Abstract

Studying and analyzing graphical codes associated with ceramic pieces from the Valdivia Province (X Region, Chile), made by the pre-Hispanic Mapuche people around the XV century, I have identified on jars and plates what is very likely a calendarical code painted using lineal patterns. These codes refer to the count of the solar and sacred year, of 365 and 260 years respectively, and the Venus synodical period of 584 days.

1. Introduction

Little work has been done about the Mapuche cosmovision. This is mainly due to their permanent struggle, since the arrival of the Europeans in Chile, to maintain their independence and cultural values. Even today, it is extremely hard to conduct ethnographical investigation among Mapuche communities because they are very reserved and usually do not explain their customs and celebrations. In a Mapuche community, the Machi has religious and medical (traditional medicine) responsibilities. Sometimes, one can participate to religious ceremonies but will be asked to leave at the most important moments. In the past, Grebe (1972, 1992) has written some interesting works about this topic but has not tried to analyze in details their understanding of time and calendars. On the archaeological side, there are also some difficulties to be authorized to realize excavations on Mapuche land, although the potential is obviously large. A few authors have described the presence of hundreds of tombs in some areas, for which it would be interesting to measure orientations (Dillehay, 1990).

2. Archaeological objects examined

Toward the end of the year 1974, a small archaeological collection (five ceramic objects) reached my hands. It came from a Mapuche area, more specifically, from Cudico, a place associated with the river basin of the Bueno river, province of Valdivia, 10th Region of the country (approximate geographical coordinates: 40º 15' S, 73º 08' W). At that time, I used to work with my university students in a museum, drawing different archaeological pieces, in order to improve our observation sense. After finishing my analysis of these five first pieces, I searched similar objects in the museums of Puerto Montt, Osorno, Lago Ranco, Rio Bueno, Valdivia, Villarica, Temuco, Angol, Concepcion, Hualpencillo and the National Museum of Natural History in Santiago. The main Mapuche geographical area covered extends from 36ºS to 41ºS. I also added some private collections from the city of Valdivia, Los Lagos, La Union and one piece documented by the archaeologist Jorge Kaltwasser (1968), who found it in the village of Valle Hermoso (32ºS). Around 1984, I had photographed some 400 objects. All of them have the geometrical elements we were interested in but only about 35% showed geometrical structures similar to the triangles and "butterflies" characterizing the collection I was given. From that set, a large proportion of the objects were broken or with graphics partly erased and, all in all, only a few tens of pieces were entirely readable. I succeeded in detecting the existence of at least nine vessels (five jars and four plates) that were closely related to the calendaric system I will describe. Among this large collection, Chilean archaeologists have dated some ceramics (with design similar to the ones I examine here) to the end of the XV century, at the time of the first contact with Europeans.

3. Ethnographical information

Here I am reporting mainly four arguments that I have obtained from Mapuche people (whose name I can not cite for obvious confidentiality reasons) and that will help my understanding: the structure and importance of the cardinal orientations of landscape (figure 1). The Mapuche people divide their environment in four quadrants according to the cardinal directions but also give an increasing importance to each of them: West is negative (- -) because this is where the sun dies, East is very positive (+ +) because this is where the sun is born and brings fertility. North is negative (-) because, in the trajectories of the sun in the sky, it represents the winter, the coldest and shortest days, and South is positive (+) because it is the highest sun at the meridian. That traces a increasing sequence in the horizon: from West to North, to South and ending East, which is the symbolic path the Machi follows to reach God and communicate with Him. From east back to west is showed the path to start a new cycle (at a new cosmic level before reaching God). Coming back to Earth, the Machi will follow the opposite path. The path has a "butterfly" shape if one looks at it with the dividing axis laid vertical.

In July 1972, a Machi (a woman) explained me how she remembered the lunar count of the year (Gonzalez 1976). She drew on the ground a kultrun (figure 2) with the cardinal divisions (double lines) and double line oblique and small lines on each side of the cardinal axis. Then, she drew two additional axis at 45º. Then, she started to count the spaces between the lines, starting from one 45º axis. In each quadrant defined between the 45º axis, she counted seven spaces. A full loop around the circle therefore gives 7x4=28. Next she counted the numbers of branches: the two northern lines form one branch, the two oblique lines on the right of the North form a second branch, etc.... and she ended up with twelve branches. Next she added the position of the center of the circle, getting a total of thirteen. She multiplied 28x13 and added one to get 365 days, i.e. the solar year of a modern calendar. This is as bit enigmatic: such a count is a mnemotechnic method she was taught to remember that cycle. We obviously do not know if the method results from the combination of modern thinking -brought by the Spanish- and ancient traditions, or if it can be trusted as a purely ancient way of using graphical codes and numbers counted on the graphics to calculate celestial cycles.

