth volcanic rock used to make weapons and tools, from highland Guatemala has been found at El Mirador, and a sculptural style that originated in the Pacific lowland region of Chiapas and Guatemala was common in the southern highlands. Kaminaljuyú was the most powerful chiefdom of the highlands, and it probably controlled the flow of obsidian to the lowlands. Control of this important resource allowed Kaminaljuyú to dominate trade networks. Economic and political institutions during this period were more advanced in the southern highland area.
III
CLASSIC PERIOD Classic Maya civilization became more complex in about AD 300 as the population increased and centers in the highlands and the lowlands engaged in both cooperation and competition with each other. Trade and warfare were important stimuli to cultural growth and development. The greatest developments occurred in the Petén jungle and surrounding regions of the lowlands where major city-states, such as Tikal, Palenque, Piedras Negras, and Copán, arose and developed from AD 300 to 900.
Society became more complex, with distinct social classes developing. Families of nobles formed a hereditary ruling class that stood apart from the common Maya. At the top of society, a hereditary king ruled over each Maya city. Kings were similar to the earlier ruling chiefs except that they formed a distinct social class along with other nobles. Under the direction of their kings, who also performed as priests, the centers of the lowland Maya became densely populated jungle cities with vast stone and masonry temple and palace complexes. The core area of Tikal, for example, covered about 9 sq km (about 3 sq mi) and included about 2700 structures with an estimated population of 11,300. The total area of Tikal, including the core, peripheral, and rural areas, is estimated at 314 sq km (121 sq mi) with an estimated population of 92,000.
During the Classic period, warfare was conducted on a fairly limited, primarily ceremonial scale. Maya rulers, who were often depicted on stelae (carved stone monuments) carrying weapons, attempted to capture and sacrifice one another for ritual and political purposes. The rulers often destroyed parts of some cities, but the destruction was directed mostly at temples in the ceremonial precincts; it had little or no impact on the economy or population of a city as a whole. Some city-states did occasionally conquer others, but this was not a common occurrence until very late in the Classic period when lowland civilization had begun to disintegrate. Until that time, the most common pattern of Maya warfare seems to have consisted of raids employing rapid attacks and retreats by relatively small numbers of warriors, most of whom were probably nobles.
Lowland Maya centers were true cities with large resident populations of commoners who sustained the ruling elites through payments of tribute in goods and labor. They built temples, palaces, courtyards, water reservoirs, and causeways. Walls, floors, and other surfaces in a lowland Maya city were smoothly covered with red or cream-colored limestone stucco, which shone brilliantly in the tropical sun. Sculptors carved stelae, which recorded information about the rulers, their family and political histories, and often included exaggerated statements about their conquests of other city-states.
ASociety and Economy Classic Maya kings carried the title k'ul ahau (supreme and sacred ruler). In the latter part of the Classic period, kings were assisted in governing by a hereditary ruling council. The power of the king existed as both a political and religious authority in this period. In contrast, the king's religious power declined during the Postclassic period (AD 900 to 1521) because the institution of priesthood appeared.
Merchants were important to Maya society because of the significance of trade. Principal interior trade routes connected all the great Classic lowland centers and controlled the flow of goods such as salt, obsidian, jade, cacao, animal pelts, tropical bird feathers, and luxury ceramics. In the early Classic period Teotihuacán in central Mexico emerged as the greatest city in Mesoamerica, an area that included modern Mexico and most of Central America. The religious and political power of Teotihuacán radiated throughout Mesoamerica. One result of Teotihuacán's influence was a highly integrated network of trade in which the Maya participated.
Highland Maya from the southern region carried obsidian for tools and weapons; grinding stones; jade; green parrot and quetzal feathers; a tree resin called copal to burn as incense; and cochineal, a red dye made from dried insects. Those from the lowlands brought jaguar pelts, chert (flint), salt, cotton fibers and cloth, balche, wax, honey, dried fish, and smoked venison. People either bartered goods directly or exchanged them for cacao beans, which were used as a kind of currency. Wealth acquired from trade enabled the upper classes to live in luxury, although there was little improvement in the lives of the lower classes.
