Chich'en Itza, the Dresden Codex Venus Table And

Discovering Discovery: Chich’en Itza, the Dresden Codex Venus Table and 10th Century Mayan Astronomical Innovation

Gerardo Aldana y V. University of California, Santa Barbara

Abstract: After centuries of scant attention and even- A new reading of Dresden Codex Page 24, the “Pre- tual repose in the Dresden Library in Ger- face” to the Venus Table, is presented, demonstrating a many, a Postclassic manuscript written in much-improved overall coherence. This reading of hie- Mayan hieroglyphs was brought to the at- roglyphic text, mathematical intervals, and calendric tention of modern scholars during the data specifically identifies the Mayan Long Count dates of the Venus Table’s historical correction. The resulting nineteenth century. Six pages of this man- Long Count placement of the manuscript’s Venus Table uscript, the “Dresden Codex,” have been suggests that it was an indigenous astronomical dis- recognized as relating to the planet Venus covery made at Chich’en Itza, possibly under the patro- since Ernst Förstemann first began work- nage of K’ak’ U Pakal K’awiil — one of the most pro- ing through them in the 1880s. minent historical figures in the inscriptions of the city Förstemann suggested that across these during its “epigraphic florescence.” Revealing the logic pages, a table of dates1 based on multiples underlying the construction of the page, the revised rea- of 584 days were used to track the observ- ding suggests a slightly less-accurate approximation to able period of Venus. Förstemann at- Venus’s synodic period than the traditional interpretation allows, but introduces a justification for the graphi- tempted a translation of the pages (almost cal layout of Page 24 that is more straightforward than a century before the decipherment of the traditional interpretations. script itself) by inferring the meaning from the calendric-astronomical patterns he re- Keywords: Maya, Astronomy, Calendars, covered. Venus, Indigenous Knowledge [W]e find that the [Yucatec scribe] de- Introduction sires to say this:

1 Dates in the Maya Calendar are made up of tropical year. Each of 18 months has 20 days; Long Count and Calendar Round compo- one final “month” is of only 5 days. The month nents. The Long Count is a tally of days con- names are Pohp, Wo, Sip, Sots’, Tsek, Xul, Yaxk’in, ceptually equivalent to the Julian Day Number. Mol, Ch’en, Yax, Sak, Keh, Mak, K’ank’in, Muwan, The differences are only that the Long Count Pax, K’ayab, Kumk’u, Wayeb. A full date would is a modified vigesimal count (base-20) and the be written, for example, as bolon pih bolon wini- “zero date” is different in each case. The Cal- khaab ka haab kan winik waxak k’in ho lamat hun mol endar Round is a combination of the 260 Day and transcribed by modern scholars as Count and the 365 Day Count. The 260 Day 9.9.2.4.8 5 Lamat 1 Mol. Within hieroglyphic Count is a combination of 13 numbers and 20 texts, dates (full or partial) are separated by Day Signs, each advancing on a daily basis. time intervals or “distance numbers” given in The Day Signs are Imix, Ik’, Ak’bal, K’an, Long Count format. A time interval of 4.8 rep- Chikchan, Kimi, Manik, Lamat, Muluk, Ok, Chuwen, resents 88 days. Three hundred sixty-five days Eb, Ben, Ix, Men, Kib, Kaban, Etz’nab, Kawak, would be represented 1.0.5 in Long Count no- Ajaw. The 365 Day Count approximates the tation. Journal of Astronomy in Culture 1(1), 2016, pp. 57-76 Copyright © International Society for Archaeoastronomy and Astronomy in Culture 58 I am here treating especially the peri- would have accumulated, and that they de- ods consisting of five successive Venus veloped a means for correcting their Table years, bringing them into harmony accordingly over very long spans of time. with the solar year and the [260 Day His interpretation was consolidated and Count]2. … [E]ach individual Venus extended by Eric Thompson at mid-cen- year [is] divided into four unequal tury, who argued that Postclassic Mayan parts, which appertain to the east, astronomers had access to an ephemeris north, west, and south and are ruled for Venus accurate to “within one day in by certain deities, which I can mention six thousand years” (1978:63). only in part, owing to lack of space. This, I suggest, is where the historiog- Lastly, I would add that each of the raphy of the Dresden Codex Venus Table five Venus years of a period is domi- takes an interesting turn. Without an abil- nated as a whole by a deity, and the ity to read the hieroglyphic text in the Ta- signs of these I give here (1894:443). ble, scholars were left at mid-century to make an argument for the Venus ephem- Förstemann’s work of over a century ago eris mainly through its purported accuracy goes a long way toward capturing the un- in predicting observable phenomena. This derstanding still current in the contempo- trope then dominated the academic con- rary literature (Aveni 2001; Bricker and sideration of the Venus Table: the better Bricker 2007; Lounsbury 1983). the accuracy it could attribute to the Ta- In the 1920s John Teeple, a chemical ble, the stronger the modern interpretation engineer turned Mayan calendar enthusi- was considered to be (Thompson 1978; ast, followed Förstemann and Eduard Lounsbury 1983, 1992; Bricker and Seler’s interpretive work to focus on the Bricker 2007). mathematical subtlety of the Venus Table. In particular, two forms of accuracy Teeple found that a sequence of four ‘un- have controlled this discourse. The first conventional’ time intervals on Page 243 of has to do with the placement of one of the the manuscript—which confounded Calendar Round dates recorded in the Ve- Förstemann (1894)— actually served as nus pages with respect to a historically re- “corrected” multiples of the 584-day ca- constructed first morning visibility of Ve- lendric period of Venus (Thompson nus (fmv).4 The second concerns how well 1978:224). These intervals suggested that the table could be re-cycled to minimize Mayan astronomers kept track of the dif- the accrued error between prediction and ference between their calendric progres- observation. In 1983, Floyd Lounsbury sion based on a Venus Round of 584 days graphically depicted his and Thompson’s and the 583.9214-day synodic period of approaches to both measures as shown in Venus. Teeple argued that these astrono- Figure 1. mers quantified the amount of error that

2 Förstemann here used the term tonalamatl, 4 Scholars in the past turned to the Tuckerman which is the Nahuatl name for the 260 Day Tables to look up idealized observations for the Count. See footnote 1. Mayan area (Lounsbury 1983:5); now it is com- 3 The apparent non-sequentiality of the Pref- mon for archaeoastronomers to utilize software ace and the Table is accidental only. The man- such as EZCosmos (Freidel, Schele, and Parker uscript had fragmented, and it was numbered 1993) or Planet’s Visibility (Bricker and Bricker out of order. In its original form, the Preface 2007:116). Either way, a Calendar Correlation immediately preceded the Table. is necessary for these studies. See footnote 5.

