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Thursday, January 06, 2011

MAYAN GLYPHS, Numbers, Calendar

"....appear to be very intricate squares laid out in a gridlike pattern.."

Quick Facts
LocationAmericas > Mesoamerica
Time300 BCE to 1697 CE
DirectionTop to Bottom in Double Columns
Once considered an unsolvable enigma, recent advances in the decipherment of the Maya writing system has not only shed light on the mechanics of the script, but also on the socio-political, artistic, and historical aspects of Maya civilization.

As a whole, the Maya people created the longest lasting civilization of the New World. It became distinguishable from other early farming cultures of Mesoamerica in the middle of the first millenium BCE, when the first great Maya cities were constructed. Their culture endured through changes, wars, and disasters until it was suppressed by the Spanish conquest in the 16th and 17th centuries. The last indepedent Maya kingdom of Tayasal, fell as late as 1697. However, the Maya survived and there is estimated to be at least one million Mayas living in Mexico, Guatemala, El Salvador, and Honduras today.

General Overview
The Maya hieroglypic writing is arguably one of the most visually striking writing systems of the world. It is also very complex, with hundreds of unique signs or glyphs in the form of humans, animals, supernaturals, objects, and abstract designs. These signs are either logograms (to express meaning) or syllabograms (to denote sound values), and are used to write words, phrases, and sentences. In fact, the Maya can write anything that they can say.

While we're on the subject of what the Maya could "say", let's talk about Maya languages. The "Maya" in general were actually not a single people but many nations with different, but related, cultures, religions, and languages. Of the many Maya languages, only two (possibly three) were written down with the hieroglyphic system. It is thought that speakers of the Ch'olan language, and possibly also those of the Tzeltalan language, were the inventors of the Maya writing system. Another group, the speakers of Yucatec, adopted the script to write their own language. However, in some places, both languages were represented on hieroglyphic inscriptions, which not only stumped archaeologists for many years but also offered tantalizing clues into how Maya languages have interacted.

The visual construction of Maya glyphs is very interesting. At first inspection, the glyphs appear to be very intricate squares laid out in a gridlike pattern. In fact, each square is a glyph block that actually contain one to five glyphs, often forming a word or even a phrase.

The order to read Maya glyphs is also not as straightforward as it would seem. Since glyph blocks are arranged in a grid, one would think that the reading order is either in rows or columns. In reality, Maya glyphs are read in "paired columns", meaning that the first glyph block is on the top left, the second is immediately to the right of the first, the third is under the first, the fourth under the second, and so forth. This yields a zigzagging reading order. When you arrive at the bottom of this "paired column", you will then go back up to the top and start the next paired column. In fact, scholars label glyph block horizontally with letters (A, B, C) and vertically with numbers (1, 2, 3). Hence, the reading order would be A1, B1, A2, B2, etc, until you hit the bottom. Then you start at C1, D1, C2, D2, etc.

 Numbers and Calendar
There were several classes of glyphs in the Maya writing system. The first class is the numeric glyphs. Like us, the Maya wrote their numbers in positional notation. This mouthful of words means that the position of a "digit" dictates its actual numerical value. For example, the digit "7" means seven if its position is at the end of a number, but if it is one position before the end, then it stands for seventy. And if it is two positions before the end, then it is seven hundred. Mathematically, you will see that digit is multiplied by the "base" of 10 raised to the position of the digit:

700 = 7 x 102
70 = 7 x 101
7 = 7 x 100

Likewise, among the Maya, the position of a "digit" also determines the actual value of the digit. However, unlike our system, which is based on powers of 10, the Maya (and Mesoamericans in general) used powers of 20. Also, unlike our system, which has an individual symbol for each digit (0, 1, 2, 3, ...), the Maya only employed three basic symbols: A dot for a value of "one", a bar for a value of "five", and a shell for the value "zero". Arithmetic combinations of these yield "digits" from zero to nineteen. For example, four is represented as four dots, seven is a bar and two dots, and nineteen is three bars and four dots as3 x 5 + 4 x 1 = 19. Numbers larger than 20 are written via positional notation, like the following example:

Closely allied to the number system of the Maya is their incredibly intricate calendar system. The Maya time-keeping involved several interlocking cycles, some of which tracked astronomical events while others seemingly followed abstract time intervals.
Similar to other Mesoamerican cultures, the Maya employed a 365-day solar calendar (jaab') and a 260-day ritual cycle (tzolk'in). The jaab' is divided into 18 "months" of 20 days, plus 5 "unlucky" days at the end called wayeb'. The following chart illustrates the signs of jaab' solar calendar.
Like the Western calendar, the days in a month are identified by numbers, but the first day of the month is zero instead of one as in the Western calendar. So for example, the first day of the month Pop is 0 Pop, although in writing the "zero" is written with the glyph that means "seating" rather than the conch shell. Therefore, the first day of the month is metaphorically called the "seating of" the month.

