Astronomical Implications of Maya Hieroglyphic Notations at Xultun

IntroductionRecently, we' reported on the existence of a group of numerically related texts painted on the walls of a room in an early ninth-century A.D. residential house (structure 10K-2) in the Classic Maya city of Xultun, Guatemala. The texts, carefully executed in fine black line over colourful underlying murals pertaining to royal rituals, with which they appear to have no apparent connection, consist of a 162-lunar synodic month semester table and a group of four relatively large day tallies, ranging in length between 935 and 6704 tropical years, used to calculate commensurations among important calendrical and astronomical cycles. Though executed in a different medium, the numbers resemble those found in the codices, or bark paper books, dated to the late fifteenth and early sixteenth centuries; therefore the major significance of the discovery is that it pushes back by several centuries the archaeological evidentiary baseline for sophisticated Maya astronomical computations.Here we analyse the aforementioned inscriptions in detail not permitted, for want of space, in our original report. We also describe and interpret additional texts discovered since the submission of that report. We refer to three text areas: Area A, near the middle of the East Wall of Structure 10K-2; Area B, immediately to the left of Area A; and Area C, on the northeast corner of the north wall2 (Figure 1).Area A: A Lunar Semester TableA neatly composed, but badly eroded, 5 cm wide by 48 cm long text located in the middle of the east wall, about 40 cm above the level of the raised floor, consists of 27 columns of black dot and bar numerals. Each column is topped by one of three alternating forms of a glyph (Glyph C) identifiable with that used on monumental inscriptions to record moon positions in a semester cycle.3 It has long been known from studies of the monumental inscriptions that the Maya grouped lunar synodic months in semesters, or lunar half-years, consisting of six lunar synodic months made up of combinations of 29 and 30 days, totaling 177 (or 178) days.As first recognized by one of the authors (Stuart), the readable portion of the text below each of the glyphs leaves little doubt of its lunar function. The last two (the 26th and 27th) columns read 4606 (12.14.6) and 4784 (13.5.4), respectively, the difference between the two being 178 days. Moreover, subtracting 177 (178) from the 26th entry, one arrives at 4429 (4428) or 12.5.9 (12.5.8), which is consistent with the readable portion, 12.5.(7), of entry 25. Fragments of the remainder of the text are consistent with its being a table of 27 lunar semesters, 22 consisting of 177 days and five (including the 26th) of 177, totaling 4784 days,4 or 162 lunar synodic months. The implied average value of the lunar synodic month is 4784 days, or 29d.530864. This is a remarkable 0d.000278 short of the value ofthat period for epoch 800 A.D. (29d.530586).5 Absent the five days added in the 178-day entry columns, the time averaged synodic period would have produced a much less accurate, though nevertheless still impressive, lunar synodic period of 29?500000, 0d.030586 short of the epoch 800 A.D. value.The restored version of the Xultun Lunar Semester Table (hereinafter LST) is given in Figure 2. This text, the only one of its kind, surely functioned as an instrument to calculate, either backward or forward, the position of a particular moon in a Lunar Series statement. Such statements are found on numerous monumental inscriptions. They consist (usually) of the name of the semester in a trimester system, Jaguar Lord Semester (columns A, D, G, ... of Figure 1), Death Skull Semester (columns B, E, H, . . .), and Female Moon semester (columns C, F, I, . . .), followed by the numbered moon (1-6) in that particular semester, along with the age (phase) ofthat particular moon, usually measured from new moon = 0d; e.g. in Column B: Skull semester, fourth moon, day 2 (a thin waxing crescent, visible low in the west after sunset). …