Codices.
Only three ancient Mayan books or codices are known to exist and these are more or less incomplete. They have all been reproduced in facsimile and are known by the following names: Dresden Codex, Peresianus Codex, Tro-Cortesianus Codex.
These illuminated manuscripts are written on both sides of long strips of amatl paper, folded like Japanese screens. The paper was given a smooth surface by a coating of fine lime and the drawings were made in black and in various colors. From the early accounts we know that books were also written on prepared deerskin and upon bark. Concerning their subject matter we are told that the Mayas had many books upon civil and religious history, and upon rites, magic, and medicine. The three books named above have been carefully studied. They treat principally of the calendar and of associated religious ceremonies.
A page of the Dresden Codex containing some interesting calculations is reproduced herewith. The numbers with the digits one above the other are transcribed in two diagrams. In the upper diagram the bar and dot numerals are simply put over into Arabic numerals and the Mayan system of periods or positions is retained. In the lower diagram these numbers are reduced entirely to the Arabic system. The columns are lettered at the top, the hieroglyphs are counted off in sixteen rows at the left and the separate groupings of numbers are shown in five sections at the right.
Among the hieroglyphs the Venus sign is especially prominent. At the base of column B is given a number in five periods that, counted from the normal beginning day 4 Ahau 8 Cumhu leads again to this day which is recorded at the bottom of column A. The long number in column C, similarly counted from 4 Ahau 8 Cumhu, leads to 1 Ahau 18 Kayab, recorded at the bottom of B. The day 1 Ahau 18 Uo is reached by another calculation which will be explained later. At the base of A is a number in three periods which amounts to 2200. Not only is this the difference between the long numbers in B and C (1,366,560 - 1,364,360 = 2200) but it is also the number of days by which 1 Ahau 18 Kayab precedes 4 Ahau 8 Cumhu. In other words we deal in this passage with the end of the seventy-second calendar round after the original 4 Ahau 8 Cumhu and with a new point of departure 2200 days earlier, which is some way involved with the calendar of Venus.
Let us now make a new beginning in the lower left hand corner of this page. In G5 we find the number 2920 which as we have already seen is exactly the number of days consumed in eight years of 365 days or five synodic revolutions of Venus of 584 days. We will now see how the Mayan scholars arrived at 13 × 2920 or 37,960, the calendar round of Venus. If we proceed towards the left in section 5 we find the second number, F5, is 5840 which equals 2 × 2920, the third is 8760 or 3 × 2920, and the fourth is 11,680 or 4 × 2920. The addition is continued in sections 4 and 3 till we reach 35,040 or 12 × 2920. To be sure the scribe made a slight error in one place, writing a 5 for an 8 but this is caught up by the day signs 9 Ahau, 4 Ahau, 7 Ahau, 12 Ahau, etc., that fall at regular intervals of 2920 days.
[Plate XXIV.]
Page 24 Dresden Codex.
Diagram showing partial reduction of Mayan numbers into Arabic numbers in the calculation shown on page 24 of the Dresden Codex ([Plate XXIV]).
| A | B | C | D | E | F | G | ||
|---|---|---|---|---|---|---|---|---|
| 1 | Hieroglyphs | 1 | 1 | |||||
| 1 | 15 | 10 | 5 | |||||
| 2 | 1 | 16 | 10 | 5 | ||||
| 3 | 14 | 6 | 16 | 8 | ||||
| 0 | 0 | 0 | 0 | |||||
| 4 | 1 Ahau | 1 Ahau | 1 Ahau | 1 Ahau | ||||
| 5 | 1 | 2 | ||||||
| 6 | 5 | 9 | 4 | 1 | ||||
| 7 | 14 | 11 | 12 | 5 | ||||
| 4 | 7 | 8 | 5 | |||||
| 8 | 0 | 0 | 0 | 0 | ||||
| 9 | 1 Ahau | 1 Ahau | 1 Ahau | 1 Ahau | ||||
| 10 | 4 | 4 | 4 | 3 | 3 | |||
| 17 | 9 | 1 | 13 | |||||
| 11 | 6 | 4 | 2 | 0 | ||||
| 12 | 0 | 0 | 0 | 0 | ||||
| 13 | 6 Ahau | 11 Ahau | 3 Ahau | 8 Ahau | ||||
| 14 | 3 | 2 | 2 | 2 | 4 | |||
| 9 | 9 | 4 | 16 | 8 | 0 | |||
| 15 | 9 | 9 | 16 | 14 | 12 | 10 | ||
| 16 | 9 | 0 | 0 | 0 | 0 | |||
| 16 | 13 Ahau | 5 Ahau | 10 Ahau | 2 Ahau | ||||
| 6 | 0 | 16 | 1 | 1 | 5 | |||
| 2 | 0 | 0 | 12 | 4 | 16 | 8 | ||
| 0 | 5 [8] | 6 | 4 | 2 | ||||
| 4 Ahau | 1 Ahau | 1 Ahau | 0 | 0 | 0 | 0 | ||
| 8 Cumhu | 18 Kayab | 18 Uo | 7 Ahau | 12 Ahau | 4 Ahau | 9 Ahau | ||
Diagram showing complete reduction into Arabic numbers of the calculation shown on page 24 of the Dresden Codex ([Plate XXIV]).
