Gerardo Aldana.
Let me attempt to begin this conversation with a simple but very important question:
Why do we follow the continuity assumption between the end of the use of the Long Count and the beginning of the Katun Count? Teeple didn't buy it, neither did David Kelley, and in 1980 Aveni said it was useful because it was simple and convenient.
But does that make it right? Justifiable?
Carlos.
Both scenarios are possible and should be examined. For the first case (continuity), the correlation constant 584285 could be the solution. For the second case, I have obtained the correlation constant 546339, whose main characteristics are:
100% agreement with the central tendency in the distribution of C-14 for sample ETH-44685/T1-3e-C from lintel 3 of Temple I at Tikal, according to the results published in 2012 by the University of Pennsylvania (since 9.13.3.7.18 is September 16, 591 [G]).
Solar correspondence of:
2.1. Era Date (ED) 0.0.0.0.0 with September 22 -3217/3218 BC [G] (autumn equinox)
2.2. Main sign 9.9.9.16.0 of the Venus Table (DCVT) with March 20, 519 [G] (spring equinox)
2.3. Origin of the Lunar Table (DCLT) on 9.16.4.10.8 with December 21, 651 [G] (winter solstice)
Correspondence between the date 9.17.19.13.16, 5 Kib 14 Ch'en (August 27, 686 [G]) and the eclipse recorded on Stela 3 of Saint Helena Poco Winik (POCO)
Correspondence of DCLT record 9.16.4.11.3 with the lunar eclipse that occurred on January 5, 652 [G]
Correspondence between the shaded new moon phase on Quirigua Stela E for 9.17.0.0.0 (Michael Closs) and the total solar eclipse of March 3-4, 667 [G] when the Sun aligns with the lunar nodes.
The Dresden record 9.12.10.16.9, 13 Muluk 2 Sip, (May 13, 579 [G]), proposed by Brayn Wells, coincides with the second stationary position (2SP) of Mars, the Mars-Spica conjunction, the first stationary position (1SP) of Saturn (Opposition - 78 days), a visible solar eclipse, and the opposition (OPP) of Jupiter - 260 days.
The Dresden record 9.18. 1.7.9, 13 Muluk 17 Wo, (April 11, 688 [G]), also proposed by Bryan Wells, again coincides with the 2SP of Mars, the Mars-Jupiter conjunction, and the OPP of Saturn.
Gerardo Aldana.
That's exactly my point. If we follow continuity by assumption, then the GMT is the best solution. But it's only a best fit given that constraint. If we don't take up that assumption, then there are other possible solutions--some even better.
So, why do we follow continuity or not?
Pros: - it is convenient; - a lot of astronomical data seem to fit with it; - it matches the historical data relatively well;
I've gone through a lot of the problems with these factors in my article on the CC problem. In the end, they are not sufficiently convincing to me.
Cons: - how do we determine which is the "right" better solution? - several other CCs can be proposed that also produce good matches to astronomical data; - now we don't really have a guide for how to handle the "historical data" from the post-Contact period.
I do think that you're right, Carlos.
But now a critical issue becomes: what are the reliable astronomical anchors from the Classic period. This is exactly what Teeple dealt with, but then got pushed aside by Thompson and his manipulation of the correction factors in the Dresden Codex Venus Table.
So for Thompson, it was (most of) the answer. I think for us, it can be just the beginning. (And in fact, I think a viable alternative will turn out to be 598,313. But the details there will hopefully turn up in a later post.)
Ed Barnhart
How about the fact that the 260-day name that the Day Keepers of modern Guatemala recognize is the same as the one for the 584283 correlation? Is it just a 1 in 260 coincidence, or is there something more to it? I have always gone with that one, if for no other reason than to respect modern Maya descendants.
Gerardo Aldana.
I'm totally sympathetic to the interest in respecting modern Mayan communities and their relationship(s) to their ancestors. Accordingly, if the calendar correlation problem were solved by someone who is Mayan and based on their own data and methods, then I would be inclined to give that solution a different kind of consideration. But no version of the GMT qualifies. And I don't think that a historical discontinuity in calendric practice takes anything away from modern Mayan communities and/or culture(s). I think we can all agree that there's plenty to appreciate independent of purported calendric continuity. But I'm open to hearing that I'm missing something here.