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Figure 1. Reconstruction of Lounsbury’s “mean error” graph of Venus observations against hypothetical Dresden Codex predictions.

Lounsbury followed Thompson’s ap- work, modifying it slightly by changing the proach to matching the long-term correc- Calendar Correlation5 by two days and ar- tion of the table, but changed the starting guing that the ephemeris was more strictly point; both models synchronize at a warning table. This move slightly altered 10.10.11.12.0 1 Ajaw 18 K’ayab, which Bricker and Bricker’s inherited notion of they assigned to October 25, 1038 A.D. accuracy since now they want a table that Lounsbury engaged the first aspect of the strictly anticipates fmv; the constraint, of Venus Table’s ‘accuracy’ by noting that his course, is that it cannot come so early that reconstruction placed the 1 Ajaw 18 the prediction overlaps with last evening K’ayab of 10.5.6.4.0 exactly on a (histori- visibility—a rather small range of possibil- cally reconstructed) first morning visibility ity over the long run, given that inferior of Venus (mean error of ‘0’). He claimed conjunction varies and can be as short as that this fmv corresponded to a conjunc- half a day. tion of Venus and Mars—in his view, a Nonetheless, the reconstructions by particularly noteworthy event (Lounsbury these scholars ascribe an impressive accu- 1983:12). racy to Mayan Venusian astronomy and in Harvey Bricker and Victoria Bricker its fundamentals create an interpretation (2007) agreed with most of Lounsbury’s

5 The Calendar Correlation is an arithmetic GMT = JDN. The GMT includes “variants,” constant used to link the Maya Long Count to however, that compensate for the prioritization the Julian Day Number. (See footnote 1) The of different data sets by the scholars utilizing it GMT is the most commonly used Correlation (cf. Aldana 2010, 2015). Constant, where GMT = 584,283 and LC +

JAC, Vol. 1, No. 1, 2016 60 that has been universally accepted by Ma- also resolve the complications of the tradi- yanists since the early twentieth century tional model with respect to the anchor (Morley 1975; Thompson 1972; Sharer and the Correction Intervals. 2006; Coe 1988). There are, however, In this essay, we incorporate a ritual complications with it. The first, as we shall utility and prioritize the internal logic of see, is that the method they all propose for the table for the interpretation of how it in- correcting the Table does not follow teracts with observable Venus phenomena straightforwardly from the information ac- and the Venus Table of dates on Pages 46- tually recorded in the Preface. The correc- 50. In doing so, we encounter a much tion interval which provides the greatest more robust reading of Page 24, recon- utility in maintaining accuracy, and which struct an hypothesis for the observed calen- drives all current interpretations, is actu- dric-astronomical patterns that generated ally not even recorded on Page 24 or any- the Venus Table as recorded, and face a where in the Venus Table. (See Figure 2) better fitting archaeological proposal for Instead, it is inferred from the two correc- the origin of the Dresden Codex Venus tion intervals that are written at the top of Table at the “Observatory” of Terminal the Preface (Thompson 1978:226, Classic Chich’en Itza. 1972:63; Lounsbury 1992a:185; Bricker & Bricker 2007:103-104). Second, the stand- Corrections ard interpretation requires that the anchor The Dresden Codex Venus pages are bro- of the Table deviate from an historical fmv ken up into two parts. The first is often by some 16 days. In other words, the called the Preface as it contains prelimi- standard interpretation requires that a ta- nary descriptive information about the en- ble designed to preserve first morning visi- suing pages and it provides contextual data bilities of Venus on dates 1 Ajaw was an- for the interpretation of the table itself. chored to an historical date that did not. The second part is the Venus Table proper In this essay, I suggest that if we set made up of calendric progressions through aside our expectations based on modern 65 Venus Rounds, each broken up into notions of accuracy, and look at the logic sub-periods marking first morning visibil- of Page 24 itself, not only does the cur- ity (fmv), (something near) last morning rently accepted interpretation of it appear visibility (lmv), first evening visibility (fev), forced, we encounter a much more com- and last evening visibility (lev).6 Occupy- pelling explication of the Table. Through ing the right hand side of each of the five the new interpretation proposed here we pages of the Venus Table is an elaboration find, for example, what we might expect: of the oracular meaning ascribed to first that the numbers recorded are the ones morning visibilities (Aldana 2008, 2015a). that are actually useful in correcting the If we focus on just the mathematical Table, i.e. we do not have to rely on num- and calendric patterns, the ephemeris in- bers that are simply implied by the ones ex- terpretation of the traditional approach plicitly recorded. Further, we find that seems reasonable. Recently, though, I there is a utilitarian purpose to the graph- have shown that the hieroglyphic textual ical layout of the intervals on Page 24. We narrative driving the Table is actually part

6 The lack of symmetry and accord with regu- lar observability of the individual sub-periods is still a matter of some debate (Aveni 1992).

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Figure 3A. Visual representation of Thompson’s method for applying the correction factors on Page 24 to the recorded base date of 9.9.9.16.0 1 Ajaw 18 K’ayab (cf. Bricker and Bricker 2007, Table 3.3).

Figure 2B. Visual representation of Lounsbury’s method for applying the correction factors on Page 24 to the recorded base date of 9.9.9.16.0 1 Ajaw 18 K’ayab (cf. Bricker and Bricker 2007, Table 3.3).

