In spite of the fact that their mathematical system was vigesimal, the Maya counted the days also by fives, thirteens and twenties. They gave numbers from 1 up to 13 to series of 20 day names in a continuous cycle. These thirteens are so important, that we have to devote a special chapter to them. In the manuscripts we can find cycles which are multiples of 13, for example, 26, 52, 65, 78, 91, 156, 182, 208, 234, 260 etc. Good examples of the Maya codices are given on pages Dresdensis 73, 32a, 44b, 63-64, 70-72, and Tro-Cortesianus 75-76, 77-78.
It is not easy to discover the
real origin of the 13-day cycle. All we can give at this moment is a working
hypothesis which no doubt approximates the origin of Maya cosmology very
closely. The Maya considered the shape of their world, their cosmos, as an
enormous cube or, as we think so, more likely as a double pyramid, which was
divided according to the four directions of the world.
First of all there is the YAXCHé, the world tree, which forms the axis and consequently constitutes the center of the world. YAX means "first", "new" or "green" (green-blue, blue) and -CHé generally means tree. Therefore one of the meanings of yaxché is "first tree". It is the ceiba (Bombax pentadrum).
It is evident that the surface of the earth is intimately to the life of the
Maya. The Yaxché tree had 4 horizontal root branches leading to the 4 quarters
of the world. There is a difference in opinion as to how to interpret the
position of the world directions.
Type A (Europe) gives the 1st interpretation, according to which the quarters of the world correspond to our directions of the wind: north, east, south and west. Type B (Girard) gives a 45-degree shift by considering the angular points instead of our European cardinal points. These points are the locations of the caryatids (BACAB), the 4 bearers of heaven.
Heaven is the high residence of the various gods who are placed in the five points of the celestial world following the calendar days.
The lower part of the stump of the Yaxché is underground. Four strong root branches point at the four quarters of the underworld. We can provide additional information on all these items. Let us first consider the axis or the center of the world. Landa also mentions the Yaxché :
..., and a tree which they call Yaxché, very cool and giving great shade, which is the ceiba, under the branches and the shadow of which they would rest and forever cease from labor.
Pages 75-76 of the Codex Tro-Cortesianus probably show a Yaxché-tree in the center of the world. Concerning the BACAB, Diego de Landa says :
Among the multitudes of gods which this nation worshipped four were very important, each of them called BACAB. They said that they were 4 brothers whom God placed, when he created the world, at the 4 points of it, holding up the sky so that it should not fall. They also said of these Bacabs that they escaped when the world was destroyed by deluge. They gave other names to each one of them and designated by them the part of the world where God had placed him, bearing up the heavens, and they appropriated to him and to the part where he stands one of the four dominical letters.Landa also gives the years along with the corresponding allocated gods (Bacab, etc.) and the quarters of the world. In several sites caryatids were found.
We have already discussed a few aspects of the quarters of the world in some publications and we shall not elaborate on it in this chapter. Girard views the cosmic diagram as shown in the figure. The east is situated between point 1 (summer solstice) and point 4 (winter solstice). The west lies between point 2 and 3. This means that east and west alike are "guarded" by the 2 deities and bordered by 2 colors.
This idea is expressed in Codex Fejérvary-Mayer 01 and on
The Maya world cube shows 4 points for each heaven and underworld, and 5 points for the earth's surface. The numbers 4 and 5 are subsequently the basic numbers of Maya cosmology because they provide: 4 + 5 = 9; and, 4 + 5 + 4 = 13. These numbers also play an important role in the functioning of thegods placed in those points following the calendar. According to their needs the Maya followed the quaternair system, the quinair system or the quincunx system. The quaternair system only takes into account the 4 points while the quinair system or quincunx system takes into account the same 4 points and the Yaxché, as a 5th point, in the center of the world. The series are as follows:
In other words: 4 + 5 + 4 = 13 cosmic points. We are convinced that a mathematical, astronomical geometrical basis is the foundation of the following arrangement of the gods in the Maya cosmos (see our Tzolkin publication) :
The first line of pages 78-77 of Codex Tro-Cortesianus gives the first 13 days of the Tzolkin, running from 1 Imix up to 13 Ben.
It should be noticed that the day numbers are placed upside down below the
glyphs. On the basis of these pages 77-78, Léon de Rosny proved that Codex
Cortesianus and Codex Troano were in fact only one manuscript, which is now
known under the name of Codex Tro-Cortesianus.
The second line shows the so-called glyphs of the "world directions or cardinal points", which are placed below the day glyphs. The relation between the first 13 days and the "cardinal points" is given in the table at the right.
We see that one of the basic characteristics of the calendar is the fact that it does not only refer to the flat earth, but also to a place in the celestial space and on earth and the underworld as well. The calendar is in fact a combined time and spatial event. This can be easily represented by means of the Maya cube. We see that the first movement of the days in space runs clockwise, going from East to North, South, West and to the Center. It is a kind of spiral movement. Subsequently the next day descends to the following level, the earth.
The second movement of the days goes then to the left, counterclockwise, from West to South, East, North, and to the Center. The next day descends to the following Center on the other level. The 13th day is located in the South. Normally we would expect another clockwise movement, although there is for the moment no proof for this. At this stage we do not wish to go beyond this limited reconstruction (a cycle of 13 days), as there appear to be additional rules for longer periods. We made indeed other reconstructions van calendar sequences. It is an established fact, however, that the calendar days are also situated in space, accompanyed by their protecting day god(s), and that the direction followed by the path of the days with their gods in the Maya cosmos is alternatively clockwise, counterclockwise, clockwise, etc., like the apparent movement of the planets in the sky. In their many ceremonies, Maya people make their turns according to the direction of the concerned feast days. It is then normal to see that for one day they turn in their dances to the left, and for another day to the right side./
We broke in 1982 the code for a sequence of 13 days and of some other small calendar sequences, but it is obvious that we will have to look further in order to discover the complete code of the alternating clockwise, counterclockwise movement of the calendar days. For more information on the subject of the "world directions", we refer to our publications or to our E.mail adress below.