The second cycle, the tzolk'in, is not divided into months but contains two parallel cycles, one of 13 and the other of 20. The cycle of 13 are identified by numbers, but the cycle of 20 has days with names.
And the following are the signs of the tzolk'in ritual cycle.

The keeping of the tzolk'in is still practiced among modern Maya, especially by Maya nations of highland Guatemala such as the Quiché or the Kakchiquel. The practioners are called "daykeepers", are open to both genders, and they also serve functions such as diviners, midwives, and bonesetters.

The Maya also combined jaab' and tzolk'in into a single 52-year cycle called the Calendar Round. By running the two cycles in parallel, a date such as 12 Chikchan 18 Sak will not be come around again for exactly 52 years. Mathematically, this can be computed by finding the least common multiple (the smallest number divisible by both 260 and 365), which happens to be 18980 days or 52 years.

The Calendar Round was widespread not only among the Maya but also among other Mesoamerican cultures too like #a @aztec#, #a @mixtec#, and #a @zapotec#.

At a level even greater than the Calendar Round is the Long Count, an immensely long system of five increasingly larger cycles that ultimately measures a time period of over 5,000 years. Like the modern Western calendar which uses three numbers to denote three time units (year, month, and day), the Long Count used five numbers to represent five time units. The smallest unit of the Long Count is a day, calledk'in. The passage of twenty k'ins (days) makes up one winal, the next higher unit. Eighteen winals yields one tun, which is 360 days, thus roughly equal to one year. Twenty tuns makes up one k'atun, which is about 19 years and 8 months. And finally, the largest conventional unit is the baktun, which is twentyk'atuns, 400 tuns, or about 394 years and 6 months. It appears that the maximum number that the baktunsunit can arrive is thirteen. Unlike the modern calendar, the smallest number for an unit is not one (such as 1/1 or 1st of January) but zero instead. In other words, a k'in starts at 0 and increments as high as 19 before going back to 0 again.

For convenience, instead of writing each number and unit name in a Long Count date, archaeologists have devised a system of writing just the numbers separated by dots starting with the largest unit. For example, 9 baktun, 3 k'atun, 17 tun, 8 winal, and 11 k'in is written as

The presence of the Long Count on ancient monuments has helped archaeologists date them to our calendar (which is called the Gregorian Calendar). This was made possible by the computation of thecorrelation between the Long Count and the Gregorian calendar. While many different correlations exist, the most accepted one states that the Long Count date was the Gregorian date August 11, 3114 BCE.

The Long Count is always accompanied by the Calendar Round (both tzolk'in and jaab) when identifying a date on a monument. Sometimes other astronomical cycles such as the Lunar Cycle and the Venus Cycle are also included in the block of dates. Because these dates always appear at the beginning of an inscription, together these dates are called the Initial Series. Because of the mathematical consistencies between these different cycles, often it is possible to reconstruct any missing date using the remaining ones.

The following tool demonstrates conversion between the Gregorian Calendar and an Initial Series that contains the Long Count and the Calendar Round.


 baktun katun
 tun winal
The Maya writing system had an extensive set of phonetic signs that represented syllables rather than individual sounds like in alphabetic systems. The following is a subset of signs in the syllabary:

Note that Roman transliteration of Maya consonants follows 16th century Spanish orthography. This means that the letter "j" is pronounced like a rough /h/. The letter "x" represents the sound /&\#x0161;/ (like the "sh" in "ship"). And the combination "tz" is the sound /ts/ like in "catsup".

The consonants followed by apostrophes are the "glottalized" versions of the plain consonants. A glottalized consonant is pronounced like a normal consonant, but immediately before the vowel is pronounced, the larynx is constricted (as if to pronounce a glottal stop) to produce a somewhat explosive sound.

The syllabic structure of the Maya language allows an ending consonant in a syllable. In fact, the "root" or most basic form of Maya words consists of a consonant, a vowel, and a consonant (CVC). In order to "spell" a word of this form, the Maya scribes used two syllabic signs. The first sign contains the beginning consonant and the vowel of the syllable. The second sign represents the ending consonant, and the vowel of this second sign is omitted by convention during reading. Most frequently the vowel of the second sign is equal to the vowel of the first sign. This is called the rule of synharmony by epigraphers.