Ethnologists already know two celebrations realized in the Mapuche communities: acknowledgements for the crops freshly collected (variable), and the start of the new year (23-24 of June). Other ceremonies are not well documented and are not necessarily part of a schedule known in advance.

Once, I showed one of the jars to an old Mapuche woman, asking her about the age of the object. Her attitude was not hesitant at all: she took the jar from the handle, turned it upside down, looked at it and said: "yes, it is very old". It can appear as a brief and insignificant piece of information but I will show later that my reading of the graphical codes use the same views (i.e. from the bottom or from the top) as the one used by the Mapuche woman. Furthermore, I have, purposely, never forced any Mapuche informants to answer lots of questions but rather to comment simple questions through very informal conversation.

4. Numerical coincidences on jars and plates

In the first set of objects, we studied four jars (this was described in long details in Gonzalez, 1984). They have a flat bottom, with symmetrical axis. They have a relatively wide neck whose mouth opens like a cone. A handle goes down from the upper rim towards the vessel's body near its union with the neck. The small annulus area, which is defined at this height, is occasionally marked with points or small crosses (figure 3).

All jars have a white or ocher tone surface and they also show lineal designs of colors that go from a reddish drab to a nearly black color. All the graphical elements drawn in the pieces show a similar distribution: there are figures on the handles - from one to three - whose shape is composed of two triangles connected by one of their apex and filled up with the color of the lines (what we call "butterfly"). At the mouth edge and going down a little towards the inside of the neck, there are lines of approximately equal length in every vessel. The outer part of the neck is covered with a group of zigzag lines, parallel to each other and that go down near the neck-body union, limited by two other lines that encircle the neck. In all these four jars, the main body of the ceramic is divided in two hemispheres, upper and lower; each containing series of geometrical figures (figure 4).

When the jars are observed from an upper and lower views, it can be seen in all of them a figure with the shape of a star (figure 5), which is formed by series of triangles distributed alternately downwards and upwards respectively. All the triangles are tidily filled in their inside with a variable amount of lines parallel to one of the triangle side and, occasionally, with other isosceles triangles decreasing in size, again parallel to each other and to the main triangle base.

Because of a constant factor present on these vessels, i.e. the existence of stars visible from the upper and lower views and whose only difference is the amount of spikes, and because of the experience of the "lunar kultrun" above described, the first step we took was to count the number of spaces seen in each triangle. I realized that this star-shaped form allowed to see the important role played by the handle, since the sequence of spikes of each star showed a tetra-partition in the observed hemisphere (in each hemisphere there are one or two raws of triangles named P, Q, R and S respectively on figure 3). Adding the amount of spaces enclosed in each triangle, and grouping them according to the tetra-partition suggested by the two axis, we get interesting numbers: sometimes they are identical (P and R on jar 1; R and S on jar 3; P and Q on jar 4) and sometimes the sum of each quadrant represent an increasing sequence following with a surprising similarity the ritual cardinal path (the butterfly) previously explained, for example 30, 31, 32 and 33 on figure 5 (this butterfly counting sequence is respected for P on jar 1, R on jar 2, P+Q on jar 3). These facts lead us to understand that the graphical design of the artist would be intentional in some cases and speculate that it could be intentional in all cases as we probably do not understand all the codes. Besides, among the sums obtained we already noticed the presence of numbers (73, 130, 236, 260) that we understood in a second phase of the investigation.

5. A calendarical plate

Our most amazing discovery was the information contained in a plate (figure 6) which we called our "Rosette Stone". The basic information we notice is:

* It has a symmetric geometry and there are tetra partitions defined by the four butterflies, the four small triangles, and the two sets of longer triangles.

* The exterior ring of the plate is painted with thirteen white marks.

* Four triangles are smaller and they have five interior spaces each. This adds up to 4x5=20. By multiplying that number by the thirteen dots (in a way similar to what the Machi woman did), we get 20x13=260, the length of a sacred year.

Starting from the small triangle following the one with eight spaces (the maximum), and counting clockwise, we see an increasing sum of spaces in the interior large triangles: six, seven, seven and eight, and in the exterior large triangles: five, six, seven and seven. This small triangle thus defines the starting point for a logical sequence (to us) of reading. The total sum of spaces is 73.

When I tried making sense of all this, I realized this last number (73) is well known in Meso-America as it is a common denominator (or multiplier), by chance, to connect important astronomical cycles between themselves:

260x73 = 365x52, i.e. 73 sacred years = 52 solar years

365:73 = 5 (denominator of the solar year)

584:73 = 8 (denominator of the synodical period of Venus)

The surprising deductions we do are:

By counting the spaces in the triangles and going on for five entire loops around the plate, one would be able to keep trace of a solar year.