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Figure 2C. Visual representation of Bricker and Bricker’s method for applying the correction factors on Page 24 to the recorded base date of 9.9.9.16.0 1 Ajaw 18 K’ayab (cf. Bricker and Bricker 2007, Table 3.3).

Figure 2D. Visual representation of Aldana’s method for applying the correction factors on Page 24 to the recorded base date of 9.9.9.16.0 1 Ajaw 18 K’ayab.

Aldana, G. 63 of a larger ideological context. ritual tied to first morning visibility when My proposal for the reading of Venus was still visible as evening star. And /k’al/—the operative verb throughout the when we turn to the corrections of the Ve- Table—as ‘to enclose,’ means that a run nus Table on Page 24, we realize that we through one row of the Table reads: are looking at a concern with the long- term: the corrections are intended for pe- On 3 Kib 4 Yaxk’in, the North is en- riods of hundreds of years. closed by Deity 1 and Chak Ek’. It is When we come to the determinations 236 days [since the previous first of long-term accuracy, then, two sets of morning visibility of Venus]. On 2 Calendar Round dates are critical: two on Kimi 14 Sak, the West is enclosed by Page 24; two on Page 50. These corre- Deity 2 and Chak Ek’. It is 326 days. spond to the placement of the table in his- On 5 Kib 19 Tsek, the South is en- torical time. Teeple’s intervention was to closed by Deity 3 and Chak Ek’. It is show that a serial application of an inferred 576 days. On 13 K’an 7 Xul, the East correction interval produces a progression is enclosed by Deity 4 and Chak Ek’. through these four Calendar Round an- It is 584 days. chors. His ‘inferred correction interval’ comes from two time intervals written on Whereas the traditional interpretation Page 24. (See Figure 2) The second row of translates /k’al/ as ‘to tie’ or ‘to bind’ and Long Count intervals from the top con- leaves the meaning ambiguous (Aveni tains the only four intervals on the page 2001), mine provides a straightforward that are not whole multiples of 2920 days narrative version of the graphic cosmo- (= 5 x 584 or one full row of the Venus Ta- gram illustrated on the frontispiece of the ble): 185,120; 68,900; 33,280; and 9,100. Central Mexican Féjérvary-Mayer Codex The difference between the second and (Aldana 2011:56). (See Figure 3) The re- third intervals explicitly recorded in this sulting equivalence between text and im- row, 68,900 and 33,280, gives the inferred age suggests that accuracy of observation correction interval, 35,620 (9.11.7.0 – may not have been the Table’s primary 4.12.8.0 = 4.18.17.0). It is this difference motivation—it is more likely that it guided that Teeple uses (and Thompson and ritual events according to Venus Rounds Lounsbury, and Bricker and Bricker) as the and sub-periods of them (Aldana 2011:64- fundamental element in the reconstructed 5). correction of the table (Bricker and Bricker In other words, the short-term accu- 2007:102). As Teeple showed it: racy was probably not tremendously im- portant—the vast majority of the popula- 1 Ajaw 18 K’ayab + 35,620 tion was probably not checking whether (1 Ajaw 8 Yax + 35,620) the ritual Venus calendar was off by a day 1 Ajaw 18 Wo + 35,620 or even a few.7 Over the long-term, how- 1 Ajaw 13 Mak + 35,620 ever, accuracy would certainly become sig- 1 Ajaw 3 Xul nificant—one could not be performing a

7 It probably was not even reasonable to expect view over the floral canopy was only available that the vast majority of the population had ac- from the upper levels of the tallest structures, cess to a view of the horizon providing the ca- which certainly would have had restricted ac- pability of checking on the Table’s accuracy. A cess.

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Figure 3. The text in the Dresden Codex Venus Table can be understood as a written translation and adap- tation to Venus cycles of the Central Mexican “cosmogram.” The “St. Andrew’s Cross” on (a) the Féjérvary- Mayer Codex frontispiece comprises dots and Day Signs, counting out a full 260 Day Count cycle. Each of the four main ‘arms’ of the cross represents a different cosmic region: East at the top, North on the left, West at the bottom and South on the right. Each direction sprouts a tree that is attended by two deities. The central image is dressed as a warrior who has vanquished a victim, whose body parts are connected by blood at the inter-cardinal vertices to the trace of time. Accordingly, each column of the text in (b) the Dresden Codex Venus Table excerpt begins with a date and then is anchored to the verb K’AL-ja (for k’ahlaj – ‘to be enclosed’), followed by one of the cosmic directions, the name of a deity and the name for Venus. The fourth column, for example, can be read as: ‘On 2 Kib 14 Wo, the East is enclosed by Jun Ajaw and Venus.’ Ritual time, therefore, encloses each of the four cosmic regions facilitated by two celestial deities (the named one and Venus). Also, compare the central figure in the cosmogram, Xiuhtecuhtli, with the warrior figure in the Dres- den Codex excerpt, who is named hieroglyphically as ‘Chak Xiwite’ (CHAK xi-wi-te).

The first, third, fourth, and fifth Calendar sequence of first morning visibilities. Rounds of this sequence are the two sets Thompson, on the other hand, ig- that show up on Page 24 and Page 50. nored the missing Calendar Round date Teeple’s serial application of the inferred and used the first correction interval, correction interval, though, produced one 4.12.8.0, to go directly from 1 Ajaw 18 “extra” Calendar Round date: 1 Ajaw 8 K’ayab to 1 Ajaw 18 Wo. He then utilized Yax. This date does not show up in the the implied interval from there on. (See Venus Pages at all. Teeple (1926:404) sug- Figure 2) While his approach required gested that the omission corresponded to that he accept an error of 16 days between an actual implementation of the set of cor- the anchor of the Table and a historically rections to match a historically observed reconstructed first morning visibility of Ve-