As for Lounsbury's take (mentioned by Carlos.
Ed Barnhart
Well, I agree that no version of the GMT solves all discrepancies, but I still feel like the 1 in 260 chance of the 584283 correlation producing the modern Tzolk'in date is quite a coincidence. On another level, I sometimes wonder if we are driving ourselves crazy striving for the unreasonable - that is that every piece of ancient astronomical evidence, be a solid reading, a good assumption or a logical guess, fit into a single correlation choice. What if some of the texts are recording events inaccurately? Or even more likely, what if we are misunderstanding what they really say?
Further, looking at other cultures' calendars (especially the Christian calendar) we see times in which they were tweaked to fall back in line with some cycle they were supposed to be tracking better. I terms of Gerardo's question, has anyone attempted to disregard the "continuity assumption" and run with a 2 or even 3 correlation constant solution, each related to a different era in Maya thinking?
Gerardo Aldana.
The latter point is exactly what I've been proposing and is the approach I recently took to generate 598,313. It looks like we'll have to create a "Notes" series on this website (akin to the Texas Notes and Copan Notes) for smallish stuff like that argument. (And independent of the Working Paper Series.) But yes, the approach is then precisely NOT to take continuity by assumption, but to allow for it as a possible solution. This again is in line with both Teeple's and Makemson's concerns about the inconsistencies of alphabetic historical records. It also respects (for the later, non-Long-Count based times) the situation that Thompson referred to in the Preface to Maya Hieroglyphic Writing (3rd Edition): "the Mixe count, in fact, varies from village to village. In one center it differs by five days from the highland Maya almanacs." (pp. vii-viii) Which in fact may also be the situation that Justeson and Tavarez found in the Zapotec records they recently studied.
So, yes, without the continuity assumption, you need to define the parameters a little more clearly and locally. Now you can look for one solution for the Long Count period, and another one for the Katun Count period--perhaps multiple... and then ??? We should be able to say something about potential revision getting from one to another, but without a more robust dataset, that would probably be speculative. (I.e. Aztec influence, etc.) But as you point out, then it really becomes an issue of how solid your individual data points are.
Carlos.
Regarding the final question posed by Ed (has anyone attempted to disregard the "continuity assumption" and run with a 2 or even 3 correlation constant solution, each related to a different era in Maya thinking?), I have something to share with the group that might be of interest.
According to the dating of the Dresden Codex, the Venus pages should synthesize the syncretic Maya-Toltec thought of the Early Postclassic. In that order of ideas, the calendrical records there recorded should reflect the fusion and assimilation of Maya-Mexica temporal elements or concepts, and it is on this line of evidence that I have developed a potential correlation between Maya and Mexica dates, applicable to the Postclassic Period and later, which operates independently of the correlation CBA 546339 (in which the discontinuity between the K'atunes of the Long Count and the Short Count is assumed).
This information will be formally presented at (and possibly recorded in the proceedings of) an upcoming Archaeoastronomy meeting to which I have been invited at the end of next January.
Santiago Marino Mojica Román, another independent researcher like myself, who actively participates in the AZTLAN lists, has highlighted in his research on correlation, two dates associated with the Mexica Calendar: [1] the defeat of the Tlaltelolcas on 5 Quiahitl-(Rain) of the month Huey Tecuilhuitl of the Xihuitl 7 Calli-(House), during the European year 1473, and [2] the fall of Tenochtitlán on 1 Cóatl-(Serpent) of Tlaxochimaco of the year 3 Calli-(House), corresponding to the Julian date of August 13, 1521.
My conclusion, after researching the topic, is that the correlation constant 584283 represents a useful chronological marker to establish correspondences between the respective Mayan and Mexica calendars, starting from the original correlation constant 584285, which would have been adjusted by two days to reconcile the conceptual difference between the Mayan count starting from zero, and the Mexica count starting from one, a concept that equally affects the selection of their respective year bearers, mutually recorded on pp. 25-28 of the Dresden Codex.
