THE DRESDEN CODEX – the book of Mayan astronomy

Bohumil Böhm, Vladimir Böhm

   The advanced Mayan culture had been developing thanks to a complex synthesis of different culture streams rising from the home agricultural base, which had been influenced by cultural values coming from regions lying out of the territory of Mayan settlement. Its forming falls to so called early phase of the initial period placed between 1500 – 800 bc. It was step by step spread to the regions of Guatemala, south-eastern Mexico, Belize, Salvador and the north-western Honduras. The construction of beautiful and splendid cathedral cities, fine arts of sculpture and painting, using their own hieroglyphic script, success in astronomy, existence of the literature and the development of handicraft and trade had been the outer expression of cultural-economic rise.

   The results of Mayan observations and calculations of astronomical phenomena are concentrated in the Dresden Codex. It represents a band of paper 3.5 meter long set up into 39 sheets making up 78 pages 8.5 x 20.5 cm. The paper was obtained from the bark of wild growing species of fig tree. It is supposed, that it originates from Yucatan as a latter transcription of an elder original. It contains a number of calendar data, written in the Mayan dating system,  concerning astronomical data and the sky mechanics, the tables of the integers multiples, that are to be used for calculations of planetar movement efemerids and tropical years, next the hieroglyphic texts and numerous depicturings of the Mayan gods and ritual scenes.

   The in the Dresden Codex contained data were studied by many researchers that have supposed they can contain even the astronomical data. M.Meinshausen (1913), C.E.Guthe ( 1921) and H.Spinden (1930) were the first who had been interested in the eclipses  tables. E.Foerstemann has drawn our attention at Venus visibility efemerids tables; he had also issued the Dresden Codex with commentary in 1892. The analysis of these efemerids has been made by J.E.Teeple ( 1926). R.W.Wilson believed that some of the data could concern the observations of Mars, Jupiter and Saturn ( 1924). The upper mentioned researchers, except lots of others, have been working with the calculation coefficient of 584,285 days accordingly to Goodman-Martinez-Thompson correlation, when transferring the Mayan dates into the Christian dating system, or have tried to calculate their own coefficient. For this reason were their conclusions very different.

   One of the most important problems during the studies of various Mayan culture phenomena had been the solving of the Mayan to our, Christian dating system correlation. In present times, we are used to calculate the Mayan dates to the Christian ones using the Goodman-Martínez-Thompson correlation coefficient. Accordingly to it, a stable coefficient of 584,285 days is added to the Mayan dates expressing the counts of days which have passed from an in advance set day to the date of a certain event. The Mayan date is transferred into the Julian days and the latter finally to the corresponding day, month and year of the Julian calendar used in the modern astronomy.

   Working with the Mayan data of the Dresden Codex we found out, that the Goodman-Martínez-Thompson correlation is unusable, even for the dates evidently concerning certain astronomical phenomena, as the observations of Venus visibility, or Sun and Moon eclipses. We have obtained a brand new coefficient of 622,261 days for the calculation of the Mayan dates to our dating system by a complete analysis of the mutual relations between the time intervals of all the Mayan dates in the Dresden Codex and 400 inscriptions from the cathedral cities. Using the so called Böhm coefficient, we were successful in proving, that  all in the Dresden Codex contained data are concerning astronomical phenomena.

   The Mayan astronomical observations were carried out by simple measuring methods. It is therefore necessary to examine them statistically while respecting unavoidable accuracy scatter. It applies first of all to the sky phenomena calculated to the past and the future during several centuries recorded in the Dresden Codex. The dated astronomical observations are concerning following:

1)     The observations of Venus visibility, when it had appeared for the first time after its conjunction with the Sun as a morning star in the sky shortly before the sunrise, or after its upper conjunction, when it had appeared in the sky as an evening star shortly after the sunset.

2)     The observations of the Mercury visibility. Its trajectory creates an eccentric ellipse. Thanks to this eccentricity, the synodic circulations of the planet lasts from 104 to 132 days. The average length of the synodic circulation is 115. 877,484 days. The considerable proximity of the planet to the Sun makes its glow suppressed by dazzling sunshine. For that reason, the Mayan astronomers could have observed it only in case, when the planet gets to the greatest angle distance during its circulation around the Sun, so called elongation. It is the western elongation, when the Mercury rises over the horizon shortly before the sunrise and the eastern elongation, when it is shortly visible over the western horizon right after the sunset. The maximal angle distances are as a rule moving between 18 to 23 degrees. The maximal elongation of 27 degrees and 49 minutes happens, when this from the Earth visible elongation runs during the epihelium,  that means the greatest distance between the Mercury and the Sun ( the Mercury gets there once for its sidereal circulation on its eccentric trajectory). The sidereal circulation is the real time of circulation of any planet around the Sun and it makes in this case 87.9693 days. During the perihelia (minimal distance from the Sun) is the maximal angle distance visible from the Earth 15 degrees and 55 minutes. It seems as if the planet stood on one place for 4-12 days in the time of maximal elongations.  Its angle distance from the Sun changes between 1-2 degrees. This insignificant movement could not have been discovered by the Mayan observing methods. For that reason their determination of the Mercury elongations moves on average inside the borders of that “mistake”.

3)     The solar eclipses and the fullmoons and newmoons.

4)     The observation of the heliactic rises and sets of the planets. The heliactic rise sets in after the planetsconjunction with the Sun, when they are visible in the morning sky before the sunrise. During their heliactic set are the planets visible in the evening sky after the sunset. In the period of conjunction are the planets invisible for a few days. By observing the heliactic rises and sets dates we are able to determine the length of the synodic circulations of planets.

5)     The observation of the planetar conjunctions  ( when two planets observable from the Earth get into one line and are nearly covering each other). The Dresden Codex is mostly describing only close approaches of the planets because some of the dates are calculated to the past and to the future.

6)     The determination of equinoxes and solstices.

All the astronomical phenomena in the Dresden Codex are counted for the visibility from geographical area of the Mayan culture.

 The Dresden Codex is divided into pages, that are numbered both after the older version set by E.W.Förstermann (F) and the newer one by Ju.V.Knorozov (D). The Mayan dates covering one, exceptionally more pages are forming whole files. We are keeping their original topological placement, during rewriting, in order to get a minimal distortion in comprehension with the original. The Mayan dates in the Dresden Codex presented in brackets are not expressed by the number of passed days, but by a calendar circle made by combination of the dates from the 260 day tzolkin and 365 day haab. From them and from the relation to the other dates is calculated the real value of passed days.

 Each Mayan date is at first rewritten in the Mayan calendar system, than transferred into the decadic counting system, by means of the Böhm coefficient (622,261 days) it is recalculated to the Julian days (JD) and in the end adjusted to the Julian calendar system.

   All the computer programs were provided by Dr.Ing. Jan Vondrák from the Astronomical Department of the Science Academy of Czech Republic, for what we are very thankful.

The scheme of calculating the Mayan dates to the Christian system of dating using the Böhm coefficient of 622,261 days:

1/ The inscriptions of Mayan dates
2/ Transfers to the decimal arithmetical system
3/ Transfers to the Julian days adding 622,261 days   
4/ Days, months and years of the Julian calendar
5/ Analysis of the astronomical phenomena related to the single dates

PAGE F 24, 46-50, /D 24-29/
PAGE F 51 - 58, /D 30 - 37/
PAGE F 58 - 59, /D 37 - 38/
PAGE F 61 - 64, /D 40 - 43/
PAGE F 69 - 73, /D 48 - 52/
PAGE F 43 - 44, /D 72 - 73/
PAGE F 45 / D 74/