their history, Mesoamerican societies used some of these materials as items of wealth and standards of value, reflected in economic, social, and political practices that were included in the original trait list. Craft specialists worked obsidian, jade and other greenstones, and feathers into ritual regalia that could be adapted as signs of distinction between social segments or insignia of specific offices and became parts of high culture. Scribes, astronomers, and calendar specialists developed ways to record indigenous wisdom. Histories of political dynasties recorded using these technologies also formed part of high culture.
Images carved in stone and painted in manuscripts provide records of marriages, wars, visits involving the offering of tribute and gifts, and ritual performances. Many are accompanied by texts specifying the time, place, and people involved. They are preserved on durable stone monuments dating as early as the late Formative period that hint at the broader existence of records written on perishable materials like the paper and deerskin in use when Europeans invaded the region. In the sixteenth century, European colonizers collected some manuscripts while destroying many others. Literate Mesoamerican people continued to produce historical texts after colonization, rapidly developing mastery of European script and working to preserve ancestral knowledge (Chapter 10).
Mathematics, Calendars, and Writing
The development of calendars, mathematical notation, and writing served to represent the distinctive perspectives of Mesoamerican peoples, making these the most diagnostic features of these societies. Indigenous calendars in use in the early sixteenth century shared a basic structure. All were based on counting sets of individual days. The earliest recorded date preserved is on a late Middle Formative monument from San Jose Mogote in what today is Oaxaca. However, it is likely that, in addition to being used to measure time, Mesoamerican mathematics were originally developed for broader use, including in economic transactions (Freidel 1993). Understanding Mesoamerican historical consciousness thus begins with understanding math.
Mathematics
The universal sign for the number 1 in different Mesoamerican writing systems was a dot. In the written texts of the sixteenth-century Mexican highlands, larger numbers were represented by rows of dots, sometimes linked by lines (Chapter 13). In the Maya manuscripts created in Yucatan at the same time, in contrast, a separate sign stood for the number 5. Represented as a solid bar, the same sign can be recognized in inscriptions on earlier Classic Maya monuments. It also appears in monuments from Classic and Late Formative Oaxaca (Chapter 8). In some examples, the bar is drawn as a thumb, suggesting it stood originally for five fingers.
Using these two symbols, numbers could be expressed through combinations of dots (standing for one digit) and bars (standing for five). One dot (1), two dots (2), three dots (3), four dots (4), one bar (5); bar and dot (6), bar and two dots (7), bar and three dots (8), bar and four dots (9); two bars (10), two bars and dot (11) two bars and two dots (12); and so on went the mathematical notation used by Postclassic Maya until after three bars and four dots (19) it reached a full set of 20, the base of the Mesoamerican mathematical system.
Rather than expressing 20 as a set of four bars, the Maya developed the use of place notation, including a third mathematical symbol that could serve as a placeholder, like the zero of Arabic math. This third symbol allowed Mesoamerican mathematicians to record multiplace numbers. Because the base of the Mesoamerican number system was 20 (rather than the familiar base 10 of European decimal mathematics), each place in Mesoamerican math recorded multiples of 20:20, 400 (20 × 20), 8,000 (20 × 20 × 20), and so on.
Sixteenth-century manuscripts recording the tribute paid to the Mexica empire used the expected units of measurement of 20, 400, and 8,000. In addition to this pure use of base 20 mathematics for counting economic goods, however, by the sixteenth century, Mesoamerican people had modified it to allow them to count long periods of time using three signs (one, five, and zero) and place notation.
Calendars
The inscription on San Jose Mogote Monument 3, the earliest preserved record of time counting in the region, is interpreted as the use of birth date as a name. The signs involved specific one day in a cycle of 260 days, a calendar that some Maya communities continue to use. Later Classic and Postclassic Oaxacan monuments and codices used the 260-cycle positions as personal names as well. Even when the birth date was not used as a name, as on Classic Maya monuments, anniversaries of birth and death were calculated using the 260-day cycle. Many Postclassic Central Mexican people used their birth date in the 260-day calendar as a name. Among the Mexica, this cycle was named tonalpohualli, or “count of the days,” and was used by diviners to assess the prospects of all manner of proposed projects. The tonalpohualli allowed divination of individual life chances based on birth date (Monaghan 1998). The close association of this calendar with human fate has led some scholars to propose an origin in human life cycles as an approximation of nine lunar months, a rough estimate of the length of human pregnancy (Aveni 1980).
Whatever its origin and use, this calendar is composed of a count of days. It combines a sequence of 13 numbers with a series of 20 day names. Beginning on the same date, the shorter cycle of 13 numbers has to restart 7 days before the longer cycle of 20 day names. Because the two series are offset from this point on, the second set of 20 day names begins with the number 8, the third set with the number 2, the fourth with the number 9, and so on, with sets of 20 day names beginning with the numbers 3, 10, 4, 11, 5, 12, 6, 13, and 7. Once 13 sets of the 20 day names are counted, a cycle of 260 days (13 × 20) is complete, and the two counts return to their first positions simultaneously. Every one of the 260 days can be uniquely specified by its combination of number (from the series of 13) and day name (from the set of 20).
While the 260-day cycle is the oldest for which we have direct evidence from inscriptions, it is highly likely that counting segments of the Mesoamerican solar year was equally ancient. The 365-day solar calendar was also based on complete units of 20 days, further subdivided into groups of 5 days. To approximate the solar year, 18 complete cycles of 20 days and one incomplete cycle of 5 days were required. This cycle of 18 “months” of 20 days, with a period of 5 extra transitional days, was the basic civil calendar of the Postclassic Maya states and Tenochtitlan. Community-wide ceremonies were scheduled in it, many with clear associations with an annual agricultural cycle.
By combining the 365-day calendar and the 260-day ritual cycle, Central Mexican peoples in the sixteenth century could record unique dates within periods of 52 years. Because the beginning points of the two cycles did not coincide until 52 solar years had passed, every single day within a 52-year cycle could be uniquely distinguished by naming its position in the 365- and 260-day cycles. This system is employed in Postclassic codices from Central Mexico and Oaxaca (Chapter 10). Because the entire cycle repeated every 52 years, a date in this system was fixed only relative to other days in the same 52-year cycle. By adding a third cycle, recording changes in the visibility of the planet Venus every 584 days, it was possible to create a continuous calendar of 104 years, with each date uniquely specified by its position in the 260-day, 365-day, and 584-day cycle. But the main way that individual cycles of 52 years were placed in order in Postclassic Mexican historical codices was actually through their relationship to the genealogical connections of major historical characters over successive generations. Dates with the same names, based on their position in the 365-day and 260-day cycles, could be distinguished because they were associated with the lives of different public actors.
The earliest records of dates in the 365-day solar year are carved stone monuments dating to the Late Formative period, found in an area extending from the Gulf Coast of Mexico to the Maya highlands of Guatemala. They are always combined with records of the 260-day cycle, evidence for the early use of the fundamental Mesoamerican 52-year calendar. These Late Formative monuments also record a different continuing time count. Most familiar from its extensive use in Classic Maya monuments,