By counting the spaces in the four small triangles and multiplying by the number of dots of the plate edge, one obtain 260 days, the length of a sacred year.

By counting the spaces in the triangles and going on for eight entire loops around the plate, we would be able to keep trace of the synodical period of Venus. This would seem a second coincidence if the positioning and characteristics of the triangles would not also allow us to represent the phases of Venus (seen from the Earth) during the 584-days cycle: 236 days as morning star, 90 days in superior conjunction, 250 days as evening star and finally 8 days in inferior conjunction. Using the plate, this can be accounted for very easily and logically by the following arithmetic: 236=(73x3)+17 ; 90=73+17 ; 250=(73x3)+31 ; 8. In other words, we use seven full loops and the eighth one is subdivided into the days missing to complement each of the four phases of Venus, ending with the eight-spaces triangle in the plate (figure 7a and figure 7b).

6. Conclusion

At the time of writing my initial synthesis, I could also report the existence of at least two bowls belonging to the Diaguita people (formerly inhabiting the 3rd and 4th Regions of Chile), in which I found the same numbers as the ones read in the Valdivia ceramic. The Diaguita objects, which were found during excavations conducted by archaeologists of the Museum of La Serena are conserved today and shown in the permanent exhibits at the National Museum of Natural History in Santiago of Chile. Three of the Valdivia objects are conserved at the Austral University's Museum, whose principal division is located in Valdivia, and the author conserves the rest (five pieces).

We are very puzzled by the fact that these kind of astronomical numbers resemble so much the ones known and used by the Meso-Americans, whose knowledge has never been found in South-America. In order to confirm my speculation of a Venus calendar hidden in the plate, I thought that an important event, among the ones recorded for the Sun and Venus, would be the re-apparition of Venus in the morning after its conjunction, as a sign of fertility for the Mapuche communities. As a matter of fact, in early 1986, after finalizing this research, I inquired at the National Observatory of Chile the date of the next inferior conjunction of Venus. I then called a Machi that I was introduced to in the past and predicted him that he would celebrate a ceremony at a particular date at the end of the year, without telling him the reason of the ceremony. His immediate answer was negative. Early November, I was stunned when he called me to invite me to a ceremony that he would actually conduct at the date I predicted. Unfortunately, I was not able to attend but I did learn that they had a celebration related to Venus... I did not know how the Machi finally decided on the date, probably through observations of the planet.

The existence of this modern knowledge of the night-time sky lead us to think that it was probably even more complete in the past, at the time of the creation of the objects we analyzed. In addition to this study, I gathered valuable information about the modern knowledge of constellations among the Chilean Mapuche, which I will present elsewhere. When conducting a numerological analysis focused on calendars, we are aware of the risk to fall in the classical trap of finding a solution at any price, just by manipulating numbers. Nevertheless, we have been cautious with that and did base our reading onto real ethnographical information and through the use of very basic and logical graphical codes. It was a surprise to find such an interesting result. We believe the Mapuche used these vessels mainly for ritual ceremonies, not so much for domestic use or even day-to-day time recording. The ceramics could also be considered as mnemotechnical tools to keep record of a knowledge, reserved to the Machi, and transmit it onto the following generations.

We would encourage people to perform similar analysis with ceramics of other parts of South America to try confirming the apparent universality of the astronomical calendars used.

I want to thank Dr. Belmonte and the VI Oxford conference committee for offering me a grant to participate and present my work, and to Brad Schaefer for useful comments.

References

Dillehay, T., 1990. Mapuche ceremonial landscape, social recruitment and resource rights, World Archaeology, Vol.22, Nº2, pp.223-241.

Gonzalez Vargas C., 1976, Un signo pintado en la ceramica Chilena, Aisthesis 9, Instituto de Estetica, Pontificia Universidad Catolica de Chile, pp65-82.

Gonzalez Vargas C., 1984, Simbolismo en la alfareria Mapuche, Colección Aisthesis, Pontificia Universidad Catolica de Chile.

Grebe Vicuna M.E., 1972, Cosmovision Mapuche, Cuadernos de la Realidad Nacional, 14, Pontificia Universidad Católica de Chile, Santiago

Grebe Vicuna M.E., 1992, Concepcion del tiempo en las culturas Sur-andinas, Time and astronomy and the meeting of two worlds, Proceedings of the international symposium held at Varsaw University, pp.265-278.

Kaltwasser Passig,J., 1968, Excavaciones en Valle Hermoso, Boletin de Prehistoria de Chile, Departamento de Historia, Universidad de Chile, Santiago, Año 1 Nº 1, pp. 99-106.