The Correlation that works Maya

The Correlation that works
Geraldine Ann Patrick Encina, PhD
Abstract
Inconsistencies produced by the Goodman-Martinez-Thompson correlation are
solved when using a radically different approach supported on epigraphic,
astronomic, colonial and modern ethnographic sources. First, I address the
dilemma of the bissextile day by shining light on the greatly forgotten agency the
four year-bearers. Next, I model how their agency is maintained by the five Bakab
that keep the world in balance, and how such capacity is lost during a small lapse,
only to be recovered after the ritual of the erection of the Bakab. I show that this is
the original means to keep the haab in alignment with the tropical year. Then,
presuming an astronomic configuration at the onset and closing of the 13 Bak’tun
cycle involving Venus and Moon, I identify epigraphic texts that give an account
of the agency of those two celestial bodies on zero date and recover the date at the
closing of the cycle. To finalize, a comparative analysis is shown between the
GMT correlation and the correlation published some years ago (Patrick, 2013).
The analysis demonstrates how the Calendar Round is kept aligned to the tropical
year thanks to the agency of the four year-bearers, a factor that had not been
considered by any of the correlations proposed until today, nor by those Aj Q’ij
who are reported to be keeping record of days in Guatemala. Only one Achi elder
from Baja Verapaz recently described the transfer of office to the next Year Bearer
as a quarter day passage that is ritual and which is not meant to be reckoned like
all the other days (Mateo Ajualip, p.c. 2016). This modern ethnographic account
strongly sustains the model of time-keeping through the haab and supports the allencompassing correlation.
Introduction
If Thompson (1935:75) wrote “I do not wish thereby to indicate that the
correlation that I have sponsored is necessarily correct. I am very far from feeling
that it is infallible, and have said so on many occasions”, then, why is it so widely
utilized? There are a handful of acceptable reasons. First, it is “in agreement with
Landa’s typical year for 1553” (Thompson 1935:71,76) and it is in correspondence
with the important list of Tun endings on page 66 of the Chronicle of Oxkutzcab
(Bricker and Bricker 2011:79). Second, the Goodman-Martinez-Thompson
correlation (GMT, constant 584,2831) has a heliacal rising of Venus happening
eleven days after 9.9.9.16.0, 1 Ajaw 18 K’ayab, a date on the introductory page of
the Venus Table on the Dresden Codex which has been interpreted as referring to
such event because the Calendar Round portion of the date (1 Ajaw 18 K’ayab)
1 appears on the Venus Table in the column of heliacal risings (Dresden, p.50).
Third, ceramic evidence from San José (Honduras) appears to favor the GMT
correlation because it equates 11.16.0.0.0 to mid fifteen hundreds instead of late
twelve hundreds of (Spinden 1924, correlation constant 489,384) or other
correlations that push it forward even to mid seventeen hundreds. Fourth, in the
Highlands of Guatemala, the Aj Q’ij keep record of days without having lost a
single day since colonial times and they are in perfect synchrony with the
Calendar Round (CR) given by the GMT.
However, the GMT correlation does not recover a date for a visible eclipse in
Mayan territory on 9.16.4.10.8 –one of the base dates on the Dresden Codex
Eclipse Table–, as Teeple (1930:109) and others suppose it should do. Neither
does the GMT correlation recover the Moon Ages provided in the Lunar Series.
Furthermore, for dates recorded by the Itzá from Tayasal –who treasured their
Postclassic calendars well into the sixteen hundreds–, there is an inexplicable
discrepancy that makes Eric Thompson feel uneasy2: for the closing of 12
Bak’tun, the date given by the GMT is 37 days sooner than that reckoned by the
Itzá chief and reported by Orbita and Fuensalida in 1618 (see Thompson 1935:59).
Kelley (1976:32-33 and Table 4) presented a list of criteria required for a
correlation to be solid. The closing of K’atun 13 Ahau at the time the Spaniards
arrived (Criterion four) is fundamental, because there is a clear reference to the
exact date (around mid November 1539, Julian date) for a Tun ending on 13 Ahau
which Morley clearly showed must correspond to the ending of that K’atun, on the
same 13 Ajaw 8 Xul annotated on page 66 of the Oxkutzcab manuscript (Morley,
1920 cited by Thompson 1935:59).
Kelley’s Criterion six refers to date 9.16.4.10.8 from Dresden Codex (p.51a and p.
51b) as making clear reference to a node passage of the Moon. Here, Kelley
(1976:32) alleges that Thompson and Spinden, “accepting the eclipse function of
the table, arbitrarily remove it from its base to the extent necessary to fit their
respective correlations.” Kelley (1976:32) also faces a real problem in trying to
comply with such astronomic requirement: according to his analysis, “the only
correlation which passes this criterion is 736,123, or better, 736,124. The next
closest to passing this criterion is 698,164.” Both of these are way-off Criterion
four (the closing of K’atun 13 Ahau upon the Spaniard’s arrival), which was a
widely annotated event in Mayapan region.
Overall, the instability of the correlation constant made Thompson (1950:
Appendix II) propose slight modifications to the original Goodman (584280)
Martínez (584281) and Thompson (584285) correlations in an attempt to match at
least one of several events recorded in early contact history or many centuries
earlier. It is clear that, while standing for one or two criteria, even these
2 correlations do not pass several other criteria that are as relevant. Like Teeple said
decades ago, “… no real progress can be made by assuming a correlation and then
trying to force agreements out of the inscriptions. By that method almost any
correlation can be made look plausible, provided no one examines it too closely.”
(Teeple 1930:113).
Furthermore, from reading several works (Sprajc 2001:130-151, Prem 2008,
Kelley 1983, Lounsbury 1978, Thompson 1935, Teeple 1930), it becomes clear
that the 365 k’in calendric system is problematic for all Mayan scholars. The haab
has been defined as ‘imprecise’ because it does not have an explicit means to
insert the bissextile day, so everyone has adhered to the idea that it lags forever.
Only one insists that it must somehow be able to stay in harmony with the solar
year cycle (Bolles 1990). Most, however, are content with the fact that
observational calendars suffice to keep solar ceremonies in place; there is nothing
to worry about if the official calendar lags because the observational one does not
(Sprajc 2001:133; Stanislaw Iwaniszewski, p.c. July 2016).
In regard to the Long Count (LC), Thompson and all calendrics researchers
assume that the LC have a k’in-to-day correspondence with the Julian Day number
system.3 The LC is considered to give “an unbroken system of days,
corresponding closely to the Julian Day number system used by modern
astronomers”, and it is also stated that “the number of days can be converted to our
system of Julian day numbers by the addition of a constant number of days, known
as the Ahau equation of correlation constant” (Kelley 1983:157). This means that
such a procedure automatically makes both the haab of 365 k’in and the tzolk’in
of 260-k’in have a lag of one day every four years (see endnote ii), since both are
seen as incapable of accounting a quarter-day each year. In such a lagging haab
model any Mesoamerican 365 day calendar requires 1507 years for it to return to
its original position! Considering how careful Pre-Classic through Postclassic
astronomers and priests were about holding solar ceremonies on precise dates as
those marked by monuments aligned to specific Moon, Sun and Venus risings and
settings as well as to solar zenith passage dates, how could they have not designed
a device to keep perfect track of time within solar year-cycles so as to be able to
prepare, ahead of time, for upcoming ceremonies related to their celestial deities?
How could they make calculations of eclipses and not miss a day in the process?
Why go through the trouble of making seasonal or water tables that will rapidly
become useless?
Teeple (1930:113) made a good point when he said
I feel sure that no real progress can be made by assuming a correlation and then
trying to force agreements out of the inscriptions. […] The work must proceed
from the other direction, assuming that we do not know equivalent Christian dates
unless and until our accumulated knowledge from the inscriptions forces them on
3 us […] This is the only method, aside from direct revelation, which will
ultimately produce a correlation inspiring general confidence.
In order to address the correlation, we must take a close look at the corresponding
cycles along which days and k’in advance. The Julian Calendar4 is the cycle that
sees the entering of each day at noon. Days accumulate into groups of 1461 every
four years perpetually. In contrast, the haab is always carried by one of four yearbearers (or should we say haab-bearers). Haab-bearers stand on each of the four
cardinal points and take office after a quarter-day ceremony has taken place at the
end of Wayeb. K’in are set on at a distinct quarter-day moment that is determined
by the haab-bearer in charge. When all four haab-bearers have taken office, k’in
sum 1460, but each group of 365 k’in is qualitatively different, as will be seen in
the next section.
In what follows it will become apparent that the Long Count System is in fact a
chronological log of 365 k’in which become activated on quarter-day moments of
a day cycle in agreement with the year-bearer in office. Also, the reader will see
how this happens while Bakab trees are standing. Every time Bak’tun cycles are
completed a Bakab tree falls, suspending office-taking by haab-bearers for a
thirteen year-cycle period.5
Four directions and four moments of the day cycle
The haab-bearer model has been shown in many different epigraphic and
iconographic contexts (Madrid pp. 34-37; Dresden pp. 30b-31b, 29c-30c and 30c31c), and so has the Bakab model (The Book of Chilam Balam of Chumayel, Roys
1933:64-65), but neither roles have been fully understood in spite of their
calendrical contexts. Even more, Fray Diego de Landa (1978) carefully described
what ceremonies were carried out every time a year went by, but the subtleness
about the implicit aspect of the six hours after the 365 k’in reckoning was not
carefully conveyed.
Authors have analyzed the meaning of cardinal hieroglyphs for decades. The most
clear assertions have been those of Léon de Rosny (1876) regarding two glyphs
with the sign k’in while he was studying the Paris Codex which he correctly
identified with east and west. Seler (1902-1923) related colors to directions, where
east is associated with red, north with white, west with black and yellow with
south.
Hopkins and Josserand (2000) provide an excellent analysis of the hieroglyphic
meanings of the glyphs and names provided for the cardinal points and conclude
that, rather than there being specific points, there are ranges. Before that, they
comment that other authors have considered that those specific points are related
4 to true east and west, that is, to the midpoint between the northern and southern
rising Sun and to the midpoint between the northern and southern setting Sun. As
a reminder, the referred authors propose that lak’in is the result of reduction and
losses from the original word (‘e)la(b)-k’in, freely translated as the front porch of
the house of the Sun, where the Sun emerges, while chik’in derives from the
original (‘o)chi(b)-k’in, freely translated as the door of the house of the Sun
(where the Sun enters), and that “the terms can be postulated for Protomayan, as
early as 2000 BC” (Hopkins and Josserand, 2000:7,8).
Both notions –based on regions or on specific loci– are complementary. In
Yucatecan ‘region’ is called cuch cabal (“regimiento o parcialidad”, vid SFM).