In Maya languages, vowels can also be complex, meaning that they can be long, glottalized (followed a glottal stop), or aspirated (followed by the /h/ sound). To represent these complex vowels, the rule of disharmony is applied where the second sign representing the ending consonant contains a vowel that is dissimilar to the vowel in the first sign. For example, the word baak ('captive') is spelled as ba-ki where the "i" is omitted from the reading but tells us that the "a" in ba is complex.

In the following example, the top row illustrates the principle of synharmony, whereas the bottom row illustrates the principle of disharmony.

In addition to syllabic signs, the Maya script also has a large number of logograms, signs that represent words or morphemes (basic units of meaning) in the language instead of sounds. The following are a few of the logograms.

With such a rich inventory of signs, both logographic and syllabic, the ancient Maya scribe combined them in bewildering ways for both functional and aesthetic purposes. Scribes could and did write the same word in multiple ways. Sometimes only logograms were used. Other times just phonetic signs were employed. And sometimes logograms are accompanied by phonetic complements, phonetic signs that serve to clarify the reading of the logogram by either spelling out the beginning or ending sound of the word. In the following example, you see two words, namely pakal 'shield' and witz 'mountain' spelled in several different ways, purely logographic, logographic with phonetic complements, and purely phonetic. Also notice how the phonetic complements can occur before the logogram (such as wi-WITZ) and after it (as in PAKAL-l(a)).

One reason for the use of phonetic complements is that a sign can have multiple functions, a phenomenon called polyvalency. For example, there were two words for 'jaguar' in Maya, namely balam and jix, but the same logogram is used for both. To remove ambiguity, when the logogram is meant to be read as balam, either the phonetic sign ba is placed in front of it or ma is placed after it. In contrast, ji is placed before the logogram if it is meant to be read as jix.

It is also possible that a glyph can function as both logogram and phonetic sign. For instance, the phonetic sign ku is also the logogram TUUN and the calendrical sign for the tzolk'in day Kawak. In this case, the logogram TUUN is usually followed by the phonetic complement ni to indicate its reading. The Kawak sign would also be easily distinguished because of numeric sign before it and its location in a Calendar Round or Long Count block.

Also note that the rules of synharmony and disharmony also apply to phonetic complements. If the logogram's vowel is short, then the rule of synharmony is used (such as BALAM-m(a)), but if the vowel is long or aspirated, then the rule of disharmony is used (as in TUUN-n(i)).

Phonetic signs are also combined with logograms to write prefixes and suffixes that conjugate or derive new words from the original roots represented by logograms. Most often suffixes are used with verbs to denote different persons, numbers, tenses, and other verbal aspects.

Of course, verbs can also be written completely phonetically, as illustrated in the following example:

In essence, the number of ways signs can be combined in Maya writing is absolutely staggering, which ancient scribes exploited for aesthetics and personal whim as much as tradition and convention.

Origin of Maya Writing
The prevalent thought about the origin of Maya writing is that it grew out of an even more ancient writing system developed by the Olmecs as early as 1000 BCE, at a time period called the Preclassic by archaeologists. Only fragmentary evidence for this writing system existed until the announcement in 2006 of the existence of the Cascajal block, a small rectangular tablet inscribed with 62 symbols resembling symbols found in Olmec art but otherwise undecipherable. You can read more about it at National Geographic or Mesoweb. However, the writing system of the Cascajal block is very different from that of the Maya, and it is impossible to say if it had any influence on Maya writing at all.

Regardless of when the Maya started to write, the earliest examples of Maya writing date from the Late Preclassic period (300 BCE to 300 CE). In the past, many of these early texts were found on portable objects that have been looted from their archaeological context, and therefore they cannot be dated using radiocarbon dating or other types of physical dating technique. Instead, their age were hypothesized purely on comparing the artistic style of the objects to archaeologically excavated artefacts.

This situation changed recently by major discoveries at the site of San Bartolo, which yielded exquisitely painted murals as well as some of the earliest Maya texts found in their archaeological context. The texts associated with the famous murals date to about 100 BCE, whereas another piece of text, found in another part of the city, date to 300 BCE, making it the oldest securely dated Maya text and one of the earliest texts in Mesoamerica in general.

The 300 BCE text can be seen here.

The San Bartolo texts cannot be read because they are quite different from later Maya glyphs (after 250 CE). This is true in general for all Preclassic Maya writing. Even though it is most certainly the same writing system, many of the signs look different and not even the most experienced epigrapher can make much sense of them.