A Maya nobleman wore an embroidered cotton loincloth trimmed with feathers; a robe of cotton, jaguar skin, or feathers; sandals; and an elaborate feather headdress that was sometimes as large as himself. His head had been fashionably elongated by being pressed between boards when he was a few days old, and his eyes had purposely been crossed in childhood by having objects dangled before them. His nose was built up with putty to give it an admired beak shape, and his ears and teeth were inlaid with jade. A noblewoman wore a loose white cotton robe that was often embroidered. Her head was also elongated, and she filed her teeth to points.
Nobles lived in houses of cut stone with plastered walls that often bore brightly painted murals. In the living room nobles gave banquets of turkey, deer, duck, chocolate, and balche. The guests were expected to bring gifts and to give a banquet in return. A dead noble was buried in a stone vault with jade and pottery ornaments, and occasionally with human sacrifices, which were provided to serve him in the afterlife.
Most of the Maya people were village farmers who gave two-thirds of their produce and much of their labor to the upper classes. Commoner men wore plain cotton loincloths and simple tunics. Women wore woven cotton blouses and skirts or loose-fitting sack dresses with simple embroidered patterns. Women and girls wore their hair long and took care that it was always combed and arranged attractively. Different hairstyles signaled the marital status of women. Both men and women tattooed their bodies with elaborate designs.
At the bottom of Maya society were slaves who were convicted criminals, poor commoners who sold themselves into bondage, captives of war, or individuals acquired by trade. Slaves performed menial tasks for their owners and they were often sacrificed when their owners died so that they could continue to serve in the afterlife.
BReligion The Maya cosmos comprised a wide range of diverse and varied supernatural beings or deities. The chief god, Hunab Ku, the creator of the world, was considered too far above men to figure in worship. He was more important in his manifestation as Itzamna, a sky deity considered lord of the heavens and lord of day and night who brought rain and patronized writing and medicine. He was worshiped especially by the priests, and he appears to have been the patron deity of the royal lineages. Closer to the common people were Yum Kaax, the maize deity, and the four Chacs, or rain gods, each associated with a cardinal direction and with its own special color. Women worshiped Ix Chel, a rainbow deity associated with healing, childbirth, and weaving. All the Maya revered Ixtab, goddess of suicide, and thought that suicides went to a special heaven. The Maya also recognized the gods who controlled each day, month, and year. See also Pre-Columbian Religions.
The Maya performed many rituals and ceremonies to communicate with their deities. At stated intervals, such as the Maya New Year in July, or in emergencies-such as famine, epidemics, or a great drought-the people gathered in ritual plazas to honor the gods. They hung feathered banners in doorways all about the plaza. Groups of men or women in elaborate feathered robes and headdresses, with bells on their hands and feet, danced in the plaza to the music of drums, whistles, rattles, flutes, and wood trumpets. Worshipers took ritual steam baths and drank intoxicating balche. Participants often ingested other hallucinogenic drugs, such as mushrooms, and they smoked a very strong form of tobacco with hallucinogenic effects. Young Maya nobles played a sacred ball game on specially constructed courts. Without using their hands, players tried to knock a rubber ball through one of the vertical stone rings built into the walls of the court. On special occasions players who lost the game would be sacrificed to the gods.
Many ceremonies focused on sacrifices to gain the favor of the gods. The sacrifices took place on the great stone pyramids that rose above the plazas, with stairs leading to a temple and altar on top. The temple, a resting place for the god, was deeply carved or painted with designs and figures and was topped with a carved vertical slab of stone called a roof comb. Some had distinctive corbeled arches, in which each stone extended beyond the one beneath it until the two sides of the arch were joined by a single keystone at the top. Before the altar, smoke rose from copal incense burning in pottery vessels.
Worshipers sometimes gave the gods simple offerings of corn, fruit, game, or blood, which a worshiper obtained by piercing his own lips, tongue, or genitals. For major favors they offered the gods human sacrifice, usually children, slaves, or prisoners of war. A victim was painted blue and then ceremonially killed on top of the pyramid, either by being shot full of arrows or by having his arms and legs held while a priest cut open his chest with a sacrificial flint knife and tore out his heart as an offering. Captured rulers were sometimes ritually sacrificed by decapitating them with an axe.