Figure 1 shows the four boundary lines drawn by the northern and southern sides
of the eastern and western segments. Those lines connect two opposite solstice
dates occurring at sunrise and sunset of June 21st and December 21st. As seen
below, the latter date is marked on the haab as day 10 of Yaxk’in. The cross
drawn by the four boundary lines is the first kind of cross out of three solar-based
crosses represented in Mesoamerican worldview.
It seems natural to imagine that the region of emerging suns was synthesized by
the observers as a single spot on the horizon; the same for sinking suns. From such
synthesis must have emerged specific chrono-topo loci: those for equinox sunrise
and equinox sunset. As will be shown later, the haab emphasizes both such dates
(March 21 and September 22) at the onset of two specific Winals.
The middle point of each of the northern and the southern regions cut
perpendicularly across the line linking equinox sunrises and sunsets. The cardinal
cross thus produced becomes the second one merging from the exercise of locating
one’s place in reference to the world.
For the Mayan skywatchers, the third cross must have been the most interesting.
Like there are four equidistant references on the flat plane, there are four
equidistant moments on the vertical plane marked by the Sun during its complete
daily cycle. Thus, a vertical cross can be conceived. The symmetrical crosses
painted by cultures of Mesoamerica seem to be an actual conflation of the second
and third crosses that were conceived. According to the Tzotzil peoples from
Chamula, the vertical cross is the “horizontal equivalence of the daily trajectory of
the Sun through the sky from east to west” (Gossen, 1974).
But when and where does the Sun produce a vertical cross? Vertical crosses we
imagine drawn by the Sun can only occur any place on the Earth’s surface
between the two tropics. Within this region the Sun through its daily cycle reaches
the zenith twice a year, on dates that are equidistant from the solstice dates
(December 21 and June 21). The Sun in the zenith at noon projects vertical rays so
5 straight bodies cast no shadow. This phenomenon has been interpreted by all
cultures within the region as the vertical axis that runs perpendicularly through the
horizontal plane, thus producing a cross (Figure 2). There are two places where
such vertical crosses happen only once a year: on the latitudes of the tropics, i.e.
23°42’ north and south. In all the other latitudes that are smaller than those of the
tropics, the vertical cross ‘produced’ thanks to the Sun’s zenith passage happens
twice a year.
Along the line of the Equator, the zenith-nadir axis occurs on March 21 and
September 22 (equinox dates). This zenith-nadir axis is unique in that it produces a
90° angle with two imaginary lines instead of just one –which is typically the
horizontal plane–. The other (unique) line is the one produced by the east-west
axis obtained by the sunrises and sunsets on equinox dates. In both cases, the
zenith-nadir axis on the Equator on equinox dates draws a vertical cross.
Figure 1. First and second kinds of cross. The first kind is produced by the solstice points
of the Sun on the two horizons. The second kind is produced by the east-west axis drawn
by the equinox loci at sunrise and sunset on March 21 and September 22. From that axis a
line at a 90° angle cutting through its middle point produces a cross.
Along latitude 15° N, the zenith passage of the Sun occurs on April 30 and August
13, so the Sun marks the zenith-nadir ends of the cross only on those dates. In the
minds of the Maya, the places where the Sun rises or sets on those dates pinpoint
6 at one end of the line on the flat plane. That line is at a 90° angle with the line
drawn down from the zenith. The projection of each of those lines produces the
vertical cross.
Figure 2 shows how the zenith-nadir axis of the model works as a 90° intersection
with the horizontal plane on August 13, which is when a symmetrical cross is
achieved by the four equidistant moments of the Sun’s daily cycle. This date is the
starting date of the haab, as will be shown below. The other date when the cross
occurs is April 30. The ceremony of the planting of the Yax Che (Ceiba tree)
through Yucatan, Quintana Roo and other Mayan regions are a continuity of
ceremonies that point at the cross described by the Sun. April 30 is the first day of
Kankin month, which in Ch’olan is Uniw. The first is a Yucatecan term that in this
context means four-suns, precisely because it is a month that calls priests to
identify the four moments of the Sun that produce a symmetrical 90° angle cross.
The Ch’olan term means ‘avocado’ and it refers to the time when trees are
flowering, just as Ceiba tree does. Date 3 Kank’in became particularly important
for the Mayan culture because it was to be the closing date of 13 Bak’tun cycle. Its
Gregorian Calendar equivalent, May 3, produced a fast assimilation of the
Christian celebration Santa Cruz (Saint Cross) on that same day, making
contemporary Mayan youth believe that there is nothing authentically Mayan in
their elder’s traditional ceremonies.
Figure 2. Third kind of cross produced from the observation of the Sun in its daily cycle
when the Sun reaches the zenith on April 30 and August 13 on latitude 15° N.
7 The conflation of the north-zenith reference appears in an early Postcolonial text
published by Bolles (2001):
“u tzolaan ah cuch haaboob
b 585 hoil Ben; utz, hahal, xaman caan, tancochi lob
b620 uaxacil Muluc; utz, ma lobi, xaman caan tancochi
b640 uacil Ahau; lob, ma utzi, xaman caan, kin u cuch”
Xaman is translated as north in various dictionaries and caan is root of caanil or
caanal (adj., above) with several entries in different dictionaries systematized by
Bolles (2012)6:
caanil cah: a heavenly place (VNS)
caanal hol: pinnacle of the temple (VNS)
caanal: means high above (NEM)
caanal kin: late in time with respect to the morning (DMM)
caanal kin: early in time with respect to the afternoon (DMM)
So xaman caan is referring to a pinnacle region for xaman which can only occur
up in the sky, which is occupied by the Sun at midday.
There is an interesting entry that is complementary for caanal
Por abajo: tal cablil por arriba: tal caanal (VNS)
This speaks of there being a concept for the opposite of caanal, which is tal
caablil, which indirectly refers to the place occupied by the Sun at midnight.
Barbara Tedlock (1992) also interprets the symbolism of directions as a reflection
of the daily path of the Sun, with north and south representing noon and midnight
positions of the sun. This can only be possible on the date of the local zenith
passage of the Sun. Justeson (1989:119) finds that Madrid Codex pp. 77-78 show
two additional directional glyphs both including sign kab (earth) which he
interprets as zenith and nadir.
Another way to sustain that there is a conflation between the second and third
crosses in the Mayan worldview is that the sequence of cardinal points follows the
same direction as the four moments of the Sun through its daily cycle beginning at
dawn, i.e. sunrise, noon, sunset, midnight. Thus, the sequence of cardinal points is
east, north, west, south. This is the sequence laid out for the world directions on
the codexes.
8 Figure 3. Year Bearers in cardinal points which conflate on the four equidistant moments
of the Sun on August 13. This is the day when the Year Bearers pass office.
The twenty Tzolk’in days present that same east-north-west-south sequence. Yearbearers, which are five days apart from each other along the twenty-day cycle
(Winal) of the haab appear in the same order. Thus, in Figure 3 the east (in red) is
the cardinal point for year-bearer Kaban to begin each Winal on Kaban. The north
(in white) is the cardinal point for year-bearer Ik’, the west (in black) is the
cardinal point for year-bearer Manik and the south (in yellow) is the cardinal point
for year-bearer Eb. In dictionary JPP there is an entry for these four days: Ah cuch
haab “asi llamaban los indios los cuatro días principales en que precisamente y
por turno principiaban los años, tomando estos sus nombres de ellos.” These
principal days were the given names of the year-bearers.
The four Year Bearers and their role in the haab cycle
Year-bearers play a role beyond that of inaugurating a haab cycle on a new
cardinal point. From what has been presented above, it is also true that each yearbearer marks the time at which each k’in deity starts its cycle. From the synthesis
presented above, when the east year-bearer takes office, the 365 k’in-deities come
to life at sunrise. Next, the north year-bearer enables 365 k’in-deities to be
activated by at noon. Then, the west year-bearer has the sunset activate the
following set of 365-k’in deities; and finally the south year-bearer brings to life
9 every 365 day-deity starting at midnight. In this rhythmic description, the reader
can realize that between the closing of day-cycle 365 in charge of one year-bearer
and the opening of day-cycle 1 of the next year-bearer there is a quarter-day time
lapse. A deeper thought makes one realize that, the inauguration of the next year a
quarter-day later than the prior 365 days produces, by default, the
conceptualization of an advancement of a quarter-day. So it is a mistake to
consider both factors (the quarter-day time lapses and the year-bearer inauguration
a quarter-day later) as producers of the quarter day necessary to complete the yearcycle. The year inauguration a quarter-day later thanks to the year-bearer officetaking is by itself a subtle and elegant way of completing the year-cycle. This
inauguration is the culmination of a ritual transposition of the haab from one
cardinal point to the next. The information about the inclusion of a quarter-day
right after the 365 is forwarded to the careful reader in a time-space code.
The year-bearer office-taking ritual keeps the quarter-k’in time in the
implicit realm. Three news about such rituals and their implications are worth
mentioning.
In the Guatemalan Highlands a cherished Mam deity is changed from one of four
oriented mountains to the next (Stanzione 2000:54). It also happens in Santiago
Atitlán, Guatemala, where the Rilaj Mam (also Maximon) –said to be bound by
rope– is transferred from a family house in one cardinally oriented ‘cantón’ to the
next one every July 26 (field notes, 2010). He is considered “the bundler of years
as he himself is the bundler of time” (Stanzione 2000:54). The tying of a tie
around the neck of Maximom derives from prehispanic ceremonies where deities
related to cycles played a special role as bundlers of time (Gronenmeyer and
MacLeod 2010:36) and particularly as agents who measured time.
Landa (1978) reports in chapters XXXV-XXXVIII about New Year rituals
celebrated in alternating cardinal points named after the positions on the Tzolk’in
cycle which are 5 k’ins apart from each other: K’an, Muluc, Ix and Cauac. On the
first two of these mentioned chapters, he mentions as follows:
In the year of which the dominical letter was Kan, the omen was Hobnil, and,
according to what they said, they both ruled in the region of the South. In this year
then they made an image or hollow figure of the god of clay, which they called
Kan u Uayeyab, and they carried it to the heaps of dry stones which they had been
raised at the southern side. They chose a chief of the town in whose house this
festival was celebrated on these days, and to celebrate it they made the statue of a
god, which they called Bolon Dzacab, which they placed in the house of the
principal, adorned in a public place where everyone could go to it [...]
