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). References Aldana, Gerardo 2001 “K’in in the hieroglyphic record: implications of a pattern of dates at Copán, Honduras”. Mesoweb www.mesoweb.com/features/aldana/Implications.pdf Aveni, Anthony F. 2001 Skywatchers of Ancient Mexico. Revised and updated edition of 1980. University of Texas Press, Austin. Bolles, David 1990 The Mayan Calendar, The Solar-Agricultural Year and Correlation Questions. www.famsi.org/research/bolles/calendar/MayaCalendar.pdf . 2001 Postconquest Mayan Literature. Report to the Foundation for the Advancement of Mesoamerican Studies. www.famsi.org/research/bolles/PostConquestMayanLit.pdf . 2012 Combined Mayan-Spanish and Spanish-Mayan vocabularies. www.famsi.org/mayawriting/dictionary.htm . Bricker, Victoria R. and Helga-Maria Miram, translators and annotators 2002 An encounter of two worlds: The Book of Chilam Balam of Kaua. Tulane University, Middle American Research Institute, Publications, 68. Middle American Research Institute, New Orleans. Bricker, Harvey and Victoria Bricker 2011 Astronomy in the Maya Codices. Memoirs of the American Philosophical Society Held at Philadelphia for Promoting Useful Knowledge, Vol. 265. American Philosophical Society, Canada. Diccionario JPP Gossen, Gary 42 1974 Los chamulas en el mundo del Sol. Gronemeyer, Sven and Barbara MacLeod 2010 “What could happen in 2012? A re-analysis of the 13-Bak’tun prophecy on Tortuguero Monument 6.” Wayeb notes 34:1-68. Hopkins, Nicholas A. And J. Kathryn Josserand 2000 “Directions and Partitions in Maya World View.” Florida State University, Florida. Unpublished. Kelley, David Humiston 1965 “Birth of the Gods at Palenque.” In Estudios de Cultura Maya, Tomo 5, pp. 93-134. UNAM, México, D.F. 1976 Deciphering the Maya Script. University of Texas Press, Austin and London. 1983 “The Maya Calendar Correlation Problem”, Leventhal, Richard and Alan Kolata, Civilization in the Ancient Americas. University of New Mexico Press and Peabody Museum of Archaeology and Ethnology, Cambridge, Massachusetts. Justeson, John S. 1986 “Ancient Maya Ethnoastronomy: An Overview of the Hieroglyphic sources.” In World archaeoastronomy: Selected Papers from the 2nd Oxford International Conference on Archaeoastronomy held in Merida, Yucatan, Mexico, January 13-17, edited by Anthony Aveni, pp. 76-129. University Press Cambridge, Cambridge, Massachusetts. Landa, Fray Diego de 1978 Relación de las Cosas de Yucatán. Porrúa, México. Looper, Matthew G. 2003 “The Meaning of the Maya Flapstaff Dance” Glyph Dwellers, Report 17. Department of Native American Studies, University of California, Davis. Lounsbury, Floyd 1978 “Maya Numeration, Computation and Calendrical Astronomy”. In Gillispie, Charles Coulson (ed.) Dictionary of Scientific Biography, 15:759-818. Charles Scribner’s Sons, New York. Milbrath, Susan 43 1999 Star Gods of the Maya. Astronomy in art, folklore and calendars. University of Texas Press, Austin. Morley, Sylvanus 1920 “The inscriptions at Copan”, Carnegie Institution Publication 219, pp. 25973. Carnegie Institution, Washington, D.C. Patrick, Geraldine 2013a “Long Count in Function of the Haab’ and its Venus-Moon Relation. Application in Chichén-Itzá.” In Revista Digital Universitaria. Vol. 5 Num. 5. http://www.revista.unam.mx/vol.14/num5/art05/ . 2013b “La pirámide de la serpiente emplumada, Teotihuacan. Su relación con Venus vespertino, las lluvias y el cierre de 13 Bak’tun”. Tlaloc ¿qué? Año 3, No.12. Portilla, Miguel León 1994 Tiempo y realidad en el pensamiento maya. Ensayo de acercamiento. Instituto de Investigaciones Históricas. Serie de Culturas Mesoamericanas. Universidad Nacional Autónoma de México, México. Prem, Haans J. 2008 Manual de la Antigua Cronología Mexicana, Miguel Angel Porrúa y CIESAS, México. Roys, Ralph 1967 The Book of Chilam Balam of Chumayel, University of Oklahoma Press, Norman. Meeus, Jean and Denis Savoie 1992 “The history of the tropical year.” In Journal of the British Astronomical Association 102(1):40-42. Espenak, Fred 2015 Fred Espenak’s Web Site at http://gsfc.nasa.gov/eclipse.html. Schele, Linda and Nikolai Grube 1997 “The Almanacs” In Workbook for the Maya Hieroglyphic Forum. University of Texas, Texas. Schele, Linda and David Freidel 1990 A Forest of Kings. The Untold story of the Ancient Maya. William Morrow, New York. 44 Sprajc, Ivan 2001 Orientaciones astronómicas en la arquitectura prehispánica del centro de México. Instituto Nacional de Antropología e Historia, México. Sprajc, Ivan y Pedro Francisco Sánchez NAva 2012 “Astronomía en la Arquitectura de Chichén Itzá: una reevaluación.” En Estudios de Cultura Maya xli:31-60. Stanzione, Vincent 2000 Rituals of Sacrifice. Walking the face of the earth on the sacred path of the Sun: a journey through the Tz’utujil Maya world of Santiago Atitlán. University of New Mexico Press, Albuquerque. Stuart, David 2005a “New Year Records in Classic Maya Inscriptions”. In The PARI Journal 5(2):1-6. www.mesoweb.com/pari/publications/journal/0502/NewYear.pdf 2005b The inscriptions from Temple XIX at Palenque. A Commentary. The PreColumbian Art Research Institute, San Francisco. 2006 “Part II. The Palenque mythology: inscriptions and interpretations of the Cross group”, Sourcebook for the 30th Maya Meetings. University of Texas Press, Austin. Thompson, Eric 1935 “Maya Chronology: the Correlation Question”. In Contributions to American Archaeology, 14:53-104. 1950 Maya Hieroglyphic Writing. An Introduction. Carnegie Institution of Washington, Washington D.C. Tedlock, Barbara 1992 “The Road of Light: Theory and Practice of Mayan Skywatching.” The Sky and Mayan Literature, edited by Anthony F. Aveni, pp.18-43. Oxford University Press, Oxford. Teeple, John E. 1930 “Maya Astronomy” Carnegie Institution of Washington Pub. 403, Contributions to American Archaeology Num. 2. Carnegie Institution of Washington, Washington, D.C. 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