CScience and Writing Although Maya builders possessed many practical skills, the most distinctive Maya achievements were in abstract mathematics and astronomy. One of their greatest intellectual achievements was a pair of interlocking calendars, which was used for such purposes as the scheduling of ceremonies. One calendar was based on the sun and contained 365 days. The second was a sacred 260-day almanac used for finding lucky and unlucky days. The designation of any day included the day name and number from both the solar calendar and the sacred almanac. The two calendars can be thought of as two geared wheels that meshed together at one point along the rim, with the glyphs for the days of the sun calendar on one wheel and the glyphs for the days of the sacred almanac on the other. With each new day the wheels were turned by one gear. The name for each day was formed by combining the name for the sun calendar day with the name for the sacred almanac day.
Maya astronomers could make difficult calculations, such as finding the day of the week of a particular calendar date many thousands of years in the past or in the future. They also used the concept of zero, an extremely advanced mathematical concept. Although they had neither decimals nor fractions, they made accurate astronomical measurements by dropping or adding days to their calendar. For example, during 1000 years of observing the revolution of the planet Venus, which is completed in 583.92 days, Maya astronomers calculated the time of the Venusian year as 584 days. The Maya method of reckoning time involved counting forward from a hypothetical fixed point and expressing the date in time periods based on the number 20 and counted in intervals of 1, 20, 360, 7200, and 144,000 days. Such dates appear on carved stone monuments dating to as early as the late Preclassic period, and they are prevalent throughout the lowlands on monuments from the Classic period.
The Maya developed a complex system of hieroglyphic writing to record not only astronomical observations and calendrical calculations, but also historical and genealogical information. Many recent advances have occurred in the decipherment of the Mayan script. These breakthroughs made it possible to conclude that Mayan hieroglyphs were a mixture of glyphs that represent complete words and glyphs that represent sounds, which were combined to form complete words. Scribes carved hieroglyphs on stone stelae, altars, wooden lintels, and roof beams, or painted them on ceramic vessels and in books made of bark paper.
DCollapse of Classic Civilization From about AD 790 to 889, Classic Maya civilization in the lowlands collapsed. Construction of temples and palaces ceased, and monuments were no longer erected. The Maya abandoned the great lowland cities, and population levels declined drastically, especially in the southern and central lowlands. Scholars debate the causes of the collapse, but they are in general agreement that it was a gradual process of disintegration rather than a sudden dramatic event.
A number of factors were almost certainly involved, and the precise causes were different for each city-state in each region of the lowlands. Among the factors that have been suggested are natural disasters, disease, soil exhaustion and other agricultural problems, peasant revolts, internal warfare, and foreign invasions. Whatever factors led to the collapse, their net result was a weakening of lowland Maya social, economic, and political systems to the point where they could no longer support large populations. Another result was the loss of inestimable amounts of knowledge relating to Maya religion and ritual.
IV
POSTCLASSIC PERIOD After the collapse in the central and southern lowlands, Maya civilization continued and even flourished in the northern lowlands of Yucatán and in the southern highlands of Guatemala. The decline of the older powers in the south led to unprecedented growth in the Yucatán Peninsula and the rise of a number of new cities in that region. Among these were Uxmal, Sayil, and Labna, characterized by a distinctive architectural style known as Puuc, which features elaborate mosaic decoration.
In Postclassic times (AD 900 to 1521) the city-states of Yucatán were ruled by a hereditary halach uinic (also called ahau) who was also the highest religious authority. The halach uinic had very broad powers. He formulated domestic and foreign policy and appointed batabs (lesser lords), who administered the surrounding towns and villages. Local councils made up of clan leaders aided the batabs. Other local Maya officials collected taxes and kept order. Postclassic merchants and professional craftworkers composed a kind of middle class.
A high priest, known as ahaucan, conducted major ceremonies and was in charge of the education of priests and nobles. He was assisted by a hierarchy of priests who took part in ceremonies, kept vigils in the temples, performed healing rituals, taught, and served as oracles for the gods. Although similar features and patterns existed in the Classic political structure, the institution of priesthood appears only in the Postclassic.
At the same time, during the 9th century, a new group of Maya, known as the Putun (or Chontal) Maya, began to arrive in Yucatán from their homeland in the Gulf Coast region of Mexico. The Putuns were warriors and traders without equal in the Maya area. At first they were interested in trade along rivers and overland routes. Eventually they became seafaring people whose merchants plied coastal trade routes around the peninsula and beyond in canoes. These large oceangoing canoes traveled the coast transporting huge loads of heavy and bulky goods much more efficiently than was possible in earlier times. Italian-Spanish explorer Christopher Columbus encountered such a canoe off the Caribbean coast of Honduras on his fourth voyage to the Americas in 1502.