In the year of which the dominical letter was Muluc, the omen was Can Sicnal;
and at the proper time, the nobles and the priest chose the principal who was to
celebrate the festival. After he had been chosen, they made the image of the god
10 called Chac u Uayeyab, as they did that of the preceding year, and they bore it to
the heaps of stone towards the eastern side, where they had left that of the year
before. They made a statue to the god called Kinich Ahau, and they placed it in
the house of the principal in a suitable place.
The description continues for the two other ‘dominical letters’: Ix and Cauac.
These four Year Bearers take office on the first day of Pop (which, as we know, is
2 Pop). In Chapter XXXIV Landa (1978) tells that years are 365 days and 6 hours
long. Both notes combined can lead to imagine quarter-day long processions to
carry the deity of clay to a heap of stones on the next cardinal point of the town.
The symbolic proceeding, year after year, had the practical finality of keeping the
haab tied to a sunrise, noon, sunset, midnight of one very particular solar date.
In the latest Congress of Epigraphy for Mayans (El Remate, El Petén, Guatemala,
2016), I was informed by an Achi researcher that the eldest person in his
community had explained how year-bearers have always been the same: Ik’,
Manik, Eb and Kaban. He said that the year-bearer days do not recess. He
explained that what makes the year-bearers always be the same is this: “while a
year-bearer passes office to the next one, a half a day goes by in which the world
is left with no protection, because no one is in charge”. Mateo Ajualip, the Achi
researcher, said that the model I describe is exactly what the elder said back in his
community. This is the most precious piece of evidence I have found to this day to
sustain the Mayan model of year-bearers and their role as shifters of the starting
time of the 365 k’in that are under their office.
Portilla (1994:91) says that he can affirm that if space exists thanks to the deeds of
the gods and it has divine connotations, the present deities acting in it are precisely
the changing faces of time (day after day). Outside of it, space is unthinkable.
Beyond cycles there is no life and nothing occurs. The color directions, divorced
from the k’in, Sun, day or time, would turn into mist without any sense. In another
reflection, Portilla (1994:87) says how the ceremonies related to the Wayeb are
precisely emphasizing the importance of orientations of the year-bearers because
the political and religious changes among the chiefs of the different districts or
divisions of the community depended on this. Certainly, the model typically in
place for the Long Count reckoning, which parallels the Julian Day accounting in
that the leap day is included, is simply not applicable in the original time-space
structure of Mesoamerica.
11 Year-bearer Groups
Year-bearer sets or groups are of five kinds: each group is known by its starting
day, which can be Ik’, Ak’bal, K’an or Chicchan. These groups were used in
different regions and at different times (Bricker and Bricker 2011:70). The K’an
set (K’an, Muluc, Ix, Kawak) was typical in Postclassic Yucatan, and although
Landa (1978:chapter XXXIV) associates them to first of Pop, we now know that
they are linked to 2 Pop. The Ak’bal set (Ak’bal, Lamat, Ben, Etz’nab) was used
in Campeche (Proskouriakoff and Thompson 1947, cited by Bricker and Bricker
2011:70), and it was related to 1 Pop.
The original and most widely used group of year-bearers in the Classic period and
through Late Postclassic was Ik’, Manik, Eb and Kaban. Stuart (2005a:3) shows
how Stela 18 of Naranjo is dedicated to a New Year celebration consisting on the
accession to office of ch’oktak, the youths, on day 1 Ik’ Seating of Pop. By
reviewing a collection of other inscriptions related to New Year rites, Stuart
unveils many truths. First, Thompson’s insistence (1950:127) that this group of
Year Bearers was associated to day 1 Pop, falls par terre. Forcing that convention
had made many scholars believe that the Tzolk’in structure was shifted in
Postclassic Yucatan so as to fit the K’an set. Secondly, contrary to what Bowditch
(1910:81) had said (that Year Bearers did not exist in the Classic period) or to
what Thompson (1950:128) reported –that there were no New Year records on
monuments–, Stuart shows that New Year dedications are present and, more
importantly, that they address the key role of year-bearers on Seating of Pop
(Stuart 2005a). Based on iconography from Rio Azul and Pomona, Stuart
concludes that Year Bearers were “ritually important” and that Ik’, Manik, Eb and
Kaban is the original set, traditionally used in lowlands and highlands and
surviving among Quiche, Mam, Ixil and Pokomchi till today (referring to Tedlock
1992:92).
Table 1. Year-bearer groups depending on starting day in Pop
Classic and Postclassic
Year-bearer related to
Seating of Pop
1 Kaban
2 Ik’
3 Manik
4 Eb
Postclassic
Four years in sequence
Year-bearer related to 1
Pop
2 Etz’nab
3 Ak’bal
4 Lamat
5 Ben
Postclassic Mayapan
Year-bearer related to
2 Pop
3 Kawak
4 Kan
5 Muluc
6 Ix
12 The local choices of year-bearer groupings did not alter the internal gear or
reckoning system of the Calendar Round (Tzolk’in and haab) and its articulation
to the Long Count. Each set of year-bearers is related to the subsequent starting
days of month Pop. As seen on Table 1, while group Ik’, Manik, Eb, Kaban relates
to Seating of Pop, group Ak’bal, Lamat, Ben and Etz’nab relate to 1 Pop and
group K’an, Muluc, Ix and Kawak relate to 2 Pop. This in perfect harmony with
the internal Calendar-Round articulation.
‘Oriented days’ and the Need for the Falling of the Bakab
From the above, a new kind of attribute emerges for the k’in: the cardinal location
of the year-bearer makes the haab and its 365 k’in relate to one of the four quarterday moments. Each grouping or bundle of 365 oriented days has an attribute of its
own, so we find sunrise-days, noon-days, sunset-days and midnight-days. Once
these groupings have participated, the elapsed time is four years long –but years of
365.25 days–. Yes, with the model described until now, the time-keeping system
works very well for several K’atun cycles, but after a whole Bak’tun, the
alignment of the year-bearer becomes three days off.7 This can be easily solved by
suspending the office-relaying ceremony of year-bearers during twelve years upon
the completion of the Bak’tun cycle. (If four office-relaying ceremonies implicitly
provide one additional ritual k’in, the suspension of four such ceremonies
discounts one ritual k’in; the suspension of eight ceremonies discounts two ritual
k’in; and the suspension of twelve ceremonies discounts three k’in). At the
completion of the thirteenth haab cycle the year-bearer ceremonies would resume
and continue year after year until the closing of the Bak’tun cycle.
The suspension of office-relaying ceremonies of year-bearers requires a justifiable
context, i.e., something out of the ordinary needs to happen. The falling of a
Bakab is a good possibility. The upright standing of Pawuatuns or Bakabs on each
corner and in the centre provide order and continuation of year-bearer ceremonies.
When a Bakab falls, there are no conditions for the next year-bearer to take office.
Take, for instance, that the north Bakab fell and the year-bearer in office was the
one on the east. Because of the world imbalance the next year-bearer (the one on
the north) would be unable to take office. Through a cycle of thirteen years8 the
only year-bearer in charge would be that of the east, having thirteen 365-day
groupings entering at sunrise. After that lapse, the Bakab would be erected in a
ceremony, bringing the world back to balance. In such conditions the east yearbearer would be able to pass office to the north year-bearer, who would start office
that day in perfect alignment with the original solar date.
The Creation of the World (Roys, 1933) is told in the Book of Chilam Balam of
Chumayel. We are told how, after a destruction period provoked by the falling of
13 one or all of the Bakab, they would rise with their corresponding colors and birds,
and that only then came “the ordering of the measurement of time”. Elsewhere we
are told that when one tree fell there was much instability in the world. The
interesting information emerging from this proposal is that the coming out of
alignment concomitantly produces a world imbalance that needs time before order
may resume.
Time Lapse in a Haab Cycle
The role of year-bearers is to take office in a ritual manner at their cardinal point
and begin working from their corresponding moment of the day-cycle so to
recover the alignment to a pre-established solar date and time every four years.
More specifically, within a complete Bak’tun cycle a haab measures 365 k’in plus
a ritual time lapse consisting of a quarter-day minus 11 minutes or 0.2423 k’in.
The length of this ritual time is achieved thanks to two rituals: the office relay
between two neighboring year-bearers and the suspension of the relay during the
time that a Bakab remains fallen (the first thirteen years of each Bak’tun cycle).
The Counting of Oriented Days
The fact that k’in is an oriented day9 is an attribute intrinsically related to the
cardinal position of the year-bearer in office. Be it a year-bearer in the typical
relay mode or a year-bearer in the non-relay mode (during the thirteen-year
suspension), the k’in still holds its oriented attribute.
Although it may seem as though ceremonies for the office-taking of year-bearers
depend on priests to the point that their agency is mandatory to keep haabs in
perfect alignment with the Sun, we must be confident that the system takes care of
itself. That is to say that if the ritual movements were to be kept at the symbolic
level only, the haab reckoning system would still manage to measure tropical
years, measuring 365 k’in plus 0.2423 implicit ritual k’in every haab cycle. Like
pyramids and other monuments, haabs were designed to mark all 365 solar dates
with utmost precision.
Only the counting of oriented days matters for the Long Count (LC), since its
measuring capacity consists of keeping track of groupings of 365 oriented days
(k’in), and by doing so it reckons the passage of every tropical year and records
1460 k’in upon the completion of four tropical years. Contrast this with the 1461
k’in calculated for the passage of four tropical years when paralleling the Long
Count with the Julian Day counting system.
14 Long Count records inscribed on stelae or on codexes must be understood as the
accumulation of oriented days or k’in whereby 365 of them equate a tropical year.
To convert a Long Count expression into tropical years the proceeding is simple:
1. First, sum up the total number of oriented days expressed in Bak’tun (multiples
of 144000), K’atun (x7200), Tun (x360), Winal (x20) and k’in (x1)
2. Second, divide the total sum of oriented days by 365. The result is immediately
expressed as solar years.
For example, 13 Bak’tun equals 13 x 144,000 k’in, which amounts to 1’872,000
k’in. The amount of tropical years is obtained by dividing 1’872,000 by 365. The
result is 5,128.7612 tropical years or 5,128 tropical years plus 280 days.
Length of 13 Bak’tun cycle
It is highly important to clarify that the oriented day model eliminates the problem
of the leap day. This means that, as time lapses on the LC increase, k’in that are
thought to be measuring leap years also accumulate. A typical mistake that
Mayanists make when first hearing about this proposal published three years ago
(Patrick, 2013a) is to think that the difference in days between the closing date of
13 Bak’tun according to the GMT and to this new correlation can be transposed to
LC 9.16.0.0.0. or to 0.0.0.0.0, as if the difference in days between both
correlations was to be identical on any of those other LC dates. Any correlation
using the Julian Day counting system is not commensurable with the LC system.
The first one includes leap days in its accounting whereas the second one does not.