| A | B | C | D | E | F | G | |
|---|---|---|---|---|---|---|---|
| Hieroglyphs | 151,840 | 113,880 | 75,920 | 37,960 | 1 | ||
| 1 Ahau | 1 Ahau | 1 Ahau | 1 Ahau | ||||
| 185,120 | 68,900 | 33,280 | 9,100 | 2 | |||
| 1 Ahau | 1 Ahau | 1 Ahau | 1 Ahau | ||||
| 35,040 | 32,120 | 29,200 | 26,280 | 3 | |||
| 6 Ahau | 11 Ahau | 3 Ahau | 8 Ahau | ||||
| 23,360 | 20,440 | 17,520 | 14,600 | 4 | |||
| 2,200 | 1,366,560 | 1,364,360 | 13 Ahau | 5 Ahau | 10 Ahau | 2 Ahau | |
| 4 Ahau | 1 Ahau | 1 Ahau | 11,680 | 8,760 | 5,840 | 2,920 | 5 |
| 8 Cumhu | 18 Kayab | 18 Uo | 7 Ahau | 12 Ahau | 4 Ahau | 9 Ahau | |
From section 3, the calculation jumps to section 1 where the numbers in the original are partly destroyed. They have, however, been restored with perfect assurance since the days in all instances are 1 Ahau and therefore must be separated by multiples of 260 days. The number in G1 has been restored as 5-5-8-0 or 37,960 or 13 × 2920. It contains 260 an even number of times and therefore every successive period of 37,960 days begins with the same day, 1 Ahau. It also equals 13 × 8 × 365 days or 104 years and 13 × 5 × 584 days or sixty-five revolutions of Venus.
Fig. 48. Mayan Ceremony as represented in the Dresden Codex. The figure at the left beats a drum while the one on the right plays a flageolet. The sound is indicated by scrolls. The head on the pyramid is that of the Maize God and it rests upon the sign caban, meaning earth.
The three numbers to the left in F1, E1, and D1 are respectively 2, 3, and 4 times 37,960. The last number, 151,840 days is therefore equal to 416 years or exactly 8 calendar rounds of 18,980 days.
The numbers in section 2 are more difficult to explain but they possibly have to do with corrections and correlations of astronomical periods. If we add to 1 Ahau 18 Kayab the number of days in E2, (68900), we arrive at a day 1 Ahau 13 Mac. This day is prominent in more detailed calculations elsewhere in the Dresden Codex. If we add to the same 1 Ahau 18 Kayab the number in D2 we arrive at 1 Ahau 18 Uo recorded at the bottom of C. Space permits no further explanation but the reader will see from the foregoing the method of experiment and cross checking that must be applied to the decipherment of the Mayan manuscripts. Fortunately, the relationships of numbers are absolute and the coincidences between the recorded numbers and astronomical periods are too close and frequent to be dismissed as accidental.
In addition to rational calculations dealing with astronomy one sees in the Mayan manuscripts many arrangements of the tzolkin supposed to bring to light good and bad days and to forecast events. A section of the Dresden Codex showing a condensed tzolkin is presented along with a diagram of its parts. At the top and right are seventeen hieroglyphs containing the symbols of the four directions, and of at least three of the principal gods. At the right is a column of five day signs with the number 3 at the head of the column. The permutation is divided into five parts of fifty-two days each and each part is subdivided into four groups of thirteen days each. It begins with 3 Akbal, the day sign at the top of the column, and after the four subdivisions of thirteen days each have been counted we arrive at the day 3 Men, the second day sign in the column. The count is repeated till the 260 days have been exhausted and we come back again to 3 Akbal. In the diagram the red numbers of the codex are represented by Roman numerals and the black numbers by Arabic numerals. Since the count in this example begins with 3 and the addition is always 13, or exactly one round of numbers, the resultant days always have the number 3.
[Plate XXV.]
(a) Detail of the Dresden Codex showing Tzolkin used in Divination.
(b) Analysis of the above Tzolkin, according to Förstemann.
| III | 1 | 2 | 5 | 6 | 9 | 10 | 13 |
| East | * | North | * | West | * | South | |
| 3 | 4 | 7 | 8 | 11 | 12 | 14 | |
| God B | † | Woman | Good Days | God G | ‡ | * | |
| 13 | III | 13 | III | 13 | III | 15 | |
| 1 | God E | ||||||
| Akbal | 16 | ||||||
| 2 | (Image 1) | (Image 2) | (Image 3) | Week of 13 days | |||
| Men | 17 | ||||||
| Ahau | |||||||
| 3 | |||||||
| Manik | |||||||
| 4 | |||||||
| Cauac | 13 | ||||||
Image 1: God B—rain and sky god of good powers. Holds Kan (maize) sign in his hand. Image 2: Goddess with serpent headdress possibly connected with floods. Holds Kan sign in hand. Image 3: God K—benevolent sun god. If space had been larger God E (the maize god) would probably have been drawn next.
The three pictures of gods give us an inkling into the significance of this particular table of chances. All of the gods carry the kan or maize sign in their hands. The first god is the benevolent rain god and the third is the benevolent sun god. Between them is seated the malevolent goddess of floods with a serpent on her head. The maize god is not shown but his hieroglyph is given. This tzolkin probably deals with agriculture and may be an attempt to determine lucky days for planting.