By establishing the Julian date of August 13, 1521, according to the correlation constant 584283, we therefore obtain the synchronization of the respective Tonalpohualli/Tzolkin 1 Coatl-Chikchan components, but not the total synchronization of the Calendar Round, since the respective Mayan and Mexica months/meztli would have been established from different solar references. It is for this reason that a coincidence that should be 1-18980, becomes only a coincidence 1-260, as Ed.
If you allow me, I can make a brief presentation of how I established the displacement between the respective Tzolk'in/Tonalpohualli components of the Mayan and Mexica calendars, and how this difference allows me to formulate a new correlation constant, complementary to 584285 and 546339.
Gerardo Aldana.
This is exactly why I'm here. I suggest you submit the paper as a Working Paper if you're going to publish it elsewhere (but you do want us to discuss it on this forum). Or if you have a version of less than 10 pages, you can submit it here in preliminary form in a new series of "Notes." (Please send it to gvaldana at gmail.com .)
Carlos.
I have a summary of only 470 words, which explains the process used to obtain the correlation constants for Mayan-Mexican dates. Could you accompany this summary with a couple of practical examples. Would it apply as an "Express" Working Paper or as a "Brief Notes"?
Gerardo Aldana.
Notes.
Carlos.
While I adjust the style and revise the wording of the document that will be presented for consideration by the Group, I would like to anticipate its conclusions.
"Conclusions
The operational and conceptual differences between the Maya and Mexica chronological systems would have been reconciled by the time the Dresden Codex was produced, through internal correlations that reflect typical intervals of separation between their base records, in the order of 2,520, 8580 and 9100 days.
Regarding the 9100-day interval, in particular, there is epigraphic evidence on page 24 of the Dresden Codex that could be interpreted, in the context of this research, as the typical separation between the Maya-Toltec syncretic count of 260 days, represented by the correlation constant T = 584283, and the original Mexica Tonalpohualli, represented by the correlation constant T – 9100 = 575183.
For its part, the chronological difference between the respective “Maya Syncretism” and Mexica Calendar Wheels would have been reconciled through the correlation constant T – 520 = 583763, while the relative difference between their respective solar structures would have been solved by shifting the original Classic Maya count by two days, represented by the correlation constant 584285, towards a new syncretic structure, represented by the correlation constant 584283.
The difference of 33 x 260 days, obtained by comparing the correlation constants [T – 9100] and [T – 520], equivalent to 23 solar years + 179 days (where the residue of 179 days represents the typical separation between the autumn equinox and the spring equinox), would allow us to finally conclude that the Mayan and Mexica Calendars were originally established through opposite solar references."
Carlos.
A few hours ago I had a problem with the paper I was going to submit for consideration by the Group. While performing the operational tests of the correlation model between Mayan and Mexica dates - based on four fundamental chronological references: Fall of Tenochtitlán, beginning of the year according to Sahagun, defeat of the Tlaltelolcas by the Tenochcas, and arrival of Cortés in Mexico - I identified two particular aspects that require a broader exposition than I can cover in a quick and practical format such as Notes.
The first of these aspects is related to the computation of leap days and "true years" of Sahagun, which leads to reformulating the initial correlation T - 520, as T - 526, and the second of them, associated with the arrival of Cortés to Mexico, which leads to reformulating the initial correlation T - 9100, as T - (9100 - 260). This would not represent any inconvenience if the structures obtained were unpublished, but as perhaps the scholars of the Aztec Culture have already noticed, the results obtained through the correlation T - (9100 - 260) coincide exactly with the proposal originally presented by Alfonso Caso in 1939, while the correlation T - 526 differs only two days from the references originally established by him for the Meztli. The above forces me to carefully review the bibliography of this illustrious character, before being able to continue.
Could the correlations T – 520 and T – 526 represent two historical moments of transition between a "syncretic" Maya-Toltec model and a somewhat more "Mexicanized" one in which the intercalary years suggested by Magliabecchi, Telleriano, Bobam, and even by the Chilam Balam of Maní were already considered?
I need to go deeper into the research, so please excuse me for postponing this presentation.
Kind regards.