Compare the time lapse in tropical years obtained by the oriented days model
applied on the LC (5,128.7612) with the time lapse conventionally calculated for
the same 13 Bak’tun cycle, i.e. 5,125.366 tropical years. This difference is
explained by the accumulation of leap days that are thought to be included in the
Long Count system when they are not. Leap days accumulate as years go by, so by
the completion of 13 Bak’tun, a total of 1243 k’in have been forced to measure
leap years when they were not originally designed for such purpose. This
accumulation is shown at the end of this paper, on Table 6.
From the need to have the start of Mesoamerican years aligned with exactly the
same solar event, archaeoastronomer Daniel Flores in 1995, and also an
independent group of researchers of the Mexica calendar (among them, Arturo
Mesa and David Wood, personal communication) in 1994, proposed that the
15 movement of the Year Bearers by a quarter day provides the equivalent to an
additional day that acts as a leap day.
Mayanist scholars prefer the linear model that explains the recession of the haab
through the tropical year. In both models there is structural flaw: when it comes to
the Long Count reckoning system each k’in on the LC is paralleled with each
Julian Day Number, so leap days occur indefinitely after every 1460 days. On the
Calendar Round these models do not obey the basic rule that says that only four
Tzolk’in days can be linked to a solar date.10
Figure 4. Model showing the recession of Tzolk’in days. This happens when a k’in is
required to name the leap day along the Long Count.
Sprajc and Sánchez (2012:38) showed there is ample evidence of observational
schemes relating to monuments and horizons throughout Mesoamerica showing
how sunrises and sunsets separated by 13-day intervals and their multiples
occurred on the dates with the same numeral, while periods of 20 days and their
multiples fell on the day having the same sign. The practicality of the calendar as
16 an instrument to reckon these intervals is underestimated by the same authors, who
consider that the haab and its accompanying Tzolk’in are perpetually lagging. In
such model where there is a recession of Tzolk’in days, any k’in sign on its own
(i.e., without a coefficient number) that marks a sunrise on a particular solar date
does not mark the same sunrise until 80 years have passed. Figure 4 shows what
would happen if there was a recession of Tzolk’in days. The association of Lamat
at the onset of Year 5 or that of Muluc for Year 9 are aberrational.
The astronomical component of the Thirteen-Bak’tun cycle
The astronomical implications of having a leap day intruding every four years
within the LC in contrast with a measuring system that implicitly reckons the
passage of 0.2423 days is enormous. The whole 13 Bak’tun cycle can be clearly
understood as an astronomical cycle when its measurement acquires the magnitude
it was originally designed to have: 5,128 tropical years and 280 days.
Since the beginning of this research about the Long Count system, the author has
considered Venus and the Moon as probable protagonists of the 13 Bak’tun cycle.
From a psychological perspective, the changing phases of the Moon and their
influence on nature are too evident to disregard. Venus, the shiniest body in the
sky, emerging at twilight and at the brink of dawn also conveys awe and a great
sense of attraction. The presence of both luminaries is patent in the Eclipse Table
on Dresden pages 51-58 and the Venus Table also tells of its importance.
Cycle is by definition ‘the return to the beginning’. If indeed Venus and Moon had
protagonist roles in the 13 Bak’tun cycle, they must have had, ideally, identical
configurations at the beginning and at the closing of the cycle. The lapse of 5,128
tropical years and 280 days is equal to 1’873,243 days.11 In that time the Moon
completes a full number of synodic cycles (of 29.530588 days each), a total of
63,434. This means that since Moon age was 23 days on 0.0.0.0.0 4 Ajaw 8
Kumk’u (according to Copán Stela 1) Moon age at the completion of 13 Bak’tun
was also 23 days. In general, Mayan astronomers counted Moon age from its first
day of visibility in the Western sky in the evening, which was age 1.
The synodic cycle of Venus is 583.92 days. At the closing of 13 Bak’tun Venus
had experienced 3208 cycles with a residue of 27.64 days. What Venus event
could be so symbolical as to represent both the starting of an era and its
completion? The amount of evidence collected regarding the particular role of
Venus on Zero point date is now considerable, but the finest pieces of evidence
come from p.51a of the Dresden Codex and from Passage 4 on the Tablet of the
Cross, Palenque. Both pieces enable us to discern: (i) whether Venus was
protagonist of Mayan Era; and (ii) whether it made a heliacal rising as evening or
17 as morning star at the onset of the Maya Era. This is crucial because it can tell us
indirectly about its configuration at the closing of the 13 Bak’tun cycle.
According to Schele and Grube (1997), on the upper left-hand corner of Dresden
p.51a it says: 4 Ajaw 8 Kumk’u, 12 Lamat, 8 days in water (Figure 5).
Figure 5. Upper left-hand corner of Dresden p.51a.
4 Ajaw 8 Kumk’u, 12 Lamat, waxak k’in ti ha
4 Ajaw 8 Kumk’u, 12 Lamat, eight days in water.
Translation by Schele and Grube (1997).
Complementarily, Passage 4 of the Tablet of the Cross states: “Four Ajaw the
eighth of Hulohl (Kumk’u) it ends thirteen Bak’tuns; two and nine-score days ago,
one year (ago) it was changed the hearth, (at) the Edge of the Sky, (at) the New
Hearth? Place, (then?) he descends from the sky, One? (proper name for Deity
GI)” (translated by Stuart (2006), see Figure 6).
18 Figure 6. Excerpt from Passage 4, Tablet of the Cross, Palenque. See text for translation.
Drawing by Linda Schele in Stuart (2005b:165, Fig. 130); transliteration from Stuart
(2006 and 2005b:166).
The quantity of days in two and nine-score days and one year ago, is expressed on
the Long Count as 1.9.2 which comes to: 360+(9x20)+2 = 542 k’in. An implicit
balance of time periods shows through: 8 + 263 + 8 + 263. The Venus synodic
cycle according to Aveni (2001:87) shows two frames of two-hundred and sixtythree days for the visibility of Venus as evening star and as morning star. The
eight days between the two periods of two-hundred and sixty-three days in the
implicit balance surely refers to the days of invisibility of Venus around inferior
conjunction. So the eight days previous to the first 263-day lapse must be those
‘eight days in water’ that are told in passage on p.51a of Dresden Codex.
Recapitulating, on 4 Ajaw 8 Kumk’u Venus was submerged in the primordial
waters and it needed eight days to emerge as evening star. By inference, Venus
must have been on its last eight days of its invisibility period around superior
conjunction, and only then, on 12 Lamat 16 Kumk’u, did it rise as evening star.
The sequence of Venus events and periods since 0.0.0.0.0, 4 Ajaw 8 Kumk’u until
day 542 registered on Passage 4 is graphically represented on Figure 7.
On Creation Day, Venus was eight days from rising as evening star, a time-frame
which corresponded to the last eight days of a 50-day period of invisibility around
superior conjunction; then there followed two-hundred and sixty-three days of
visibility as evening star on the west horizon; then eight days of invisibility around
inferior conjunction, and for the last two-hundred and sixty-three days Venus
acted as a morning star on the eastern horizon. On the very last day of this period,
Venus descended on the east. We are told in Passage 4 of the Tablet of the Cross
that on that day Deity GI descended. Complementarily, we are told in a carved
greenstone that GI was present on day 4 Ajaw (Stuart, 2005b:165) Creation Day.
The neatness in the distribution of Venus events within the first 542-k’in time
lapse leaves no doubt that Deity GI is the personification of Venus. Kelley (1965)
inferred such association from its birthdate on 9 Ik’ (nine Wind), which is
Quetzalcoatl’s birthdate in the Mexica narrative. A preliminary analysis for dates
chosen by Mayan governors (Patrick, 2013b:47).
For the Mayan Palenque elite and also for that of Copán and Quiriguá –to name a
few– Deity GI established world order. Any governor or governess willing to be
respected by his people had to prove he was a genuine descendant of Deity GI and
had to replicate the orderly cycle (Schele and Freidel 1990:255).
19 Figure 7. Synodic model of Venus with canonical periods. Date 4 Ajaw 8 Kumk’u was
reported to occur 8 days before first visibility of evening Venus on day 12 Lamat
(Dresden p.51a), and 542 days after that date, Deity GI (a personification of Venus) is
said to have descended (Passage 4, Tablet of the Cross, Palenque).
Knowing the configuration of Venus and of the Moon on Creation Day, knowing
too that 5,128 tropical years plus 280 days after, Venus completed 3208 synodic
cycles plus 27.64 days, and the Moon completed exactly 63,434 synodic cycles,
the next step in this procedure required looking for Venus in its first days as
evening star and for Moon age 23 around GMT correlation (584,283) date
December 21, 2012 –calculated as that of the closing of 13 Bak’tun–. The date
with such astronomic conditions was May 3, 2013 (Figure 8).
From the closing date of 13 Bak’tun 4 Ajaw 3 Kank’in on May 3, 2013, we can go
back 5128 years and 280 days to arrive to July 27, 3117 BC (Figure 9), which, in
the Calendar Round system, corresponds to 4 Ajaw 8 Kumk’u. The astronomic
program Starry Night (MEADE) shows Venus rising as an evening star 8 days
later (on August 4, 3117 BC) –on 12 Lamat 16 Kumk’u– with the Moon age 1
(Figure 8). This is in perfect agreement with the moon-age registered on Stela 1 in
20 Cobá: 23 days on 4 Ajaw 8 Kumk’u for a Moon lasting 30 days. This means that
on the eighth day since Creation the Moon was on its first day of visibility.
Figure 8. Venus on first days of heliacal rising in the evening of May 3, 2013 =
13.0.0.0.0 4 Ajaw 3 Kank’in. Image from Starry Night MEADE.12 Moon has an age of 23
days, exactly as its age 63,434 lunations ago, on Creation day, according to St. 1 of Cobá.
21 Figure 9. Venus not yet visible on the evening of July 27, 3117 BC = 13.0.0.0.0 4 Ajaw
8 Kumk’u. Note that this astronomical program registers dates on the Julian calendar
until 1582, hence the date in agreement with Gregorian date July 27, 3117 BC is 25 days
after. Image from Starry Night MEADE.
22 Figure 10. Eight days since Creation, it is 13.0.0.0.8 12 Lamat 16 Kumk’u. The Moon
has just been born while Venus is on its first day of visibility as evening star. Image from
Starry Night MEADE.
Submitting the correlation to various tests
The correlation to equate a Long Count into a proleptic Gregorian date is simple.
