Mayan versus our calendar:
astronomy supports the Bohm not the GMT correlation
A new discovery of Czech mayanists, mathematicians, astronomers, and geodesists
Jaroslav Klokočník,
CEDR and Astronomical Institute, Czech Academy of Sciences, CZ 251 65 Ondřejov Observatory, Czech Republic,
Jan Kostelecký,
CEDR and Research Institute for Geodesy, CZ 250 66 Zdiby 98, Czech Republic,
Vladimír Böhm, Bohumil Böhm,
CZ 280 02 Kolín,
Jan Vondrák,
CEDR and Astronomical Institute, Czech Academy of Sciences, CZ 140 00 Prague,
Spořilov, Boční II, Czech Republic,
František Vítek,
Prague 7, Na Maninách 50, .
Abstract. The Dresden Codex describes (among other matters) observations of various astronomical phenomena (eclipses, conjuctions, maximum elongations, heliacal aspects, etc), made by the Maya. Modern celestial mechanics enables us to compute exactly when the phenomena happened on the sky for a given position on the Earth far back in time. The Maya used their own and very precise calendar, we have also our own calendar; the correlation between both is surprisingly very uncertain. However the calendars can be connected by analysing various historical data and astronomical phenomena from the Codex and other sources. The correlation between the two calendars has been investigated by many researches and very diverse values of the correlation (nearly 50 different values) were computed; they differ by hundreds years, yielding significant uncertainty in Mayan history in relationship to other civilizations. The most frequently used correlation is GMT (Goodman-Martínez-Thompson) based largely on historical evidence. But astronomy (celestial mechanics) may resolve the problem of the correlation, provided that historians have decoded the astronomical phenomena from the Codex correctly. Here we check and confirm results from Böhm and Böhm (1996, 1999). We suggest rejection of the often used GMT correlation [584283 days] and its replacement by Böhm´s correlation [622261 day]. The history of the Maya would then be closer to our time by 104 years.
1. Introduction, description of the problem, aim of this work.
1.1. Introduction.
The Maya had a very elaborate and accurate calendar, as is well known (see, e.g., Morley, 1956, Thompson 1962, Knorozov 1963, Coe 1972, Ruz, 1981, Santos 1981). Partly the so-called Long Count (LC) was used (days counted day by day from a selected begining of Maya chronology), partly a 260 days long tzolkin (religious calendar), also a 365 days long year called haab, a nine-day cycle and a katun cycle with 93 600 days (consisting of 13 katuns having 7 200 days) were in use. Each katun consisted of twenty tuns 360 days long. The Maya took this knowledge from the Olmecs but developed it further (Drucker 1959, Chan and Covarrubias 1964, Palacios 1965, Wicke 1966, Bernal 1968, Coe 1968).
Since the first day of the Maya chronology, 4 calendar cycles run simultaneously; their relationships are the following:
260 d tzolkin after 18 980 days these
365 d haab two coincide again
(calendar circle) after 170 820 days
they meet again
9 day cycle all cycles repeat
after 6 832 800 days
the katun circle of 93 600 days was divided into
13 katuns having 7 200 days each.
Each katun consisted of twenty 360 day tuns.
After the spanish conquest (cca 1521) very few written documents of Mayan culture survived. Those that did were in a form of hand-written folded books called codices. Not all have been decoded, but the calendar system has been deciphered. The codices are named according to the place of their discovery; we have Codex Parisian (found in 1859), Codex of Madrid (1865), Groliér (1971) and the Prague’s Codex (1956) [Villacorta and Carlos 1930, Knorozov 1963, Santos 1981, Loukotka 1956, Böhm and Böhm 2003, BB]. The most important is the Dresden Codex (DC), a book of Mayan astronomy. Already Meinhausen (1913), Guthe (1921) and Spinden (1930) recognized that some data in theDC may contain astronomical information, namely tables of the solar eclipses and tables of visibility of Venus. Now we know that besides the eclipses and Venus ephemerides, in the DC there are tables of heliacal rises and sets of planets, their maximum elongations and conjuctions (even multiple conjuctions). Other astronomical information is available from hieroglyphic texts (inscriptions) on monuments in temple cities (e.g. in Copán, Piedras Negras or Quiringuá about equinoxes or solstices, or in Palenque about conjuctions of the planets).