Aldana, G. 65 nus, Thompson explained that away by “corrected” for the slippage between the suggesting that the scribe was using it only idealized 584-day period and the actual for its numerological value (1972:63). 583.92-day synodic period. We can then Only slight modifications to Thompson’s take VGC = Venus Great Cycle = 37,960; method have been used since (Bricker and CIn = nth Correction Interval recorded on Bricker 2007:102-104). Page 24; and CVIn = nth corrected Venus It turns out, however, that there is an- interval. These produce the following re- other method for producing the sequence lationships. of Calendar Rounds recorded in pages 46- 50, and this one significantly more 1 VGC + 1 CI1 = CVI1 straightforward. 5.5.8.0 + 4.12.8.0 = 9.17.16.0 37,960 + 33,280 = 71,240 Mathematical Coherence There is a viable alternative to Teeple’s ap- This can be compared to the uncorrected proach. As noted in my treatment of the interval it is meant to replace, which would operative verb within the Venus pages (Al- be 2 Venus Great Cycles (2VGC): dana 2011), the correction intervals explicitly written on Page 24 themselves take the 2 x 5.5.8.0 = 10.10.16.0 Venus Table base date through each of the 2 * 37,960 = 75,920 explicitly recorded anchors: So that: 1 Ajaw 18 K’ayab 1 Ajaw 18 K’ayab + 4.12.8.0 + 33,280 CVI1/2VGC = 71,240/75,920 1 Ajaw 18 Wo 1 Ajaw 18 Wo = 137/146

1 Ajaw 18 K’ayab 1 Ajaw 18 K’ayab Similarly, for the second Corrected Venus + 9.11.7.0 + 68,900 1 Ajaw 13 Mak 1 Ajaw 13 Mak Interval:

1 Ajaw 18 K’ayab 1 Ajaw 18 K’ayab 1 VGC + 1 CI2 = CVI2 + 1.5.14.4.0 + 185,120 5.5.8.0 + 9.11.7.0 = 14.16.15.0 + 4.12.8.0 + 33,280 37,960 + 68,900 = 106,860 1 Ajaw 3 Xul 1 Ajaw 3 Xul And for the 3 VGCs it is meant to correct: Notice that where Thompson’s method applies the correction intervals serially, the 3 x 5.5.8.0 = 15.16.6.0 sequence here shows that each interval ap- 3 * 37,960 = 113,880 plied independently more cleanly reproduces the Calendar Round dates. This alternate So that: approach to the correction interval opens up a provocative mathematical coherence CVI2/3VGC = 106,860/113,880 to the Table and generates a more robust = 137/146 interpretation overall. To see it, we first define a new term: the Corrected Venus The comparison yields: Interval, which is that time interval used to move from one recorded Calendar Round CVI1/2VGC = CVI2/3VGC date to a future Calendar Round date

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Each corrected Venus interval (CVIn) rel- Besides the denominators as whole num- ative to its parallel, uncorrected interval ber multiples of the arithmetic base of all produces the same ratio. The same ratio is intervals on Page 24, these are standard used according to the same method for arithmetic relationships readily available correcting projections for the periods of to the Mayan calendric specialist (Aldana two Great Cycles into the future and that 2007; Lounsbury 1978; Thompson 1972). of three Great Cycles. Notice that with this Nor are the numbers of a scope unattested approach, there is no skipping around and within the Dresden Codex itself, as they arbitrarily using inferred correction inter- are dwarfed by, for instance, the serpent vals or unscripted applications of one ver- numbers on Pages 61-73 of the same man- sus another. (See Figure 2) The method of uscript (Thompson 1972:80-88). Finally, correction is straightforwardly represented the result is a very respectable 583.934 (= in the table of intervals. 71,240/122 = 106,860/183) average syn- The equivalence of these ratios sug- odic period for Venus, which is not as ac- gests that they were constructed to be ap- curate as the traditional model (583.92), plied independently and not serially as but which we find is productive in other Teeple originally proposed. It also allows ways. us the hypothesis that they were intention- The mathematical coherence of Page ally constructed at least in part around this 24 under the new interpretation is further relationship. Moreover, we do not have to corroborated by Lounsbury’s 1992 essay appeal to opaque origins for these inter- on the mathematical structure of the Cor- vals. The two correction intervals were rection Intervals. Lounsbury showed that created with very “Mayan numbers”: each correction interval takes the form of a Diophantine Equation (1992b:208) and he CVI1 = 71,240 = 137 x 520 identified the term 2,340 as being funda- = 137 x 2 x 260 mental to the construction of each. Here we define 2,340 as the Correction Factor, 2VGC = 75,920 = 146 x 520 CF. = 146 x 2 x 260 = 73 x 22 x 260 CI = xVGC – yCF (x, y ∈ I) = 26 x 2,920 While: CI1 = 4.12.8.0 = 1 x 5.5.8.0 – 2 x 6.9.0 = 1 x 37,960 – 2 x 2,340 CVI2 = 106,860 = 137 x 780 = 33,280 = 137 x 3 x 260 CI2 = 9.11.7.0 = 2 x 5.5.8.0 – 3 x 6.9.0 3VGC = 113,880 = 146 x 780 = 2 x 37,960 – 3 x 2,340 = 146 x 3 x 260 = 68,900 = 73 x 2 x 3 x 260 = 39 x 2,920 CI3 = 1.5.14.4.0 = 5 x 5.5.8.0 – 2 x 6.9.0 = 3 x 37,960 – 2 x 2,340 The prime number 73 is critical to Mayan = 185,120 calendric manipulations as shown by Lounsbury (1978) since it is a common fac- even tor of 365 (= 5 x 73) and 584 (= 8 x 73).

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Figure 4. Eight-day drop in the average error between the Venus Table prediction and an idealized projection forward of first morning visibilities from 9.9.9.16.0 1 Ajaw 18 K’ayab.

