Astronomical Implications of Maya Hieroglyphic Notations at Xultun

Saturno W. Stuart D. Aveni A. Rossi F. , “Ancient Maya astronomical tables from Xultun, Guatemala”, Science, ccxxxvi, no. 6082 (2012), 714–17.

Here we adopt the locational nomenclature employed by Zender M. Skidmore J. , “Unearthing the heavens: Classic Maya murals and astronomical tables at Xultun, Guatemala”, Fig. 4 (2012 mesoweb.com/reports/Xultun.pdf). It differs from our convention by renaming our original Area B ( Saturno , op. cit. , Fig. 1), Area C and calling a text we had previously recognized but did not comment upon, Area B.

Teeple J. , “Maya astronomy”, Contributions to American archaeology , i/2 (Carnegie Institution of Washington, Washington, DC, 1930); Schele L. Grube N. Fahsen F. , Texas notes on Precolumbian art, writing and culture , no. 29 (University of Texas at Austin, 1992); Linden J. , “The Deity Head variant of Glyph C”, Eighth Palenque Round Table , ed. by Macri M. McHargue J. (Pre-Columbian Art Research Institute, San Francisco, 1996), 343–56.

Milbrath S. notes that Jupiter (synodic period = 398^d.9) may be involved here as well; thus 12 × 398^d.9 = 4786^d.8, which errs by three days in 13 years. While there is no known mention of Jupiter in the codices, it has been implicated in calculations on monuments (cf. Milbrath S. , Star gods of the Maya (Austin, 1999), 233–40).

For epoch-dependent values of astronomical periodicities we employ the interpolation formulae given in Meeus J. , Astronomical algorithms (Richmond, 1999). Relevant quantities dealt with in this paper would be: .

Cf. Linden , op. cit. (ref. 3).

For a detailed discussion of the presentation of these intervals, see Bricker H. Bricker V. , Astronomy in the Maya codices (Philadelphia, 2011), 258–9.

Teeple , op. cit. (ref. 3), 67.

That is, 11 × 7200^d (the fourth unit in the Maya Long Count). For a review of other possible Maya lunar groupings, see Justeson J. , “Ancient Maya ethnoastronomy: An overview of hieroglyphic sources”, World archaeostronomy, ed. by Aveni A. (Cambridge, 1989), 83–91.

We owe the foregoing explications to Linden, op. cit. (ref. 3), 353–4.

For a review of the evidence, see Aveni A. Skywatchers: A revised and updated version of Skywatchers of Ancient Mexico (Austin, 2001), 200–5.

We are indebted to V. and H. Bricker for pointing out this relationship.

Bricker Bricker , op. cit. (ref. 7).

The Octaeteris, meaning eightfold or octal, commensurates five Venus synodic cycles, 99 lunar synodic months, and eight tropical years: .

Bricker V. Bricker H. , “Some alternative eclipse periodicities in the Maya codices”, paper presented at Society of American Archaeologists Meeting, Memphis, TN, April 2012 (in press).

Or perhaps, more appropriately, 69 × 173.3098 (epoch 800 a.d.) = 11958^d.3760.

For an extended discussion of this number, see Lounsbury F. , “Maya numeration, computation, and calendrical astronomy”, Dictionary of scientific biography , xv, suppl. 1, 759–828, and Bricker Bricker , op. cit. (ref. 7), 76.

Lounsbury , op. cit. (ref. 17), 787.

Bricker Bricker , op. cit. (ref. 7), 235ff, 330–1.

So-called aberrant multiples (in days) in the codices include 4 × 780 + 260, 16 × 780 + 2 × 260, 39 × 780 + 2 × 260, 89 × 780 + 9 × 260, and 93 × 780 + 260 in the Mars Table (Bricker and Bricker, op. cit. (ref. 7), 370; 31 × 11960 + 260 in the Eclipse Table (ibid., 253); 15 × 584 + 340, 57 × 584 −8, 118 × 584 −12, and 317 ×584 − 8 in the Venus Table (ibid., 169); and 32 × 1820 − 80 and 4 × 1820 − 163 in the Lower Water Table (ibid., 417).

We are indebted to MacLeod B. Kinsman H. (Aztlanlists 17 May 2012), Kinsman H. (p.c. to MacLeod B. ), and Drew H. (p.c. to Saturno W. ) (19 May 2012) for pointing out this relationship.

For other less likely astronomical connections with this number, cf. Thompson J. E. S. , Maya hieroglyphic writing: An introduction (Washington, DC, 1950), 215. MacLeod notes that Thompson had remarked (p. 214) that “only once every 63 CR will a day with a coefficient of 1 also mark the start of the 819^d cycle. The fact that the first day with a coefficient of 1 before 13.0.0.0.0 4 Ahau 8 Cumku is a base in the 819-day cycle argues strongly for that count being primarily ritualistic”. Thompson's study was based on the analysis of four DNs in monumental inscription dates from Quirigua and Yaxchilan that all possessed 819 as the highest common factor. MacLeod concludes that the following property, a unique rationale for interval A: , which yields the well known equation 4 × 819^d = 9 × 364^d, is the lowest common multiple of 819 and the CR. She further posits that the tzolkin date at the top of Interval A must be 1 Kaban (not Kimi), which is the base date of the 819-day count that commenced three days before the present creation epoch 12.19.19.17.17 1 Kaban 5 Cumku.

Drew (op. cit., ref. 21) also deduces a pair of hypothetical cycles that commensurate, respectively, with LRs C and D, those being (underlined). He suggests that it may be that the lack of abundance of data explains why these cycles have not turned up before, though we think there may be evidence that one of them actually has. Thus, the first of these two cycles is close to the 1210^d.75 cycle commensurating lunar synodic (41) and draconic (44.5) months cited as among those most likely to have been used to predict eclipses (cf. Aveni, op. cit. (ref. 11), Table 5). The number 1211 is prominently featured in the Dresden Eclipse Table. It marks the close of the sixth semester of that table and its second, third, fourth, and sixth multiples are among other cumulative intervals written in the table.

Noted by MacLeod B. (p.c. 20 May 2012) and haecceities.wordpress.com/2012/05/11/2012-the-xultun-discovery-in-swedishnews/.

Aveni A. , “Maya numerology”, Cambridge archaeological journal, xxi (2011), 187–216.

We are indebted to Jacobs J. Q. (p.c. 13–14 June 2012) for first noting these simple ratios among the Xultun LR numbers. Expressed in difference form, the way the Maya would likely have thought of it, all the near commensurations yield the number 56940 (cf. Table 1, entry (12)); for example, C-2A = 56940, etc. This certifies the centrality of this particular number in setting up the array.

We are indebted to Bricker V. Bricker H. (famsi.org/pipermail/aztlan/2012-June/012227 and June/012235) for pointing this out.

Justeson J. , “A decipherment of Epi-Olmec writing”, Science, cclix (1993), 1703–11.