1.2. The Problem.
The Mayan calendar is very precise, but its relationship to our calendar (Julian, Gregorian, Christian) is not well established; the possible error is surprisingly large, of the order of centuries! The correlation or constant between the calendars has been estimated by means of various historical events recorded by the Maya and may also be computed by diverse astronomical phenomena listed in the DC and in other sources. But this latter task is not so easy for the Maya as it is for the correlation between the Europoean and Chinese calendars which use the mutually observed supernova of 1054 AD (Crab nebula). As far as we know the Maya did not observe this supernova. Thus, to find the correlation between the Mayan (MD) and our Julian (JD) calendar we have to rely upon other astronomical phenomena, observed and recorded by the Maya and we must be sure that the observations are correctly identified. However we must recognize that a mathematical solution from astronomical evidence may not be unique because although many astronomical phenomena show (nearly) periodic behaviour the periods are generally short (months or years). We prefer long-periodic features like multiple conjunctions of the planets (they repeat after decades) to the observations of solstices or maximum elongations. A review of all possible atronomical phenomena which might be used to evaluate the correlation is given in tab.1; the phenomena actually used in our analysis (data from the DC and on stellae) are labelled by stars in this table.
Stated algebraically, the correlation question seeks a solution for the value of the constant τ in the equation
JD = MD + τ,
where τ is sometimes called the Ahau equation (related to the starting date in MD). Various authors based their computations of the correlation on different historical or astrono-mical data. More than 50 different values of the correlation have been published (for a part of them see tab. 2, for more see, e.g., Vollemaere 1994). These correlations differ significantly – up to about 1000 years, typically by hundreds of years. The most common is the correlation GMT (Goodman-Martínez-Thompson), derived from historical data; we have to add τ = 584283 days to theMD in order to get JD (Thompson, 1950).
The ideal correlation should fulfill all astronomical data in the DC without any exception; it must be in accord with astronomical meaning (if any) of inscriptions on stellae, etc. It also must be consistent with evidence provided by historical documents, it must respect the shift of the Mayan calendar by 17 days after the invasion of the Yucatan by Mexicans (Knorozov 1963, Coe 1972), and should be consistent with evidences from ceramics, styllistic considerations, C14 data (if availbale), and with various geoscience indications. The GMT does not fulfil these requirements (see Sects. 4.4.2. and 4.4.3., 4.5.-4.6.).
Many authors have criticized the GMT correlation (e.g. Böhm and Böhm 1991, 1996, BB; Vollemaere 1994, Vol; Verbellen 2001, Ver), they computed their own correlations and found many good arguments against it, but this correlation remains in use. For example the difference GMT – BB is – 104 y, GMT – Vol is - 520 y. Clearly the timing of the Mayan calendar and the history of Mesoamerica with respect to other civilizations may be uncertain by centuries if GMT is invalid. Can a correct correlation be found?
1.3. Goal of this work.
We continue the work of (Böhm and Böhm, 1999) and test here the GMT, BB, Vol, Ver and other correlations by means of astronomical observations mainly deciphered from the DC (see tab. 3). At first (Sect. 2.1), we critically outline data in the DC, then we mention sources of the present-day astronomical computations of aspects of the planets and of the eclipses (Sect. 2.2.) which we used, further on we introduce two mutually independent methods for determining the correlation (Sects. 3.1. and 3.2.) which yield the same numerical result (i.e. the BB correlation of 622261 days). Finally we review all the results of our tests of the correlation (Sects. 4.1.- 4.4.). We will discuss the discontinuity in the Maya calendar (Sects. 4.5.-4.6.) whose impact on the correct value of the correlation is important, and further on we note an historical context supporting certain and rejecting other correlations. We will find that (1) the established and often used GMT correlation is – from the point of view of astronomy and data now available from mayanists – wrong, and that (2) it should be replaced by the BB correlation.
b
a
c d e f
Fig. 1. Outline of trustworthly, unquestionably deciphered hieroglyphs with an astronomical meaning, taken mainly from the Dresden Codex. Fig. 1a shows the hieroglyph for the Venus, the symbols for the Sun are on Fig. 1b, and Figs. 1c-f depict variants of the symbol for a solar eclipse.
Tab. 1. Summary of astronomical phenomena which might be used to test
the correlation relationship) between the Maya and our calendar. The phenomena actually registed in the DC are labelled by one star symbol, what we used in our testing are shown with double stars.