CI4 = 1.5.5.0 = 4 x 5.5.8.0 – 61 x 6.9.0 val (Lounsbury 1992b). The first, 4.12.8.0, = 4 x 37,960 – 61 x 2,340 would be used to invoke an 8-day correc- = 9,1008 tion. It follows that it would be useful for making up an accumulated error of The Correction Factor works as such be- around 8 days, which would occur after cause 2,340 is divisible by 260 (9 times), so 60,736 days (= 8 x 13 x 584 (= 1.6 Great it will preserve the same date in the 260 Cycles) since 13 x 584 produces 1 day of Day Count—in these cases it preserves the error). More straightforward, an interval date 1 Ajaw. Also, 4 x 584 = 2,336, so sub- of 2 full Great Cycles (75,920 = 2 x 37,960) tracting intervals of 2,340 (or 4 x 584 + 4) would accumulate 10.2 days of error, so a compensates for the difference between correction of 8 days would bring predic- the synodic period and the idealized Venus tions within observable tolerances. Round (Lounsbury 1992b). In application, the correction interval The above equations also show that actually truncates the progression and re- the coefficient y of the 2,340 Correction sets the anchor earlier than the completion Factor corresponds to the number of 4-day of an integral number of full tables. That corrections built into the correction inter- is, a complete Venus Great Cycle would

8 This last interval has been considered enig- its legitimate function (Aldana 2011; Louns- matic since Förstemann’s time, and has even bury 1992b). been dismissed by Thompson as an error, although recent work has resulted in proposals for

JAC, Vol. 1, No. 1, 2016 68 have ended at the 130th Venus Round; ra- In 1980, Anthony Aveni noted that ther than wait for the accumulation of 10 Chich’en Itza, located in the heart of the days of error, the correction would have northern Yucatan Peninsula, would have found that a 1 Ajaw date occurred eight been a strong candidate for the origin of VR earlier, on the 122nd. (See Figure 4) the Venus Table. Aveni’s extensive study Shifting to this 1 Ajaw date as a new an- of Terminal Classic Structure 3C-15, also chor brings the Table back into observa- known as the “Caracol” or the “Observa- tional tolerances. tory” (Aveni, Gibbs and Hartung 1975; The pattern continues with the second Aveni 1980), led him to suggest that the correction interval. Here, the coefficient of Dresden Codex Venus Table may have CF (2,340) is 3, so we would expect this to been constructed there. First, he pointed correct an accumulated error of 12 days. to the irregular orientation of the structure Three uncorrected intervals would accu- relative to the rest of the site as an indica- mulate 15 days, so again, an application of tion of potential astronomical alignment this correction would bring three full un- (Aveni 2001:274); then he focused on the corrected tables back into check with Ve- windows and niches in the circular struc- nus’s observability. Here again, the inter- ture that aligned with Venus events such as nal mathematical structure of the intervals the planet’s northern extreme. Establish- suggests an independent applicability of ing an architectural connection between the correction intervals, not a serial one. the Caracol and Venus, Aveni then turned One final observation favors the new to the Dresden Codex. interpretation presented here. When we look at the graphical layout of the Preface, [As we have seen,] the Venus tables the 2 CF (8-day) correction interval is provide a means of relating ritual site placed underneath the interval for two un- function to observations of the planet corrected cycles, and the 3 CF (12-day) at about the time the Caracol was correction interval is placed directly below erected. … [I]t is possible that the as- the interval for three uncorrected cycles. tronomical observations delineated in The first correction “fixes” a projection the Venus table in the Dresden Codex forward of two full tables, while the second were collected by astronomers correction “fixes” a projection of three full perched in the observation chamber of tables. This is a graphical relationship to this tower and others like it in northern Page 24 that has no parallel in the tradi- Yucatan. (2001:275) tional interpretation. We will see here that the revised interpre- An Observational Hypothesis tation proposed in this paper more strongly We do not have to appeal only to an ele- supports Aveni’s assertion than the tradi- gant numerology here (though the Venus tional approach. Table scribe included plenty of it); by ap- If we take the Long Count anchor to plying the correction intervals to the dates the Table, 9.9.9.16.0 1 Ajaw 18 K’ayab, on Page 24, we encounter a very practical written on Page 24 as a historical anchor, source for the hypothetical observational then we can explore the application of the origin of the Venus Table. To see this pat- Corrected Venus Intervals in Long Count tern, we shift back to the observational time. For the first corrected projection: context of an astronomer of the Terminal Classic. 9.9.9.16.0 1 Ajaw 18 K’ayab + CVI1

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Figure 5. Structure 3C-15, or “the Observatory,” at Chich'en Itza, Yucatan.

= 9.9.9.16.0 + 5.5.8.0 + 4.12.8.0 low the Classic Mayan practice of record- = 9.19.7.14.0 1 Ajaw 18 Wo ing historical and/or ritual events related to the dedication of ritual architecture. This corrected anchor would have run for K’ak’ U Pakal K’awiil is named as the a full 37,960 days to end on: companion of several deities as well as mortal contemporaries in the inscriptions 9.19.7.14.0 1 Ajaw 18 Wo adorning the Monjas Structure, the Casa + 5.5.8.0 Colorada and the Caracol, all written dur- = 10.4.13.4.0 1 Ajaw 18 Wo ing what Nikolai Grube and Ruth Krochok (2007:229) have called the “epi- And for the second: graphic florescence” at Chich’en Itza. In the Caracol Panel, K’ak’ U Pakal K’awiil 9.9.9.16.0 1 Ajaw 18 K’ayab + CVI2 is referred to as the protagonist of an event = 9.9.9.16.0 + 5.5.8.0 + 9.11.7.0 occurring ‘on the seventeenth tuun of 1 = 10.4.6.13.0 1 Ajaw 13 Mak Ajaw.’ Since we have both Long Count dates and Short Count dates at Chich’en The latter 13 Mak date is the anchor for Itza, K’ak’ U Pakal K’awiil’s event can be the table that we have running the full converted to 10.2.17.0.0 with confidence length of Pages 46 through 50 of the Dres- (Aldana 2011). This date is right in the den Codex. This table would have ended middle of the dates implied by the Correc- on 10.4.6.13.0 + 5.5.8.0 = 10.9.12.3.0 1 tion Intervals as we have recovered them. Ajaw 13 Mak. These Long Count dates Returning to the Long Count dates in easily fit within the use period of the Cara- the Venus Table, the difference between col at Chich’en Itza. the end date of the first correction and the Specifically, there is evidence concern- beginning date of the second correction ing the relationship between the manu- are not far apart. script and the building that went un-no- ticed in Aveni’s study. The Caracol itself 10.4.13.4.0 - 10.4.6.13.0 = 6.9.0 contains hieroglyphic inscriptions that fol-

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Figure 6. Three first morning visibility events occurring on 1 Ajaw dates, observable during the Terminal Classic.