Ports of trade, such as Xicalanco (now in Tabasco, Mexico), served as international meeting places that attracted not only Maya but also traders from highland Mexico to the west and Central America to the south. Wealthy Maya merchants organized expeditions that traveled great distances in fleets of canoes or over well-constructed stone roads and causeways. Along the routes they built warehouses for goods and rest houses for their carriers. The need to protect the trade networks led the Putuns to develop very aggressive military forces.
Ethnically Maya, the Putuns adopted many stylistic influences from central Mexico in their art and architecture. Especially common was the image of the feathered serpent representing the deity known as Quetzalcoatl in Mexico and as Kukulcan to the Maya. One very powerful Putun group, the Itzá, founded their capital at Chichén Itzá.
AChichén Itzá The Itzá brought their Mexicanized Maya culture to Chichén Itzá in the northern part of the Yucatán Peninsula. During their rule, Mexican-influenced cultures produced certain changes in the traditional Maya way of life. In the social structure military lords rose in power, and the institution of a formalized priesthood separated from political rulers. This change was echoed in religion, in which the feathered serpent-god Kukulcan dominated all others. The use of human sacrifice in worship became increasingly important. There were also new forms of sacrifice; the Itzá threw victims into a sacred cenote, or natural well, along with offerings of pottery, gold, jade, and other valuables. This cenote, in fact, determined the location of Chichén Itzá and was responsible for the city's importance as a pilgrimage center.
Chichén Itzá was a very large city with a central area covering about 5 sq km (2 sq mi). Its architecture shows the introduction of columns, wider rooms and doorways, and sloping zones around the base of the buildings. The core area includes numerous temples and ball courts, one of which is the largest known in Mesoamerica. One distinctive structure of the city is a round temple that functioned as an observatory. Statues and motifs of Kukulcan appeared on buildings, staircases, roofs, columns, and doorway lintels. Life-size stone figures supported the altars, and great reclining stone figures, called Chacmools, were sculpted. Warriors depicted in bas-relief columns lack the Classic Maya distortion of head and eyes. Pottery became monochrome, or single-colored, instead of multicolored, as it had been in the Classic era, but it was often carved or incised with intricate designs. Gold, copper, turquoise, and onyx were used in jewelry. Painted books, called codices, were made of bark fiber or deerskin. Trade and commerce, especially maritime exchange, increased.
BMayapán In about 1221 Mayapán, which became the dominant state in the northern lowlands, conquered Chichén Itzá. Mayapán was smaller than Chichén Itzá but more densely settled. Among its 3500 buildings were houses for nobles and commoners, and it was surrounded by a fortified stone wall 8 km (5 mi) long to protect it against neighboring groups. Structures were packed very tightly in the 4 sq km (1.5 sq mi) area of this walled city. Warlords and merchants continued to gain in importance, and the continual call to arms took up the time of the common people, who spent less and less time on their crafts. Architecture, pottery, and carvings of the period are crude in comparison to those of earlier periods. Finally, in about 1450, a competing lineage defeated the rulers of Mayapán, and the entire peninsula fell into civil war. The following 100 years of warfare left the Maya vulnerable to the invading Spaniards.
CSpanish Conquest The first Spaniards to encounter the Maya were a party of shipwrecked sailors who landed in Yucatán in 1511. Next came the expedition of Francisco Fernández de Córdoba in 1517. In 1527 Francisco de Montejo attempted to conquer Yucatán, and in 1546 his son succeeded. By 1524 Spanish explorer Pedro de Alvarado had conquered the southern highland area, which had also fallen into tribal warfare. Spanish domination of the entire Maya region was achieved in 1697, when the small group of Maya in the central Petén area was conquered by Martin de Ursua, the Spanish governor of the Yucatán. Many Maya were killed or died of European diseases that the Spanish brought with them. The Spanish forced most of the remainder to labor on Spanish farms or in gold and silver mines.
The modern descendants of the Maya still live as peasant farmers throughout the Maya region. They speak a mixture of Mayan and Spanish. One group, the Lacandón people of Mexico, still retains some ties with the past. They make pilgr_images with copal-burning incense pots to worship the old gods among the ruins of ancient pyramids and temples.