- aspects of the planets (elongations** , conjuctions**, including multiple conjunctions
among more than two planets**, opposition*
- heliacal rising/setting of the planets**
- time of solstices/equinoxes**
- eclipses of the Sun and the Moon, *
mainly total or annular eclipses of the Sun **
- occulations of the planets by the Moon
- (super)novae
- comets
- extra bright bolids and meteoritic storms
Tab. 2. List of some of about 50 correlations to transform Mayan to
Julian/Gregorian dates.
(The last column contains informative rounded values of the correlations given in years, by taking
the length of the mean year 365.25 days)
Author year of publ. correlation [days] [years]
Bowditch 1910 394 483 1080
Willson 1924 438 906 1202
Spinden 2 1924 489 384 1340
GMT 1950 584 283 1600
Bohm and Bohm 1996 622 261 1704
Kreichgauer 1927 626927 1716
Hochleitner 1970 674265 1846
Verbelen 1 1991 739 601 2025
Verbelen 2 1999 739 615 2025
Vollemaere 3 1984 774 083 2119
2. Data
2.1. Hieroglyphs
The basic time-elements in the DC which are well known, are the glyphs for the individual days of the 20-day cycle, and the Mayan numbers for the twenty-day calendar system. Also several glyphs from the DC for the astronomical observations are considered to be reliably identified, in particular the symbol for the planet Venus (Fig. 1a) [see, e.g., Förstemann, 1880] and for the Solar and Lunar eclipses (Figs. 1c-f) [e.g. Knorozov 1963]. The hieroglyphs showing numbers are also well known (we know when the particular phenomenon took the place, according to the MD), but some non-calendar glyphs remain uncertain.
Also well established are dates of various astronomical observations and series of observati-ons of certain phenomenon, or predictions (ephemerides), all together there are 47 cases in the DK (see tab. 3). Other data (from inscriptions in temple cities) define solstices or equinoxes (Böhm and Böhm, 1999).
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Tab. 3. Astronomical data in the Dresden Codex and on stellae.
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Page in DC dates in days (MD) phenomenon used to compute the correlation
by BB 1996 here
D 24 – 29 1 366 560 full Moon yes
Mercury west elong. yes
1 364 360 Venus, heliactic rise yes
new Moon
Mercury west elong . yes
1 397 640 Venus, heliactic rise
1 433 260 Venus, heliactic rise
autumn equinox yes
Mercury east elong. yes
1 373 460 conjunction of Mercury, Venus
and Jupiter yes
D 30 – 37 1 412 848 Solar eclipse yes yes
1 412 863 full Moon
1 412 878 new Moon
1 412 893 full Moon
1 412 908 new Moon
to date 1 412 848 days,
the assumed cycle of solstices
is added,
6 of them were observable
from the Maya territory
1419257 Solar eclipse yes yes
1420 290 Solar eclipse yes yes
1420 822 Solar eclipse yes yes
1421 855 Solar eclipse yes yes
1424 808 Solar eclipse yes yes
D 37 – 38 1 426 360 conjunction of Venus and Mars yes yes
1 426 109 conjunction of Venus and Mars yes yes
1 386 580 conjunction of Venus and Mars yes yes
1 386 069 maximum angle distance
of Mars and Jupiter between
two conjunctions
D 40 – 43 1 272 921 Jupiter, heliactic set
Saturn, heliactic rise
autumn equinox yes
1 272 465 Mercury, west elong. yes
summer solstice yes
1 272 544 Jupiter , heliactic set yes
Saturn, heliactic rise
Mercury, near east elong.
1 272 423 Mercury, east elong . yes
1 234 220 Jupiter, heliactic set
Mercury near west elong. yes
1 233 985 Saturn, heliactic rise
Mercury near west elong
1 268 540 Jupiter heliactic set
1 268 523 Mercury, west elong. yes
1 499 004 Mercury west elong. yes
1 538 342 Saturn, heliactic rise
1 486 923 Saturn, heliactic rise
D 48 – 52 1 394 120 Venus, heliactic set
Mercury, heliactic set (?)
1 393 514 Mercury east elong. yes
1 437 020 Mercury near west elong. yes
1 435 374 Mercury, heliactic rise (?)
1 567 332 Mercury east elong. yes
1 520 654 Mercury, heliactic rise (?)
1 201 200 Mercury, west elong. yes
1 201 114 Mercury, heliactic set (?)
1 274 240 Mercury, heliactic set (?)