1. First, sum up the total number of oriented days expressed in Bak’tun (multiples
of 144000), K’atun (x7200), Tun (x360), Winal (x20) and k’in (x1)
2. Second, divide the total sum of oriented days by 365
3. Third, understand that the result is immediately expressed as tropical years
4. Fourth, add the complete tropical years to -3116
5. Fifth, convert the fraction of tropical year obtained in (3) into days by
multiplying by 365.2423 and add those days to July 27
6. If the date obtained in (5) is between January 1 and July 26, the resulting year is
after the one obtained in (2)
To calculate the Tzolk’in and haab dates the procedure was initially done using
Excel. The algorithm developed helped create an application now found in the
page of the institution that helped the author produce it. It can be accessed in
http://damixi.jl.serv.net.mx/convertidor/index.jsp.
23 Over the past few years the correlation has been submitted to many tests. Some
relevant ones for Mayanist scholars are presented below and speak for themselves
regarding the consistency of the correlation.
First test. Synchronicity of haab’ with solar seasons
The intervals of each Winal of the haab are perfectly synchronized with seasonal
events throughout a tropical year. This intuition has brought David Bolles (1990)
to propose a fixed haab.
From the dates obtained for the opening and for the closing of 13 Bak’tun, we can
calculate that the starting date of the haab (Seating of Pop) is perpetually linked to
Gregorian13 date August 13. Table 2 shows dates of the Seating of and of the
completion date of each Winal. The Wayeb spans between August 8 and 12. The
starting moments of each haab on the daily cycle depends, as has been amply
explained above, on its Year Bearer.
There is a semantic association between most –if not all– of the Yucatec names
and the specific time intervals of the year. After three workshops with over twohundred Yucatec speakers held in Universidad Intercultural Maya de Quintana
Roo and in Universidad de Oriente, and after many interviews carried out by
Yucatec speaker and linguistic researcher Narciso Tuz Noh in the outskirts of
Valladolid, Yucatán, we have integrated a manuscript to demonstrate precisely
how each Winal is in synchrony with practices and natural events that are still part
of the socio-ecological scenario in Mayan lowlands.
Table 2. Winal intervals of the haab along the Gregorian Calendar
Pop
Wo
Sip
Sotz’
Tzek
Xul
Yaxk’in
Mol
Ch’en
Yax
Sak
Keh
August 13 – September 1
September 2 – 21
September 22 – October 11
October 12 – 31
November 1 – 20
November 21 – December 10
December 11 – 30
December 31 – January 19
January 20 – February 8
February 9 – 28
March 1 – 20
March 21 – April 9
24 Mak
Kank’in
Muwan
Pax
K’ayab
Kumk’u
Wayeb
April 10 – 29
April 30 – May 19
May 20 – June 8
June 9 – 28
June 29 – July 18
July 19 – August 7
August 8 – 12
Kank’in can mean four suns, meaning four moments of the Sun an image that can
be conceptualized on the day of a zenith passage, as explained in the introduction.
Kank’in goes from April 30 to May 19, which corresponds to each of the zenith
passage dates of the Sun from latitudes 15°N to 19°41’N, i.e., from Copán and
Izapa areas in the southern limit of Mesoamerica to Teotihuacan, the northern
limit of Mesoamerica (at least in political and economic terms for the Classic and
Postclassic periods).
Pax
Summer
Solstice
Yaxk’in
Winter
Solstice
Zip
Autumnal
Equinox
Keh
Vernal
Equinox
Figure 11. Winal glyphs for Pax, Zip, Yaxk’in and Keh are the only ones of all winal
signs that almost invariably show two parallel thick black lines. They may be acting as
signifiers of solstice and equinox events. Drawings by Raúl Rubio.
Also, it is very interesting to note that 12 Pax = 21 June, Seating of Zip = 22
September, 10 Yaxk’in = 21 December and Seating of Keh = 21 March. More
25 interesting is the fact that the corresponding glyphs contain two parallel thick
black lines like no other Winal glyphs do (see Figures 16-19 in Thompson, 1950).
Such iconography could be denoting the symmetrical partitioning of the year into
four quarters (Figure 11).
Second Test. Solar Ceremonies in Yaxchilan
Yaxchilan, where identical Flapstaff (Jasaw dance14) events were celebrated by
Bird Jaguar, Shield Jaguar and father and son together on different years over a
span of eleven years, have been considered linked to the Sun because of the solar
signs on their dresses. The ‘regressive pattern’ of the dates of the Jasaw Dance
dates according to the GMT correlation (June 27, 26, 25, Gregorian) shows the
kind of aberrational results that must be accepted by specialists when it is utilized.
The correlation here proposed does not produce a regressive pattern at all, which is
highly convenient when trying to explain the realization of identical events (in this
case, all dedicated to the Sun).
Considering Mesoamerican cosmovision, it is expected that such events are
carried out on identical haab dates which, in turn, are fixed to meaningful solar (or
Venus) events. In this case, the repetitive date for 19 Yaxk’in –which is December
30 (see Table 3)– is what makes the Jasaw dance meaningful, since it is the day
when the Sun resumes its northernward movement on the horizon after having
remained almost still on its southernmost solstice position. Carolyn Tate (1992,
app.2), Susan Milbrath (1999:69) and Mathew Looper (2003) have already said
that the Jasaw Dance events were most probably carried out to confirm the tight
time-space linkage to the solstice day, as can be attested by the fact that every
temple Bird Jaguar IV built expressed a relationship with the summer and winter
solstice sunrise axes (Milbrath 1999:69). After apparent stillness nine days before
and nine days after the solstice on December 21, the very young, newborn Sun
(yaax k’in) may have had to be ritually helped to begin moving along the horizon
by means of the Jasaw Dance, on 19 Yaxk’in (December 30).
Table 3. Yaxchilán Jasaw Dance dates according to two correlations
Yaxchilán Stela
Long Count
Calendar
Round date
St. 16
9.15.4.16.11
St. 11
9.15.9.17.16
Lintel 33
7 Chuwen
19 Yaxk’in
12 Kib
19 Yaxk’in
5 Kimi
GMT
Correlation
(Gregorian)
June 27,
736
June 26,
741
June 25,
Patrick (2013a)
Correlation
(Gregorian)
December 30,
735
December 30,
740
December 30,
Jasaw Dance
Shield Jaguar
Shield Jaguar
and Bird Jaguar
Bird Jaguar
26 9.15.16.1.6
19 Yaxk’in
747
746
Third Test. Copán Stelae
In Copán Valley (14° 57’ N) there are seven stelae which seem to be in function of
Stela 23, one which holds a k’alk’in glyph meaning Sun-bound or Sun-binding
(Aldana 2001). Aldana (2001) tried to show that the k’alk’in glyph was there to
explain how the date on St. 2315 was somehow bound to a solstice or an equinox,
and that all the other dates might be also distributed in some solar logic. But after
a long analysis, he concluded that the GMT correlation must be several months
off, because it did not help him prove a hypothesis that seemed so easy to sustain
at first glance.
The Copán Valley LC dates were run with the alternate correlation proposed here.
Compared to those obtained with the GMT correlation there is a positive
difference of 195 days for year 648 A.D. (from St. 2) and of 197 days for year 652
A.D. (from St. 13). When the Winal dates are placed in sequence along a full haab
cycle and solstice and equinox dates are added there merges a pattern (Table 4 and
Figure 12).
Table 4. Copán stelae dates in order, and distance-days between them and in
function of solstices and equinoxes
Copán
monument
St. 23
St.10
St.13
9.11.0.0.0
St.3e
9.10.19.5.0
Gregorian dates according to
correlation (Patrick 2013a)
Dec. 12, 650
Dec. 19, 651
Dec. 21
Jan. 8, 648
Jan. 28, 652
March 21
March 22
March 29, 652
June 22
July 12, 651
St.3w
9.10.19.5.11
July 23, 651
St.12
9.10.19.6.0
August 1, 651
Sept. 22
Sept. 23
St. 2
St.19
Long Count
9.10.18.12.8
9.10.19.13.0
9.10.15.13.0
9.10.19.15.0
Calendar Round
8 Lamat 1 Yaxk’in
3 Ajaw 8 Yaxk’in
10 Yaxk’in
6 Ajaw 8 Mol
4 Ajaw 8 Ch’en
0 Keh
1 Keh
12 Ajaw 8 Keh
13 Pax
12 Ajaw 13 K’ayab
10 Chuwen 4
Kumk’u
6 Ajaw 13 Kumk’u
0 Zip
1 Zip
Distancedays
9
20
20
52
73
20
9
73
52
27 The Winal dates of Copán Valley stelae show a solar distribution in function of
solstices and equinoxes. Stela 23 provides date 1 Yaxk’in, 12 December, which
considered by experts as the first day the Sun slows down its trajectory along the
horizon.
Anthony Aveni (2001:252-54) in Skywatchers of Ancient Mexico, explained that
astronomers from Copán located the monuments to allow an observer to partition
the solar year into twenty-day (Winal) periods as an observational analog to the
partitions of the haab.
The Winal periods of the haab presented in this paper perfectly agree with Aveni’s
(2001:252-54) hypothetical segmentation of the year into Winal. As shown in
Table 2, Seating of Keh starts on March 21 and runs through to April 9,
integrating twenty days. From April 10 inclusive to April 29, there are twenty days
and also the thirteen Winal of the fixed Tzolk’in come to an end. One-hundred and
five days (divided into two groups of 52.5 days either side of summer solstice)
elapse until the beginning of the haab occurs again on August 13.
28 Figure 12. Distribution of dates from stelae in Copán, showing distance-days.
Stela 19 (January 28) is fifty-two days from vernal equinox on March 21 (Seating
of Keh), while St. 2 is one winal before (January 8), so from this date seventythree days elapse to March 22, also related to vernal equinox. Likewise, St. 12 is
fifty-two days from autumnal equinox on September 22 (Seating of Zip), while St.
3e is seventy-three days from the paired equinox date of September 23. Also, fiftytwo is a fifth of that tzolk’in, while seventy-three is the only possible dividend for
a 365-day cycle (73x5), as well as for the canonical synodic Venus cycle (Jesús
Galindo, personal communication).
Aveni (1980:254) proposed that “Copán seems to have been deliberately arranged
and oriented to reflect Maya calendric principles”. All in all, we are evidencing a
complex manner of integrating winal dates from stelae that consists of a
combination of spatial arrangement and calendar-time arrangement.
29 Fourth Test. Dresden Codex Base Dates of the Eclipse Table
Eric Thompson (1935:63), by using the GMT, finds that the base date on the
Eclipse Table (Dresden p.52a) concerns a new moon but not a node day –which
would produce an eclipse somewhere on the planet–. With the proposed
correlation (Patrick 2013a), date 9.16.4.10.8, 12 Lamat 1 Muwan is equal to May
21, 755 A.D.. The next date is 15 days away and the following one 15 days later is
on 9.16.4.11.18 3 Etz’nab 11 Pax = June 20, 755.