It is not just that this interval is small and first morning visibilities of Venus during represents an overlap between one table the Terminal Classic at Chich’en Itza. If and a subsequent one. This interval (6.9.0 so, then most of what is written on Page 24 = 2,340) is the Correction Factor that we follows directly. That is, if we assume that saw above, utilized in all Diophantine 9.9.9.16.0 was a first morning appearance Equations as Lounsbury showed in 1992. observed somewhere in the Mayan region In other words, according to the revised in- and maintained in textual records, then we terpretation presented here, the basic fac- get the progression of Venus fmvs shown tor used to construct the Correction Inter- in Figure 6 based on a 583.9214 synodic vals on Page 24 would have dropped out of period. (Notice that the variability is purely the observations made by an astronomer for illustrative purposes. Without a calen- during the Terminal Classic. Rather than dar correlation, and without meteorologi- propose this as some part of a proof for my cal data, actual visibility is purely hypo- interpretation, I suggest that this provides thetical.) a window into the construction of the Ve- The three single data points in Figure nus Table itself. 6 are those 1 Ajaw dates falling near a first Specifically, let us assume that the morning visibility event.9 Notice in Figure early Long Count anchor on Page 24 was 6 that the first fmv (at the 183rd VR after preserved as an accurate historical record 9.9.9.16.0) occurred only 2 days from an by a Postclassic astronomer and that s/he idealized projection of a zero-error fmv was viewing the night sky and recording event on 9.9.9.16.0. Two days of error

9 One Ajaw dates are clearly central to the con- 1972:63). Every interval on Page 24 is con- ceptualization of the Venus Table (Thompson nected to or intended to retrieve a 1 Ajaw date.

Aldana, G. 71 over 292 years is certainly noteworthy. 9.9.9.16.0 1 Ajaw 18 K’ayab Given the variability of Venus fmv for any + 3 x 5.5.8.0 given Venus Round, it is indeed possible = 10.5.6.4.0 1 Ajaw 18 K’ayab that this 1 Ajaw date fell precisely on an fmv event. Regardless, it would have been 10.4.6.13.0 1 Ajaw 13 Mak ideal for an interest in proximity to 1 Ajaw = 9.9.9.16.0 1 Ajaw 18 K’ayab dates. + 3 VGC – 3 CF Whether it was exactly on, or even if it = 9.9.9.16.0 1 Ajaw 18 K’ayab was off by a few days, the astronomers + 1 VGC + 1 CVI2 would have recognized an opportunity. If they witnessed and recorded this event, 10.4.13.4.0 1 Ajaw 18 Wo they would have found two 1 Ajaw fmv = 9.9.9.16.0 1 Ajaw 18 K’ayab events separated by 106,860 days (= + 3 VGC – 2 CF 10.4.6.13.0 – 9.9.9.16.0). Remaining vigi- = 9.9.9.16.0 1 Ajaw 18 K’ayab lant for the next four Venus Rounds (or + 2 VGC + 1 CVI1 about 7 years) would have resulted in a tre- mendous payoff. And so: The fmv of the 187th Venus Round (after 9.9.9.16.0) would have fallen only 7 9.19.7.14.0 = 10.4.13.4.0 1 Ajaw 18 Wo days (or as few as 4 days) from another 1 – 5.5.8.0 Ajaw date. When we consider this progression relative to Page 24, we recognize 9.19.7.14.0 1 Ajaw 18 Wo that these are not “just any” 1 Ajaw dates. = 9.9.9.16.0 1 Ajaw 18 K’ayab The 183rd VR fell on 1 Ajaw 13 Mak; the + 2 VGC – 2 CF 187th on 1 Ajaw 18 Wo. Both of these Cal- = 9.9.9.16.0 1 Ajaw 18 K’ayab endar Rounds are highlighted within the + 1 VGC + 1 CVI1 Venus pages as we saw in the traditional interpretation of the correction mecha- The derivation of all of the material on nisms. More importantly, though, is the Page 24 would have dropped out of these recognition that these two 1 Ajaw dates (13 two observations, seven years apart, along Mak and 18 Wo) are separated by 2,340 with one historical record. Furthermore, if days—the Correction Factor, noted above, s/he had access to other historical records built into all of the Correction Intervals as of observed fmv (or fev), they would have noted by Lounsbury (1992). Even more fit within tolerance to the back-projected suggestive is that the 18 Wo date is two of model this pattern produced, as shown in these 2,340-day intervals from the next 1 Figure 7. In this way, the derivation of the Ajaw date near an fmv, which fell on 18 Correction Factor and the procedure for K’ayab. correcting the Venus Table over long This bears emphasis. The Correction spans of time in the Dresden Codex may Factor and two of the three Correction In- reflect a cross-cultural analogue to Hippar- tervals as well as three of the four Calendar chus’s dependence on his Chaldean prede- Round dates all play roles in this one win- cessors in his recognition of precession. dow of hypothetical observations during The 1 Ajaw 18 Wo date would then the early part of the eleventh baktun. have been recognized as 2/3 of the way An attentive astronomer could have from 1 Ajaw 13 Mak to 1 Ajaw 18 K’ayab. put this all together. It is again straightforward to have recog-

