MesoAmerican Calendars

maya calendar

Geraldine Patrick Encina presented her paper The century‐old error. On how formula ‘365 k’in on the Long Count = 1 tropical year’ solves ‘the correlation problem’ and recovers the astronomical sense of the great cycle 13 Bak’tun

as part of a lecture series sponsored by the Alfonso Ortiz Center for Intercultural Studies and El Centro de la Raza in collaboration with the Indigenous Nations Library Program with the support of Student Affairs.

geraldine patrick encinaAbstract
The century‐old ‘Correlation Problem’ has a solution: the Ha’ab –the Maya calendar that has been
interpreted as an imprecise or vague instrument to measure a tropical year– in fact measures
‘explicit time’ within the tropical year, which is exactly 365 days long. I propose that there are two
stages to solve (1) the additional quarter of a day of each year and (2) the excess 11 minutes from
that quarter day. The first stage of the solution merges from the fact that the Ha’ab has four
different year bearers. Each one is referring to one particular world direction (east, north, west,
south –in that order) but more importantly, the ‘yearly horizontal plane’ conflates into a ‘daily
vertical plane’ holding four moments of the day (dawn, noon, sunset, midnight ‐respectively). This
model is identical to Flores’s (1994) in one sense and radically different in another. He proposed
that the yearly change in orientation of the year‐bearer implicitly represented the elapse of ¼ day.
I agree to this. However, he took for granted that this quarter‐day was added up after four years,
thus representing a leap day within the Long Count. However, I have gone a step further by taking
into account a typical Maya ceremony where the year is personified by Maximón (in Santiago
Atitlán, Guatemala) whose ‘bearing’ one year and then the next one, implies a ritual movement
from one Cantón (there are four spatial sections in Atitlán, each one referred to one world
direction) to the next. This particular ritual allowed me to conceive how the ¼ time‐space
conceptuation belongs to the ‘implicit’ realm. Hence, my hypothesis was that the ¼ day after a
365‐day is not considered in the Long Count (LC). The second stage of the solution –also in the
ritual dimension– keeps the Ha’ab aligned to solar dates despite the excess 11 minutes in the
referred ‘¼ day’. It provides an interesting explanation to the ‘falling of the Bakab’ narrations in
several of the Chilam Balam books.
This new approach provides a new formula to calculate any LC expression: it must be divided by
365 in order to obtain the total amount of tropical years (ty). Regarding 13 Bak’tun, 1872000
k’inoob represent 5,128 ty and 280 days. It is within this time range –and not within 5,125 ty and
133 days –as all other LC correlations assume–, that an exact number of Venus and Moon cycles
elapse. This provides a broad understanding of date 12 Lamat at the beginning of the Eclipse Table
(p.52a on Dresden Codex) in terms of its astronomical implications, since a fundamental event
happened eight days after 13.0.0.0.0, 4 Ajaw 8 K’umk’u (the Olmec‐Maya ‘Creation of 13 Bak’tun
Era’): the first rising of both vespertine Venus and vespertine Moon (it was their first appearance
in the night sky).
Since an exact number of Venus and Moon cycles elapses within 5,128 tropical years and 280 days
(the 13 Bak’tun period, as proposed here), then on 4 Ajaw 3 K’ank’in, at the closing of 13 Bak’tun,
an astronomic event with the same characteristics as the one that inaugurated the ‘Creation’ will
occur, the date being May 3, 2013. Calendric and astronomic demonstrations turn down
Goodman‐Martínez‐Thompson Correlation and the concept of ‘vague year’.
I would like to share with knowledgeable colleagues how I designed my research and particularly, I
would like to show the high degree of precision with which the correlation has responded to the
tests I have submitted it to –in contrast with the GMT Correlation.
Furthermore, the epistemic implications of these results –in terms of how researchers have
interpreted Mesoamerican science as a pseudoscience, questioning for instance, whether
astronomical tables of the Maya and other Mesoamerican cultures are useful at all, and how
precise or vague they were their calculations–, is another issue that I would like to discuss with
interested researchers at the University of New Mexico.

Geraldine Patrick Encina, Doctor in Social Science mention in Ethnoecology. Postdoctoral
research at CIECO‐UNAM, 2011‐2012.
Adscription: 2012 onwards: Universidad Autónoma Metropolitana, Unidad Lerma.
2007‐2012: Universidad Intercultural del Estado de México

SPANISH VERSION
Título: El error del siglo, o de cómo la fórmula ‘365 k’in en Cuenta Larga = 1 año trópico’ resuelve
el ‘problema de la correlación’ y recupera el sentido astronómico del gran ciclo 13 Bak’tun
Resumen
El ‘Problema de la Correlación’ –de más de un siglo– tiene solución: el Ha’ab mide tiempo explícito
en un año trópico (es decir, 365 días) mientras que, de un Ha’ab al siguiente, el cambio de
orientación del cargador representa el lapso de ¼ día transcurrido de manera implícita. El ritual de
Maximón en Santiago Atitlán, Guatemala –trasladándolo de un cantón al siguiente cada año–
permite concebir cómo el ¼ tiempo‐espacio está implícito. Asimismo, aquel ¼ día no debe
contabilizarse en la Cuenta Larga (CL). Otro mecanismo, también en el ámbito ritual, mantiene al
Ha’ab alineado a las fechas solares a pesar del exceso de 11 minutos en el referido ‘¼ día’. Así,
cualquier expresión en CL debe dividirse por 365 para calcular los años trópicos (at) transcurridos.
En el caso de 13 Bak’tun, 1872000 k’inoob representan 5,128 at más 280 días. Es en este lapso –y
no en 5,125 at y 133 días, como asumen todas las correlaciones de CL– que se obtiene una
cantidad exacta de ciclos lunares y venusinos, lo que justifica el énfasis, al inicio de la Tabla de
Eclipses, en la fecha 12 Lamat asociada a las primeras salidas vespertinas de Venus y de la Luna
ocho días después de 13.0.0.0.0, 4 Ajaw 8 K’umk’u. En 4 Ajaw 3 K’ank’in, al cierre de 13 Bak’tun,
un evento astronómico de las mismas características que en la ‘Creación’, acontecerá el 3 de mayo
de 2013. Comprobaciones calendárico‐astronómicas desmienten la Correlación Goodman‐
Martínez‐Thompson y el concepto de ‘año vago’.

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