A three-day window ending on given dates forms part of the Eclipse Table, thus
telling the astronomer to consider such a time frame when expecting an eclipse.
Date 9.16.4.11.3 1 Ak’bal 16 Muwan happened on June 5, 755 A.D. (which is
June 1, 755 A.D. on the Julian calendar). The three-day window span in this case
goes from Julian calendar date May 30 through June 1. On May 30, 755 A.D.
(Julian) a moon eclipse was seen in Mayan territory (Figure 13).
Figure 13. Lunar eclipse within three day window till date 9.16.4.11.3, 1 Ak’bal 16
Muwan = June 5, 755 A.D., the first eclipse base date on Eclipse Table (Dresden, p.52a).
Note date in figure is Julian. Image courtesy of Fred Espenak, NASA/Goddard Space
Flight Center.
30 Fifteen days later, a solar eclipse occurred as predicted in the almanac, and it was
also seen from Mayan territory (Figure 14).
Figure 14. Solar eclipse within the three-day window till date 9.16.4.11.18, 3 Etz’nab 11
Pax = June 20, 755 A.D., the second eclipse base date recorded on the Eclipse Table
(Dresden p.52a). Note date in figure is Julian. Image courtesy of Fred Espenak,
NASA/Goddard Space Flight Center.
The full analysis of the Eclipse Table in the Dresden Codex (which shows that the
almanac works as a means to date not only these first eclipses but all those
occurring in the following thirty-three years) will be published promptly in the
Memory of the 2014 Meeting of Sociedad Internacional de Astronomía Cultural
(SIAC).
Fifth Test. Colonial Dates
This last section demonstrates how 11.16.0.0.0 13 Ajaw 8 Xul correlates to a date
in 1539. For this, I will refer to several historical and ethnographic dates which
have always been used (as dates for the two deaths in the Xiu lineage) plus some
very relevant ones from field diaries in the sixteen hundreds and the nineteen
hundreds.
31 “The 11.16.0.0.0 is the only possible correlation”
As the Bricker couple (2011:85) conclude, “if the 12 tun endings in the Chronicle
of Oxkutzcab are accepted as referring to the 12 consecutive years and if the
calendar-round dates (except that containing the month of Ceh) are correct when
translated to a common calendar, the “11.16” correlation is the only possible one.
The initial series date 11.16.0.0.0 occurred during the European year 1539 A.D..
This aspect of the Maya “correlation problem” has a unique solution.”
I totally agree with the line of argument of Bricker and Bricker (2011:85) as well
as that of Thompson and others who stand firmly for the 11.16 correlation. The
correlation here proposed produces the same year equivalence. However, when it
comes to the precise date on that year 1539, there is a slight difference (of some
days), which makes the whole difference.
The separation by days between the two dates obtained with respective
correlations can be explained by two factors. The first is that Landa’s correlation
1st Pop = July 16 (Julian) in Relación de las Cosas de Yucatan is taken for granted
by everyone –except for Teeple (1930:105), who said that according to his
calculations “12 Kan 2 Pop was July 16, 1553 […] or let us say within 20 or 30
days of that date”–.
There is a high chance that Landa may have juxtaposed the celebration of the
anniversary of Creation –i.e., the starting of the 13 Bak’tun cycle– with the
celebration of the starting of a new haab cycle. That Creation anniversary
happened on 8 Kumk’u every July 17 (Julian) according to the correlation here
sustained. The actual new haab on 2 Pop (1st Pop in the Mayapan notational
system) happened on August 5 (Julian). If the festivities to commemorate Creation
were as important as those for the new haab celebration, Landa could have easily
got confused and associated the celebration on the eve of July 17 (i.e. July 16) to
that of the renewing of the haab cycle. We must recall that this friar was by no
means a person with an open mind and heart in regard to Yucatec ‘religious’
affairs.
If celebrating the anniversary of Creation began on ‘vísperas’, meaning on the eve
of 8 Kumk’u, then the difference between 7 Kumk’u and 2 Pop becomes twenty
days. This day difference may vary by one day because of the time on which the
k’in cycle was starting and also depending on whether the year of record was leap
or not.
The second factor is that any correlation proposed by researchers –including the
GMT– uses a model that invariably makes a day name from the Tzolk’in and from
32 the haab that would otherwise fall on March 1, fall on February 29 (the leap day
of the European calendar). This produces a structural aberration. It is the officerelay of year-bearers what testifies the passage of the last quarter-day of the yearcycle, a ritual that takes place within the more complex ceremony related to the
falling and raising of the Bakab. This time-keeping choreography ensures that the
haab-bearers measure exact tropical years and keep their k’in aligned to
corresponding solar days. Interfering with this time-keeping system is what has
produced such a distorted concept of the Long Count.
The inability to comprehend (or unwillingness to respect) the role of the year –
bearers has produced that, ever since the early fifteen hundreds there was an
unwritten but mandatory provision for time-keeping priests, including those from
Guatemalan highlands. The provision arrived with the very first friars who brought
with them the European calendars. It was a very subtle mandate: to simply include
February 29 –a day lived by all Christians whose calendric day-cycle always
begins at midnight– in their time-keeping and ceremonies. Landa’s correlation was
certainly passed on to friars throughout the region. Evidence of this are the Chilam
Balam books that were copying the equation July 16 = 1st Pop with no question.
Given the penurious conditions of timekeepers vis a vis the friars operating in their
territories, the artificial calendric equivalence must have been assimilated as a
political means to survive. The apparently harmless procedure of naming February
29 became customary, reinforced in the remotest areas once printed copies of the
Bristol Almanac came in with the merchants in early eighteen hundreds.
Because using the calendar brought from Europe to keep track of Mayan days
seems so natural, there is the common illusion that everyone is preserving the
model of continuity: scholars and local traditional people are all on the same page
because of the seemingly harmonious relation Tzolk’in-Gregorian calendar.
Both factors just mentioned mean that:
1) by assuming the July 16 = 1st Pop equation is correct, a twenty or twentyone day difference was immediately installed on the very anchoring point
of the GMT correlation.
2) by giving Tzolk’in and haab day names to every February 29, the distance
in days from the anchoring point grew bigger along the timeline (with
positive integers towards the zero point date and negative integers towards
the 13 Bak’tun date).
Let us take a look at the two correlations here discussed. For 11.16.0.0.0 13 Ajaw
8 (7th) Xul the correlation proposed (Patrick 2013a) relates it to November 29,
1539. The Bricker couple (2011:91) conclude, after some cross-analysis, that such
date fell on November 13, 1539 although the GMT 584,283 gives one day before.
33 Here there is a difference of sixteen or seventeen days between correlations
compared.
Dates ‘2 Pop’ (Mayapan 1st Pop) dates are placed a day earlier than July 16 (Julian
calendar) every four years after 1552. By the same logic, ‘2 Pop’ dates are placed
a day later than July 16 (Julian calendar) every four years before 1552 going down
the timeline. So, for 1539, 2 Pop is happening on July 19 according to Bricker and
Miram (2002:69). In contrast, in the correlation proposed here, 2 Pop is always
linked to August 5 (Julian) or August 15 (Gregorian).
As years went by since the mid-fifteen hundreds, the accumulation of named leap
days increased, producing a longer distance between the original position of
Tzolk’in and haab’ dates and the calculated positions by Mayanists. By 1553,
almost fourteen years had elapsed since 1539, which explains why named leap
days increased from sixteen or seventy to twenty or twenty-one.
By the turn of the seventeenth century, the difference is such that it becomes
problematic for Mayanists: Thompson (1935:59) realized there was something in
his formula that was not quite right after he learned about a historical record
“which couldn’t have been tampered with” made by two friars, Padres Orbita y
Fuensalida. The record speaks of the turning of a K’atun cycle. He wrote: “the
fathers reached Tipu on their return from Tayasal five days after leaving the lake.
Their arrival at Tipu was at the beginning of November, so the memorable
conversation must have taken place near the end of October” of 1618. During that
conversation they were told that K’atun 3 Ahau had just commenced.
With the correlation proposed in this paper, the beginning of K’atun 3 Ahau was
on 12.0.0.0.0 5 Ajaw 13 Sotz’, October 25, 1618 and its closing was on 12.1.0.0.0
3 Ajaw 18 K’ayab, July 17, 1638.16 As can be seen, there is a perfect coincidence
with the historical record. On the other side, the 11.16.0.0.0 correlation proposed
by Thompson (1935) 584,285 calculates that K’atun 3 Ahau began on September
18, 1618, which is evidently far earlier than the date which Thompson himself
worked out from the entry in the diary, that near the end of October of 1618.
Between 1553 and 1618 sixty-five years had elapsed, which means sixteen leap
days had gone by. When adding these to the twenty-one-day difference existing in
1553, we obtain the thirty-seven-day difference.
Between 1553 and 1977 (the year Tedlock (1992) made a registration in a K’iche’speaking community in Momostenango) there are 424 years. The amount of leap
days in that interval is one hundred and three (424/4 = 106, from which three days
related to centuries 1700, 1800 and 1900 are excluded). Adding the twenty-oneday difference existing in 1553, the difference amounts to one hundred and
34 twenty-four days. This means that the 4 Ik’ reported by Tedlock (1992:103, Table
4) for K’iche’ people for March 2, 1977 would have actually occurred –if they had
had continued using the original Mayan calendar system– a hundred and twentyfour days later, on July 4, 1977. If we consult the correlation here proposed, 4 Ik’
5 K’ayab happened precisely on July 4, 1977.
These few examples show that the accumulation of leap days is the central
problem that was posed by the apparently inoffensive coming together of the
Tzolk’in and the Gregorian calendar. In the remaining space of this paper the
reader will be shown how one date on the haab calendar (11 Zip), which can be
drawn from three historical events through a period of almost eighty years,
produces a fixed solar date that is recorded by an impeccable historical record of
1618, where the GMT correlation cannot. The slippage of dates produced by the
GMT correlation as it calculates dates that move further away from its anchor is
neatly laid out in Table 6 for a total of seventeen dates that any calendric specialist
may demand.
Death of Nah Pot Xiu and death of the Xiu ambassadors
Bricker and Bricker (2011:85) clarify the confusion between two historical events.
Two elements produced the confusion: the first, that the people involved were of
the Xiu family; the second, that both events happened in month Zip. The intention
here is to show how, while on the correlation proposed month Zip remains fixed
on one solar date, in the GMT correlation it lags, so nine years after the first event
there is an apparent slip of two days.
