Pohualli 1.01

A Computer Simulation of the Mesoamerican Calendar System

Created by Arnold Lebeuf (Institute for the History of Religions, Jagiellonian University, Krakow, Poland)

and Arkadiusz Soltysiak (Department of Historical Anthropology, Warsaw University, Warsaw, Poland)


The calendar system used by all Mesoamerican nations since at least the middle of the first millenium BC was built on the basis of the observation of celestial bodies, reduced to mathematical conventional circular models. For this very reason, it can easily be adapted to modern computers in the form of simple algorithms.

A few calendar programs have been produced in the past and some of them are available from their authors or colleagues. However, most of them were written for the personal use of their respective authors, and as such are based on one single correlation each (the correlation each author prefers). Their main purpose is to convert quickly a date in the Christian calendar into the Maya or the Aztec calendar, or vice-versa. Some of these programs also give the positions of planets.

But the problems of calendars and chronology in Mesoamerica are far from being all solved. Even such a basic problem as the equivalence of a particular Maya or Central Mexican day with a particular Julian date has not yet received unanimous agreement. Therefore, a flexible system in which all the conventional wheels of time-counting could be set separately, and which would permit the user to ask complex questions, was needed.

A simple program to do this, bearing the Name of 'Pohualli', the Nahua name for 'computing', was created during the year 1995 at the Department of Historical Anthropology, Warsaw University. The program is written in Turbo Pascal 6.0 with the use of Turbo Vision 1.0, so that the interface is easy to learn and to use, permitting to all researchers to install their own conventions, try new combinations, and test new hypotheses. We hope in this way to contribute to the study of Mesoamerican archaeology, history, chronology and astronomy.

All variables and parameters are set in dialogue boxes available in logically ordered menus. The status line at the bottom of the screen gives a short notice about current user's actvity. The main part of the screen displays numerous reports, tools and help windows as well as the dialogue and message boxes. At any moment contextual help may be shown by pressing the <F1> key.

Messages, descriptions and topics are written in the Spanish language, the official language of Mexico and Guatemala, the centres of interest of Mesoamerican studies.

The most important dialogue box is displayed on command <Calendario \ Hoja de datos>. It contains the main variables used to search dates: Julian day number, Julian date, Gregorian date, week-day name, Long Count date, 13 numbers of the 260-day cycle, 20 names of the 260-day cycle, 365-day cycle, 9-day cycle, year bearers, Moon age, distance from the Sun to the nodes of Moon's orbit, age of Venus before or after inferior conjunction, position of the Sun in the conventional zodiac, position of the Sun in the real constellations of fix stars, position of the earth in the tropical year, notedby the corresponding date in the Gregorian calendar. The scope of each parameter can be defined separately, and expressed in full days. It is treated by the logical operator AND. In addition, an interval between two examined dates can be defined. The scope of cyclical variables can be positive (first value lower than the second), or negative (first value superior). One can change independently the reference points of some of the cycles (using the cells in column <correccion>). After defining the variables and selecting a question, by pressing confirmation button, the programme starts to calculate and search the required dates. The experiment can be stopped any time by pressing <Esc>.

Once the searching is completed, a report window is displayed containing the full result of the selection with the list of days filling the chosen conditions. The report is available in three different formats: a table where one date occupies one line; a form in which the variables of one date are presented on a separate card; and lastly a file with the records delimited by commas. The last type is assigned for transmitting the data to other applications such as databases, spreadsheets or text processors.

During one session of the program, numerous report windows can be simultaneously placed on the screen; the sole restriction results from the capacity of the operating memory. The commands collected in menu <Ventanas> enable one to introduce changes in the size and position of the selected windows and re-arrange all the windows on the screen.

Each report is displayed automatically at the end of calculation. It is possible to clean the screen and save the reports in a file by using the commands <Archivo / Guardar informe>. Each report is numbered. The command <archivo / Imprimir informe> gives the possibility of printing selected reports, naturally if the printer is connected to a port chosen in the dialogue box <Optiones/ Impresora>.

The structure of the reports is flexible. All three types of records can be edited, removed or replaced by other ones. This also applies to the header containing the report number and the description of the experiment. The list of titles and parameters, separately for headers, tables, formulae and comma-delimited records are available in the menu <Optiones/Disenar>.

Besides the main data sheet, the program also includes some dialogue boxes enabling to set up less important calendrical and astronomical variables and to fix the correlation between the Mesoamerican and the European calendars as well as between particular componants of these calendars. All commands are grouped in the menu <Calendario / Variables>. The first one: <Establecer referencia> enables the user to change the shift of the 260-day cycle, 365-day cycle, 9-day cycle, and the Long Count day number compared to the Julian Day Number.

In the following ones, we can set:

The next option <Ciclos opcionales> serves for testing hypothetical cycles not yet documented. The dialogue box displayed by this command consists of a table of six columns and three lines. These three lines offer the possibility of instalating integral number, real number and repeated cycle. The last one consists of twelve digits used analogically to the Long Count notation, but with no restriction of each digit. In the line one must define the following variables:

The last dialogue box in the menu <Variables> enables the user to set up automatically the shifts of Mesoamerican calendar variables according to a given date (For example from an inscription). All variables are divided into three groups: European dates, Mesoamerican most important cycles, and Mesoamerican additional cycles. In the beginning the dialogue box is empty. One can fill one or more cells but always keep in mind some principles, namely that at least one date in the first two groups must be given. In some cases if too many dates are set in the two last groups, the counting should be separated into two stages (for example to install 260-, 365-day cycles and the year bearer convention together, installate first the 260- and 365-day cycles, accept this, and only then set the year bearer).

In the program two parallel calendar conventions are implemented, the Maya and the Nahuatl which can be switched on by the command <Opciones/Lenguaje>. They differ from each other not only in the languages used but also structurally. In the Maya system the first day of a month carries the number 0, and in the Nahua system it carries number 1. In the Maya convention, the year bearer is the first day after the five epagomenes and names the next 365 days. In the Nahua convention, the year bearer is the last day before the five epagomenes and names the preceding 365 days. The basic correlations adopted here are:

Furthermore, the menu <opciones> contains three other dialogue boxes enabling to set up the system options: colours of all views of the program, with a palette dependent on the current display mode, the printer port and selection of the type of report.

In the sub-option of the menu <Utilidades> are three useful tools:

The changed options, other variables, descriptions of experiments and designs of report types may be saved in a memory file or loaded from a file.

The program runs under DOS.


Click here to download the program.

Click here to return to "Archaeoastronomy programs".


Authors: Arkadiusz Soltysiak and Arnold Lebeuf

Page mounted by Clive Ruggles