JAC, Vol. 1, No. 1, 2016 72 Figure 7. Reconstructed first morning visibilities of Venus for comparison against historical records.

nized this as a possible prior correction: 1 Lounsbury 1983:13). It also takes the cor- VGC – 2 CF should have corrected a pro- rection intervals as serially applied. This jection forward of 2 VGCs. And herein paper takes the anchor as a historical rec- lies the logic that reflects the pattern noted ord and the Correction Intervals as inde- above. The two ratios of Correction Inter- pendently applied to the base date. The vals to full Venus Great Cycle projections archaeological record corroborates the lat- are equal. ter two suppositions. The only explicit Venus record we 1VGC – 2 CF to 2 VGC have from the Classic period is that of Co- = 2 VGC – 3 CF to 3VGC pan Structure 10L-11, which records a Ve- = 137/146 nus /k’al/ event on 9.15.15.12.16 5 Kib 9 Pohp. As noted elsewhere (Aldana 2011; With one historical record and direct ob- Fuls 2008) this event fits extremely well as servations of Venus over less than 10 years, an historical record of fev when we assume the internal logic of Page 24 can be recon- (against the traditional interpretation) that structed. The implication is that the Venus 9.9.9.16.0 was an accurate record of fmv. Table captures and maintains an astro- As such, it also suggests that the Venus nomical innovation – the discovery of the Round was partitioned into the sub-peri- correction factors and their utility for Cor- ods reflected in the Dresden Codex Venus rected Venus Intervals. Table by the Late Classic at Copan. The traditional approach, however, Moreover, the 9.15.15.12.16 Venus event takes the anchor not as a historical record, was itself a historical record for the ruler but as a numerological contrivance in er- who included it in his textual patronage. ror by 16 days (Thompson 1972:63; Yax Pahsaj Chan Yopat used this Venus

Aldana, G. 73 event as an anchor to his own ritual event continuity between the Venus Table Long occurring 40 years later (Schele and Count dates and the Long Count of the Freidel 1990; Aldana 2011). By direct Classic period. These dates make a com- analogy, the 9.9.9.16.0 anchor to the Ve- pelling case that the long-term correction nus Table may have been a historical rec- of the Venus Table was derived at ord. Chich’en Itza during the Terminal Classic Finally, the traditional interpretations at the Caracol, perhaps even under K’ak’ put the effective use of the uncorrected ta- U Pakal K’awiil’s initiative. bles up through anchors at 10.5.6.4.0 or 10.10.11.12.0. They then call for cor- The Third Correction Interval rected tables starting at 10.9.18.12.0 The reconstruction proposed above is (Lounsbury and Thompson) or 10.15.4.2.0 driven by the interpretation of the middle (Bricker and Bricker). And they place the two correction intervals on Page 24. The 13 Mak anchor at 10.14.17.11.0 (Louns- third correction interval in that row differs bury and Thompson) or 11.0.3.1.0 significantly from these in size; it is almost (Bricker and Bricker). These traditional 3 times the size of the 2nd correction inter- models, therefore, put the 13 Mak dates af- val (~506 years vs. ~188 years). In fact, ter 10.15.0.0.0, or up to 12 k’atun (~240 this makes sense relative to another feature years) after the Caracol was dedicated and of the manuscript that has been long rec- being used at Chich’en Itza. Even though ognized. The Dresden Codex is clearly a Aveni suggests that the Table was devel- copy (and probably a compilation) of ear- oped at Chich’en Itza, the corrections were lier manuscripts (Thompson 1972:19). As not utilized in the traditional interpreta- all scholars studying the table have recog- tions until over a century after Chich’en nized, the 13 Mak version of the Venus Itza was abandoned. Here, though, I sug- Table—the one taking up pages 46-50— gest that the 13 Mak table was derived and was not the one current when the manu- implemented between 10.4.6.13.0 and script was copied (Thompson 1972:15-16; 10.4.13.4.0, within 20 years of Chich’en Bricker and Bricker 2007:116). The re- Itza’s “epigraphic florescence,” and that it construction proposed here speaks to the was created to fit their own observations inherited 13 Mak Venus Table’s extension to with historically recorded events. a later time. In other words, the Correc- The upshot is that rather than the am- tion Factor and the Corrected Venus In- biguous placement of the Dresden Codex tervals had already been discovered hun- Venus Table somewhere in the very late dreds of years before the scribe copied the Postclassic, the interpretation of Page 24 table into the manuscript that we now call presented in this essay puts its formulation the Dresden Codex. Again, this re-copy- within 25 years of the dedication of the ing was probably not a Postclassic innova- Caracol. Twenty-five years of observation. The Copan record shows that Venus tions from the same building amounts to events were preserved for later reference at three full 8-year cycles of Venus, or three least since the Late Classic period. rows of the Venus Table on Pages 46-50. As noted above, the third correction Notice also that, as opposed to the tradi- interval only produces a correction of 8 tional approach, this reconstruction of fit is days, but it approaches 5 Great Cycles in entirely independent of the Calendar Cor- scope. With each Great Cycle introducing relation Constant chosen. It requires only 5 days of error, a correction much closer to Long Count dates and the assumption of 25 days would have been necessary. On