Regarding the first event, the First Chronicle of the Book of Chilam Balam of
Chumayel states (Gordon 1913:76, cited by) as follows:
XIII oxlahun ahau cimci ah pula
XIII 13 Ahau was when the rain-bringer died.
Uac pel u binel u xocol haab ti lakin cuchie
For six years the count of the years was going in the East still.
Chronicle of Oxkutzkab has complementary information. The transcription and
translation from Bricker and Bricker (2011:79) is as follows:
1537 años
The year 1537
vaxacil cavac tu hunt e pop
8 Cauac was on the first of Pop
cincio [b ah] pul haob te otzmale When the rain-bringers died there at Otzmal
hek laob lae
Here they are:
ah sun tutul xiu
Ah Dzun Tutul Xiu
(4 more names)
ha…. Vinicob te mane
… they were the men there at Mani
35 ah pul haob
tu chiche ytza cuchi
he u puz[o]be
na hau vech
na pot covoh
tu lahun hi ςip
lahca ahau hi
he tun tu ca te yaxkine
bay bin kahebal
the rain-bringers
at Chichen Itza then.
here are the ones who escaped:
Nahau Uech
And Napot Couoh
It would have been on the 10th of Zip
In 12 Ahau
Here is the tun on the second of Yaxkin
Thus it will be remembered
From these passages we can identify three time-keeping cycles: the thirteen-haab
cycle, the haab cycle based on the 1st of Pop (2 Pop) and the Tun cycle based on
the Long Count system. The Tun dates appearing on the Chronicle of Oxkutzcab
are coherent with those of the LC system.
The thirteen-year cycle and the haab cycle based on 1st of Pop are combined, as
presented on Table 5. Here, the thirteen-haab’ cycle to the east started on 1529
with 1 Kan 2 Pop (Table 5a), so by year 1536 seven years had gone by and six
remained (including 1536), which explains the statement in the First Chronicle of
the Book of Chilam Balam cited above.17
Table 5a. Year-bearers of thirteen-year cycles to the east (top) and to the
north (bottom)
East Thirteen-year Cycle starting with 1 Kan
1
2
3
4
5
Kan
Muluc Ix
Kawak
Kan
1
2
3
4
5
1529
1530
1531 1532
1533
6
Muluc
6
1534
7
Ix
7
1535
8
Kawak
8
1536
9
Kan
9
1537
10
Muluc
10
1538
11
Ix
11
1539
12
Kawak
12
1540
13
Kan
13
1541
North Thirteen-year Cycle starting with 1 Muluc
1
2
3
4
5
6
Muluc
Kawak
Kan
Muluc Ix
Ix
7
Kawak
8
Kan
9
Muluc
10
Ix
11
Kawak
12
Kan
13
Muluc
1542
1548
1549
1550
‘51
1552
‘53
1554
All year-bearers are linked to 2 Pop.
‘43
1544
1545
1546
‘47
All year-bearers are linked to 2 Pop.
Since there is a reference to 10th of Zip on the Chronicle of Oxkutzkab, Table 5b
was produced. In the Mayapan system used there, 1st Pop refers to 2 Pop, so 10th
Zip refers to 11 Zip. Given that for year 1536 the haab started on 8 Kawak (Table
5a, in bold) we calculate that on 11 Zip it was 5 Lamat (in bold as 11/5/L in Table
5b), though only the haab component (10th of Zip) is mentioned on the Chronicle,
which is fair enough. The Julian calendar date is September 23, 1536 (Julian).
36 Contrast this with the date obtained with the GMT 584,283 correlation of
September 6, 1536 (Julian).
Table 5b. Month Zip on 1536 and on 1545 for comparison
Zip on 1536 (for year starting on 8 Kawak 2 Pop = August 5, 1536, Julian)
S
7
K
1
8
Et
2
9
Ka
3
10
Aj
4
11
Im
12
13
14
15 16
5
12
Ik’
6
13
Ak
17
18
7
1
K’
8
2
Ch
9
3
Ki
10
4
M
11
5
L
12
6
M
13
7
O
14
8
Ch
15
9
Eb
16
10
B
17
11
Ix
18
12
M
19
13
K
24
25
26
27
28
29
30
1
September (Julian calendar)
19
20
21
22
23
Zip on 1545 (for year starting on 4 K’an 2 Pop = August 5, 1545, Julian)
S
3
Ik
1
4
A
2
5
K’
3
6
Ch
4
7
K
12
13
14
15 16
5
8
M
6
9
La
17
18
7
10
M
8
11
O
9
12
C
10
13
Eb
11
1
Be
12
2
Ix
13
3
M
14
4
K
15
5
Ka
16
6
Et
17
7
Ka
18
8
Aj
19
9
I
25
26
27
28
29
30
1
September (Julian Calendar)
19
20 21
22
23
24
First row: S= Seating of; numbers: coefficients of Zip. Second row: coefficients of day
name on the third row, where initials stand for first letters of names of the Tzolk’in days.
Note how day 2 Zip holds same Tzolk’in name (Kawak) as day 2 Pop, which is expected
since Tzolk’in k’in names recycle every twenty days. Fourth row: coefficients of
September on the Julian Calendar. Dates are according to proposed correlation (Patrick
2013a).
Bricker and Bricker (2011:79-81) make a detailed account of the circumstances of
the death of Nah Pot Xiu and demonstrate that year 1536 is the correct reference to
the death of the rainmakers in p.66 of Xiu Chronicles. They explain that the event
mentioned in the Books of Chilam Balam of Tizimin (n.d.: fol. 19r) and Mani
(Códice Pérez n.d.:136; both references by Bricker and Bricker 2011:81) involves
an embassy of other Xiu leaders who went to Sotuta between 1540 and 1546 to
urge the Cocom leader to submit to the Spaniards. In that particular case they were
ambushed on day 9 Imix 18th Zip (19 Zip) on a year 4 Kan 2 Pop. This date also
happens on month Zip, and thanks to the Tzolk’in dates we can calculate that it
happened nine years after 1536. Months Zip of 1536 and 1545 are shown
alongside for comparison in Table 5b, which shows several things: that the
ambush happened on October 1, 1545 (Julian); that date 11 Zip on 1545 correlates
to September 23 just like it did on 1536; and that the interval for Zip is fixed
(between September 12 and October 1, Julian dates), something that the GMT
correlation cannot offer.
37 The correlation proposed (Patrick 2013a) is near to perfect synchronicity with the
11.16.0.0.0 correlation that most Mayanists agree on for year 1539. What needs to
be carefully discerned is that the GMT correlation produces dates which, as years
advance, become distant from the actual events, which for historians and
astronomers, is problematic. Let us take 11 Zip, for which there are three different
events on three separate years. Two were just analysed: 5 Lamat 11 Zip when
Napot Xiu was killed in 1536; and 1 Ben 11 Zip, eight days before the Xiu
embassy was ambushed in 1545. The third is 9 Etz’nab 11 Zip, twenty-two days
before 5 Ahau K’atun was completed, as reported by the Itzá (marked in grey on
Table 6).
The reason why the Patrick correlation casts the same date (September 23 Julian,
i.e., October 3 Gregorian) for 11 Zip regardless of the year, is the following: since
oriented haabs reckon time according to the office-relay of year-bearers within a
Bak’tun cycle, they immediately measure the 0.2423 k’in to stay aligned with the
solar year. On the other hand, dates obtained with the GMT correlation, which
inserts leap days in the reckoning process, spread along a wide range of time. The
earliest 11 Zip date is September 16 (Gregorian) while the next date, which is nine
years later, is two days less because of two leap days in between (February 29 of
1540 and 1544). The next 11 Zip happens, according to the GMT correlation, on
August 27, 1618 (Gregorian). Time has apparently shrunk on the haab k’in record,
for 11 Zip is now eighteen days earlier than it was in 1545! The leap days that
were needlessly named by the Tzolk’in and the haab during those sixty-three years
account for this (Table 6).
Date 11 Zip of year 1618 was twenty-two days earlier than 13 Sotz’ (from 5 Ahau
13 Sotz’, a very important date –also known as 5 Ahau K’atun– because a 12
Bak’tun cycle was completed). Correlation GMT gives September 18, 1618 for
that 5 Ahau 13 Sotz’. This date is not compatible with the ethnographic accounting
mentioned above. The Itzá priest in Tayasal had maintained his people in isolation
from the Christian preachers, which means that he had obviously been keeping
track of time in the traditional way. Thompson (1935:59) knew that the Itzá priest
was right when he told fathers Fuensalida and Orbita that K’atun 3 Ahau had just
started running its course a few days ago. The beginning of K’atun 3 Ahau on
12.0.0.0.0 5 Ajaw 13 Sotz’, had been October 25, 1618 and its closing would be
on 12.1.0.0.0 3 Ajaw 18 K’ayab, July 17, 1638. Twenty-two days earlier than
October 25 is indeed October 3, the constant equivalent to day for 11 Zip in the
correlation proposed. This is yet another strong proof of its internal consistence.
38 Table 6. Distance between dates spanning over five thousand years obtained
with two compared correlations
Difference
(days)
LC
Calendar Round Date
GMT correlation
(Gregorian date)
Patrick correlation
(Gregorian date) Date description
-133
13.0.0.0.0
4 Ajaw 3 Kank’in
21 Dec. 2012
3 May 2013
Completion of 13 Bak'tun
-124
12.18.3.12.2
4 Ik’ 5 Kayab
2 March 1977
4 July 1977
K’iche’ date reported by Tedlock
-37
12.0.0.0.0
5 Ajaw 13 Sotz’
18 Sept. 1618
25 Oct. 1618
Itzá of Tayasal refers to 3 Ajaw
-37
11.19.19.16.18
9 Etz’nab 11 Zip
27 Aug. 1618
3 Oct. 1618
Twenty-two days before 3 Ajaw
-21
11.16.13.16.4
12 Kan 2 Pop
25 Jul. 1553
15 Aug. 1553
Landa refers new year festivity
-19
11.16.5.16.13
1 Ben 11 Zip
14 Sept. 1545
3 Oct 1545
-17
11.16.0.0.0
13 Ajaw 8 Xul
12 Nov. 1539
29 Nov. 1539
-17
11.15.16.14.8
5 Lamat 11 Zip
16 Sept. 1536
3 Oct. 1536
-17
11.15.16.11.19
8 Kawak 2 Pop
29 Jul. 1536
15 Aug. 1536
New haab cycle (Mayapan)
-17
11.15.16.11.17
6 Kaban 0 Pop
27 Jul. 1536
13 Aug. 1536
New haab cycle (Classic style)
