At the time of the Spanish conquest of the New World in the early sixteenth century, the peoples of Mesoamerica and the Andes were living in highly developed civilizations supported by well-integrated political and religious organizations. The Aztec, Mixtec, and Maya of Mesoamerica produced codices in which are described their gods, priests, religious paraphernalia, and so on. Their knowledge was organized by way of an elaborate calendar that bore no relationship to any kind of calendrical system known to the Spanish. The chroniclers soon realized, however, that an important aspect of these Mesoamerican calendars was the repeating succession of 260 days. The 260-day "year" was divided into thirteen "months," each comprising twenty days irrespective of observations of the sun, moon, and other celestial bodies.

Unlike the Mesoamericans, the Andean peoples did not leave codices or a hieroglyphic script (as was used, for instance, by the...