JAC, Vol. 1, No. 1, 2016 74 the other hand: tween the original anchor 9.9.9.16.0 and this historical date would then just have to 9.9.9.16.0 1 Ajaw 18 K’ayab + CVI3 be doubled to arrive at the 10.19.16.10.0 = 9.9.9.16.0 + 1.5.14.4.0 date directly observed. S/he could then = 10.15.4.2.0 1 Ajaw 18 Wo have used the Table exactly as previously written with only a shift of the 365 Day The latter is a date that can also be derived Count to a base of 3 Xul. directly from one of the observed fmvs at Understood in this way, the scribe of Chich’en Itza: the late Postclassic copied the necessary material from the Table’s first correction, 10.4.13.4.0 1 Ajaw 18 Wo + 2 x 5.5.8.0 and then provided the interval necessary to = 10.15.4.2.0 1 Ajaw 18 Wo make it useful for her/his contemporary times. Why did s/he not reconstruct the If we assume a similar method for the 3 table entirely rather than copy the 13 Mak Xul base shift as that for the 13 Mak shift, table for Pages 46-50? In fact, s/he did. then the utility of this relationship and that The rows at the bottom of these five pages of the third interval fall out straightfor- provide the haab’ shift required to go from wardly. 13 Mak to 3 Xul. The 260-day Count That is, if we assume that a late Post- dates do not have to change since the 1 classic astronomer observed an fmv near Ajaw anchor is preserved regardless of 10.19.16.10.0 1 Ajaw 3 Xul, s/he could shift. Furthermore, I have proposed else- have made sense of it in accord with the 13 where that the verb accompanying these Mak table s/he inherited. If the late Post- lower 3 Xul rows is *tzekya’n as ‘to be cor- classic astronomer possessed a manuscript rected’ (Aldana 2011:46). That proposal describing the observations from the Car- clearly gains currency given the recon- acol at Chich’en Itza, s/he could have rec- struction of the full table’s implementation ognized that the interval from 9.9.9.16.0 to as presented here. one of the recorded data points, One complication with this proposal is 10.4.13.4.0 produced a difference of that 10.19.16.10.0 1 Ajaw 3 Xul is 13 days 15.3.6.0. This interval then added to from an idealized projection of synodic pe- 10.4.13.4.0 yielded the fmv that s/he ob- riods from 9.9.9.16.0 1 Ajaw 18 K’ayab. served: Thirteen days may test the credibility of the interpretation for some readers. In- 9.9.9.16.0 1 Ajaw 18 K’ayab deed, 13 days would almost certainly be + 15.3.6.0 excessive if the records came from obser- = 10.4.13.4.0 1 Ajaw 18 Wo vations at the same structure or even the + 15.3.6.0 same city. But here we are considering: an = 10.19.16.10.0 1 Ajaw 3 Xul. early Classic record at 9.9.9.16.0 that most likely came from observations at a south- In other words, if the late Postclassic as- ern lowland city; an early Postclassic rec- tronomer observed an fmv near ord from Chich’en Itza in the northern 10.19.16.10.0 1 Ajaw 3 Xul, s/he could Yucatan peninsula; and then a late Post- have consulted the manuscript in her/his classic record from somewhere else in the possession to find that 10.4.13.4.0 1 Ajaw Yucatan peninsula from an unknown 18 Wo was also close to a historically ob- structure. Given the tolerances on each of served fmv. The correction interval be- these observations, and given the emphasis

Aldana, G. 75 on ritual events—not ephemeris accu- Acknowledgments racy—13 days of difference becomes rea- This essay in early draft form benefitted sonable for fmv events near 1 Ajaw dates from comments provided by Edwin Barn- separated by over 500 years. hart and Harold Green. Bruce Love, Marc Zender and George Stuart contrib- Conclusion uted insightful commentary when a ver- I have argued elsewhere that the recon- sion of this material was presented at the struction of the correction procedure for “Maya at the Playa” conference in Florida. the Dresden Codex Venus Table by mod- The article form of the argument was then ern scholarship has been unduly burdened edited based on discussion with the partic- by an interest in the correlation of the Ma- ipants at Oxford X. Finally, I am grateful yan Long Count calendar with Christian to two anonymous reviewers, who pro- chronologies (Aldana 2010, 2011). This vided useful suggestions in the final peer essay adds to that study the complications review before publication. that arise when we base our expectations for ancient science on modern conceptual- References Cited izations of accuracy. From the perspective Aldana, G. of matching up cross-Atlantic chronolo- 2002 “Solar stelae and a Venus window: sci- gies, these interests have been extremely ence and royal personality at Late Classic useful. But it has also left some basic com- Copan,” in Archaeoastronomy Supplement to the Journal for the History of Astronomy, no. 27 plications unconsidered. (JHA xxxiii), pp. S30-S50. In this essay we have prioritized the in- 2003 “K’uk’ulkan at Mayapan,” in Journal for ternal logic of the historical manuscript it- the History of Astronomy, xxxiv, pp. 33-51 self over its outside utility. In doing so, we 2007 The Apotheosis of Janaab’ Pakal: Science, have had to go against the traditional in- History, and Religion at Classic Maya Palenque. terpretation of Page 24 and the conven- University Press of Colorado, Boulder. tional wisdom supporting the currently ac- 2008 “An Oracular Hypothesis” Paper pre- cepted calendar correlation. By suspend- sented at the 71st Annual Meeting of the ing the collective disbelief in the possibility Society of American Archaeology. of an alternative, this investigation has pro- 2010 “The Maya Calendar Correlation Problem,” in Calendars and Years, Volume 2. duced an interpretation of the correction J. Steele (editor). Oxbow Press, Oxford, mechanism for the Dresden Codex Venus pp. 127-179. Table that makes better use of what is ac- 2011 Tying Headbands or Venus Appearing: new tually written in the manuscript, and pro- translations of /k’al/, the Dresden Codex Venus duces a much stronger chronological link pages, and royal ‘binding’ rituals. B.A.R. Inter- to the manuscript’s affiliation with the Car- national Series. Archaeopress, Oxford. acol at Chich’en Itza. Although we must 2015a “An Oracular Hypothesis: the Dres- sacrifice the extreme accuracy for which den Codex Venus Table and cultural the document (and Mayan culture) is translations of science,” in Archaeoastronomy known, we generate an interpretation that and the Maya. G. Aldana and E. Barnhart (editors). Oxbow Books, Oxford. is more productive in interpreting the ex- 2015b “14C and Maya Long Count Dates: us- isting record and that provides new ave- ing Bayesian modeling to develop robust nues for further research. Moreover, it ar- site chronologies,” in Archaeometry, DOI gues for the recovery of an ancient Mayan 10.1111/arcm.12200 astronomical discovery at Chich’en Itza. Aveni, A. F.

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Aldana, G.