0
11.12.3.11.17
12 Kaban 0 Pop
13 Aug. 1464 A.D.
13 Aug. 1464
165
9.17.17.14.8
12 Lamat 16 Yax
8 Aug. 788 A.D.
25 Feb. 788
173
9.16.4.10.8
12 Lamat 1 Muwan
10 Nov. 755 A.D.
21 May. 755
Correlations match
End of 11,960 k’in cycle on
Eclipse Table
Start of 11,960 k’in cycle on
Eclipse Table
279
8.14.3.1.12
1 Eb 0 Yaxk’in
15 Sept. 320 A.D.
11 Dec. 319
Leiden’s Plaque
364
7.16.3.0.0
5 Ajaw 3 Sotz’
14 Oct. 36 BC
15 Oct. 37 BC
Chiapa de Corzo
810
3.0.0.0.0
1 Ajaw 8 Yax
7 May 1931 BC
17 Feb. 1933 BC
1111
0.0.0.0.0
4 Ajaw 8 Kumk'u
11 Aug. 3114 BC
Eight days before ambush of Xiu
Chronicle of Oxkutzcab p.66
Rainmaker Napot Xiu is killed
27 July 3117 BC Era Date
Figure 15 shows how the distance between the dates obtained with each of the
compared correlations has changed over time. The first date of the 13 Bak’tun
cycle was 0.0.0.0.0, 4 Ajaw 8 Kumk’u. Correlation GMT converts it to August 11,
3114 BC. Correlation by Patrick (2013a) converts it to July 27, 3117 BC. This
produces a day difference of 1111 days, which is shown in the graph on Figure 15
as the maximum distance between dates. As Bak’tuns go by, the distance becomes
shorter because GMT is shrinking the time-length of the Long Count. Both
correlations coincide on August 13, 1464, on 12 Kaban 0 Pop, but this coincidence
is produced artificially. Had Landa not committed the mistake of misinterpreting
anniversary celebrations (of Creation versus beginning of haab), the coincidence
would have happened on 1553.
39 Figure 15. Graph showing distance between dates obtained with GMT 584,283
correlation and Patrick (2013a) correlation.
All in all, the GMT 584,283 correlation and all the other ones based on the JDN
system have provided a conversion system that shrinks the Long Count time cycle.
Within the 13 Bak’tun cycle it is forced to become 1243 days shorter than it
actually is. Within cycles like that appearing on the Eclipse table (33 years long)
dates get shrunk by 8 days when comparing the starting date with the ending date.
This of course makes it terribly difficult for archaeoastronomers to obtain any
intelligible results. There is no way someone figure out whether Mayan almanacs
are astronomical by using the data produced by those correlations. No wonder Eric
Thompson and many others said that LC dates on the tables are wrong and that
among the Maya there was no real astronomy taking place.
Conclusions
The fundamental contribution of this paper is that it proves that Mesoamerican
cultures developed Astronomy as a science, becoming experts in specific fields
such as eclipse events and recurrence of combined synodic cycles; they did not
merely practice astrology as Thompson (1935) and others have argued.
40 There was a profound understanding of time-space order among Mesoamerican
cultures, who designed devices to keep precise tracks of cyclic events. The
instruments they produced were designed as a means to live in synchrony with all
agents participating in measuring time-space at different scales. These were
fundamentally the Moon, the Sun, Venus, Mars, the Milky Way and the Pleiades.
The need to live in synchrony emerged from a belief system that acknowledged
their roles and their periodic abilities to affect weathers, winds, waters, rocks and
in general all entities of the world around them, regardless their sizes and their
degrees of materialization.
The instruments had to work with absolute precision, thus useful cycle after cycle
so to measure the spectrum of time-space –for which they had been originally
designed– over and over. Such instruments were of two kinds: the observational
ones, such as standing stones, mountain peaks or creeks, pyramids, monuments
and chambers (to observe rising or setting suns that happened in specific time
intervals, to observe light-shadow phenomena and to measure zenith passages) and
also devices to measure the cyclic transition of basic units of time-space within
larger cycles of time-space, like almanacs and calendars.
The principle of order and synchrony required that the 260 and the 360+5
calendars started in function of the same event: the 15°N zenith passage on the
equivalent Gregorian calendar date August 13. Once proven to be precise and
long-lasting, these calendars were preserved as the most exquisite synthesis of
humankind’s comprehension of its existence as a unit in the whole. They were
applied in an ample social field with a complex combination of astronomical,
religious, political and economic interests in the quest for cultural transcendence.
The correlation explained here since its first publications (Patrick 2013a, 2013b)
opens a new window of opportunities for Mayanist colleagues to revisit
governors’ strategies and narratives in light of the actual time-framework and the
celestial bodies in play. Until now correlations had offered weak proofs of real,
timely interaction between ceremonies and celestial bodies.
The way by which the haab measures time can be described as a choreography. It
is a precise dance, whereby the haab measures de facto time and then experiences
a transitioning time while its year-bearer relays office to the next year-bearer. This
happens while the Pawatuns are all standing to keep the world in balance, a
condition that is periodically lost due to increasing stress to the point of falling –
which is taken as favorable because it releases stress and calibrates the year
measurement. De facto time and transitioning-ritual time equally contribute in
measuring cycles, but the nature of the first kind enables its explicit reckoning
scheme while the nature of the second considers an implicit account. This is
coherent with Mesoamerican cosmovision where humans and deities alike
interplay in the world’s lattice.
41 Acknowledgements
I am thankful to Andrew Finegold for a encouraging me to write this paper and for
his review of the first manuscript, which Anna Blume has also reviewed. This
piece would not be possible without the fellowship from Union Theological
Seminary (2015-2016).
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45 1
Unless otherwise noted, ‘GMT correlation’ refers to correlation constant 584,283.
The historical record is one “which clearly has not been tampered with or altered by copyists
(...) a Katun 3 Ahau was [just beginning] running its course when Fathers Orbita and Fuensalida
reached Tayasal late in October of 1618” (Thompson 1935:59). Unfortunately, the GMT
correlation produces a date in mid September instead. This noticeable mismatch is crucial in
explaining the underlying problem of all correlation constants; in fact, it is so important that it
will be dealt with in a subsequent section of this paper on the testing of Colonial dates.
3
The Julian Day number system enables the consecutive numbering of days counting from midday to mid-day since January 1, 4713 BC. on the Julian period, a system used until today by
astronomers to refer to astronomical events. It was conceived by Joseph Justus Scaliger (15401609), a classicist and literary French son of Julius Caesar Scaliger, who combined the Metonic
19-year cycle with a 28-year cycle (in which the date of the solar year of the Julian calendar
occurs on the same day of the week, i.e., 4x7) and the 15-year cycle of the Indiction fiscal period,
so as to fit all of these small periods into a big period called the Julian period of 7,980 years. He
then worked out when the starting point of the three cycles had coincided, and it turned out to be
January 1, 4713 BC. He called it Julian cycle after his father. This system must not be confused
with the Julian Calendar which was set in place on year 46 before current era by Julius Caesar of
Rome when advised by Sosigenes, an astronomer from Alexandria.
4
The Julian Calendar installed by Julius Caesar consisted of making the year 365.25 days long by
having eleven months of 30 or 31 days plus February of 28 days, and inserting a bissextile day
every four years (February 29). We now know the length of the year is currently 365.2422 so this
requires including February 29 in century years only if they are multiple of 400. Hence the reform
from the Julian to the Gregorian calendars which happened on October 4, 1582 as promulgated by
Pope Gregory XIII, producing a Gregorian date of October 14, 1582.
5
The author has proposed this elsewhere (Patrick, 2013a). The calculation is as follows: 11
minutes excess ritual time at the turn of every haab-cycle (where the haab-cycle measures 365
k’in plus 0.25 k’in of ritual time) produces 72 hours excess ritual time after 394.52 years have
gone by in a Bak’tun cycle. (11x394.52 = 4,339.726; 4,339.726 / 60 = 72.32 hours = 3 k’in of
ritual time). So the excess ritual time can be cancelled out when the year-bearer rotation is
suspended due to the falling of a world-bearer, i.e. a Pawatun or Bakab.
6
Bolles, David (2012). Combined Mayan-Spanish and Spanish-Mayan Vocabularies. Code letters
stand for: JPP Pío Pérez, Diccionario de la Lengua Maya, SFM Diccionario de San Francisco,
Mayan-Spanish, DMM Combined Solana - Motul II - S.F. Spanish Mayan, MTM Motul MayanSpanish (Calepino Maya de Motul), NEM Barrera’s Nomenclatura Etnobotánica Maya, VNS
Viena Spanish-Mayan. Availabe online in Famsi website, obtained in May 2015.
7
There is 72 hours excess time because each tropical year is actually 365 days and one-quarter
day minus 11 minutes long, whereas the year-bearers take office one-quarter day ahead from the
previous year-bearer.
8
The thirteen-haab cycle of year-bearers is derived from the New Year pages in Dresden Codex
pp. 25a-28a, where bundles of thirteen years Eb, Kaban, Ik’ and Manik are shown.
9
Through the rest of the paper, the terms ‘oriented day’ and k’in are used as equivalent and
interchangeable.
10
The reckoning system by groups of twenty days (Winals) along a 360+5 day cycle produces the
repetition of eighteen Winals from Ik’ (inclusive) through Ik’ (day 361) and the reckoning of the
following four days after Ik’: Ak’bal, Kan, Chicchan, Kimi, so accomplishing 365 days in total.
The following day, Manik, becomes the first day of the new 360+5 cycle. After repeating this
four times, the cycle is back to Ik’. The four k’in that participate in the accounting of four
consecutive years are Ik’, Manik, Eb’ and Kaban.
2
46 11 This is the result of 5128.76712 x 365.2423 (the average value in days, of tropical years
between BC 2000 and 2000 AD, after Meeus and Savoie, 1992).
12
Starry Night Bundle Edition 2.1. Copyright Sienna Software.
13 All dates in this paper are proleptic Gregorian (before October 4 1582) or Gregorian (after
October 14, 1582) unless otherwise stated, in which case (Julian) meaning Julian calendar will
appear after the date.
14
Erik Velazquez, personal communication, November, 2010.
15
The Long Count combination for Stela 23 proposed by Sylvanus Morley (1920), who
participated in the archaeological Project in Copan in 1910, is used here.
16
Note how the closing date (3 Ajaw) is the one that gives the name to the K’atun cycle.
17
Bricker and Bricker (2011:86) clarify: “The statement [about the massacre involving the
rainmakers and Napot Xiu] in the Book of Chilam Balam of Chumayel is a statement about the
placement of 1536 in the calendar round, not (in the twenty-Tun-round-cycle of) the katun.”
47