Like later monuments, the theme of this mask is political power. While no dates are inscribed, and most of the glyphs undeciphered, what can be interpreted suggests that the mask records the accession of a ruler by the name of Chan Muan, which is most prominently inscribed to the right of the ruler's figure. These two same glyphs appear again in the text cells C2 and D2, and also conflagrated or merged into a single glyph in cell B6. The glyph in A5 appears to be the lower body and thighs of a sitting man, which in later Maya writing signified "enthronement". So, taking together, the phrase consisting of A5, B5, A6, and B6 together appears to approximately the ascension of Chan Muan to kingship in an unidentified city.
You can also find more information about the beginning of Maya writing in #a @ma_ws#.
The Decipherment of Maya Hieroglyphs
The story really started with Bishop Diego de Landa, who avidly committed to destroy every Maya book that he could find. Ironically, though, when he was composing his Relación de las cosas de Yucatán, he included a very sketchy and rather erroneous "summary" of Maya hieroglyphics. Apparently, he assumed that Mayas wrote with an alphabet, and so he asked his native informants on how to write "a", "b", "c", and so forth, in Maya. The Mayas, on the other hand, heard the syllables "ah", "beh", "seh" (as "a", "b" and "c" would be pronounced in Spanish), and so forth, and naturally gave the glyphs with these phonetic values. So, in a sense, Landa recorded a very small section of the Maya syllabary, and the Mayanist equivalent of the Rosetta Stone.

In a sense, for all Landa did to destroy any traces of Maya writing, he also unwittingly preserved for us the key to rediscovery and decipherment. He, therefore, defeated himself. One point for knowledge and zero for ignorance.
The next step came really when the Maya civilization was rediscovered by John Lloyd Stephens and his talented artist companion Frederick Catherwood in the mid 19th century. Not only were their books bestsellers but also the drawings in them were (and still are) extremely accurate.

No doubt Sir Eric Thompson is one of the greatest Mayanist ever lived. Among his greatest contribution to the field was a systematic catalog of all Maya hieroglyphs. He divided the glyphs into three sets, affixes,main signs, and portraits. The affixes are usually the little squished glyphs while the main signs are usually somewhat square in shape. The portraits are usually heads of humans, gods, or animals, and usually can appear as either affixes or main signs. Thompson gave each one a number, the lowest number going to the most frequent glyph to appear on texts, and higher numbers for less frequent signs. Affixes start at 1 and stops at 500. Main signs go from 501 to 999. And Portraits from 1000 up. You can take a lot at this cataloging by going to Maya Epigraphic Database.
However, Thompson was set in his mind that Maya hieroglyphs were "ideographic", which literally means that each glyph expresses an abstract idea in the human mind. These ideograms were, according to him, the main signs, while the affixes were modifiers of the ideogram (like numbers, verbal endings, plurals, etc). As for phoneticism, he thought that rebus was the major way for the Maya to "spell" something. He considered the Landa's "alphabet" completely wrong.

On the other side of the coin was Yuri Valentinovich Knorozov, who advocated phoneticisms, and saw the key in Landa's work. He was not the first to advocate a phonetic approach to Maya glyphs, though. The great linguist Benjamin Whorf had also tried to "read" Maya glyphs earlier without success, because he took Landa's alphabet as if it really was an alphabet. What set Knorozov apart was that he realized Landa's alphabet was really part of the Maya syllabary, and he succeeded in identifying many of the syllabic glyphs.

As for the content of the texts, Thompson strongly argued for esoteric knowledge like astrology and pointless mathematics. This view was derived from his opinion that the Maya were peaceful astronomy priests. However, evidence soon emerged that the texts recorded something other than Maya science.
The German-Mexican Heinrich Berlin identified a set of glyphs with similar affixes but different main signs. Each of these glyphs appear most frequently in one site, so it is quite possible to assume that each glyph identifies a site. He called these "Emblem Glyphs".

But perhaps the greatest advance was made by Tatiana Proskouriakoff, who took a logical approach to monuments and texts on them. She noticed that stelas come in groups. Many of the recorded dates in a group do not seem to apply to any religious or astronomical events. In fact, the dates on these monuments fit with that of a person's life time. Proskouriakoff therefore theorized that at least some of Classic Maya texts recorded the lifetime of a ruler.

Once the historical approach is opened, myriad of glyphs were identified with events in life, such as birth, accession, death, and so on. In the early seventies, it became possible for the first time to work out dynastic lists of rulers in particular sites. From around the same time, Knorozov's phoneticism became more widely accepted, and further advances in deciphering syllabic signs continued. With these major tools of decipherment in hand, Maya texts started to come to light for the past 20 years. New discoveries continue to come to light, and any paper published six months ago might already be obsolete.

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