Monumental Inscriptions and the Observational Basis of Maya Planetary Astronomy

Thompson J. E. S. , Commentary on the Dresden Codex, a Maya hieroglyphic book (Philadelphia, 1972), 23.

Proskouriakoff T. , “Historical implications of a pattern of dates at Piedras Negras, Guatemala”, American antiquity, xxv (1960), 454–75.

Berlin H. , “El glifo ‘Emblema’ en las inscriptiones Mayas”, Journal de la Société des Americanistes (Paris), n.s., xlvii (1958), 111–19.

Marcus J. , Ancient Mesoamerican writing (Princeton, 1992).

This point is made in a more general context by Ruggles and Saunders in Ruggles C. L. N. Saunders N. J. , “The study of cultural astronomy”, in idem (eds), Astronomies and cultures (Boulder, Col., 1993), 1–31.

Closs M. , “Some parallels in the astronomical events recorded in the Maya codices and inscriptions”, in The sky in Mayan literature, ed. by Aveni A. (New York, 1992), 133–47.

E.g., Bricker V. Bricker H. , “A method for cross-dating almanacs with tables in the Dresden Codex” in Aveni (ed.), op. cit. (ref. 6), 43–86.

See Aveni A. F. , Skywatchers of ancient Mexico (Austin, 1980), 89. Schaefer's theoretical models give 251.6, 69.4, 250.6 and 11.2 for these periods ( Schaefer B. E. , “Heliacal rise phenomena”, Archaeoastronomy (supplement to Journal for the history of astronomy), no. 11 (1987), S19–34). But cf. below and ref. 35.

Gibbs S. , “Mesoamerican calendrics as evidence of astronomical activity”, in Native American astronomy, ed. by Aveni A. (Austin, 1977), 21–35.

Justeson J. , “Ancient Maya ethnoastronomy: An overview of hieroglyphic sources”, in World archaeoastronomy, ed. by Aveni A. (Cambridge, 1989), 76–129, p. 94; Aveni A. , “The moon and the Venus table in the Dresden Codex: An example of commensuration in the Maya calendar”, in The sky in Mayan literature, ed. by Aveni A. (Oxford, 1992), 87–101.

Lounsbury F. , “The base of the Venus Table of the Dresden Codex and its significance for the calendar-correlation problem”, in Calendars in Mesoamerica and Peru: Native American computations of time, ed. by Aveni A. Brotherston G. (British Archaeological Reports, International Series, no. 174; Oxford, 1983), 1–26.

Therefore, it is incorrect to say, as we often read in textbooks, that the Maya could follow Venus to an accuracy of one day in five centuries. The written evidence allows us a precision of only four days per Venus round (65 Venus rounds = 103.93 tropical years). Moreover, we must remember that this conclusion is heavily based on interpretations of the correction table on p. 24 of the Dresden Codex, and not upon any explicit statement.

But see ref. 49 below.

See e.g. Alexander H. , “Celestial links to ancestors: A pattern analysis of celestial events for twelve dates recorded on Tikal Stela 31”, U. Mut Maya, iv (1992), 48–60.

Schele L. , Maya glyphs: The verbs (Austin, 1982), Chart 10.

Closs , op. cit. (ref. 6).

Schele L. Freidel D. , A forest of kings: The untold story of the ancient Maya (New York, 1990).

For a study of its propagation across Mesoamerica, see Baird E. , “Star and war at Cacaxtla”, in Mesoamerica after the decline of Teotihuacan A.D. 700–900, ed. by Diehl R. Berlo J. C. (Dumbarton Oaks, Washington, 1989), 105–22; and Carlson J. B. , “Venus-regulated warfare and ritual sacrifice in Mesoamerica”, in Ruggles Saunders (eds), Astronomies and cultures (ref. 5), 202–52.

Schele L. Miller M. , The blood of kings (Fort Worth, 1986), chap. 5.

Schele Freidel , A forest of kings (ref. 17), 444–7.

See for example Freidel D. Schele L. , Maya cosmos (New York, 1993); Wertime R. Schuster A. , “Written in the stars”, Archaeology, xlvi/4 (1993), 27–32.

For a summary of the correlation problem and a full discussion of the justification of the use of the ‘283’ correlation number in the present context see Aveni , Skywatchers of ancient Mexico (ref. 8), chap. 4, pp. 204–10, Appendix A.

Cf. refs 8 an.

Aveni , op. cit. (ref. 10).

Oppenheim Leo A. , “Man and nature in Mesopotamian civilization”, Dictionary of scientific biography, xv, 634–66, p. 643.

E.g., Tuckerman B. , Planetary, lunar and solar positions, 601 bc to ad 1649 (2 vols, Philadelphia, 1964).

The celestial latitude of Venus, which can be as great as 9°, is often not taken into account in the determination of the elongation of the planet.

Cf. Aveni , Skywatchers of ancient Mexico (ref. 8), chap. 5.

Three of the events fall in the overlapping time zone between Last PM and First AM and can be counted either way. We have chosen the phenomenon closest to the actual event.

Whether the Dresden Venus Table might be propagating a category of Venus observation that had been more readily accessible in earlier times awaits investigation.

Šprajc I. , “Venus and Temple 22 at Copan revisited”, Archaeoastronomy [bulletin], x (1992), 88–97; “The Venus-rain-maize complex in the Mesoamerican world view, Part I”, Journal for the history of astronomy, xxiv (1993), 17–70; “Part II”, Archaeoastronomy (supplement to Journal for the history of astronomy), no. 18 (1993), S27–53. Having read and commented on earlier drafts of this paper, Ivan Šprajc (personal communication, 9 March 1991) calculated the mean arcus visionis (the sub-altitude of the sun when Venus lies at the astronomical horizon) for a sample of dates in Table 1 for first evening appearance. He obtained a result of 5°.84 and noted that this is surprisingly close to Schoch's limit of 5°.8 ( Schoch C. , “The ‘arcus visionis’ of the planets in the Babylonian observations”, Monthly notices of the Royal Astronomical Society, lxxxiv (1924), 731–4). This result, he believes, strengthens the notion that first evening star appearances were specifically being recorded by the Maya.

Closs M. Aveni A. Crowley M. , “The planet Venus and Temple 22 at Copan”, Indiana ix (1984), 221–47.

Larios R. Fash W. , “Architectural history and political symbolism of Temple 22, Copan”, paper presented at 7th Mesa Redonda de Palenque, 1988.

Baudez C. , “Archaeoastronomy at Copan and elsewhere: An appraisal”, Indiana, xi (1987), 63–71. Baudez's objections should have been cited explicitly in an earlier paper on Venus observations presented at the Sixth Mesa Redonda de Palenque ( Aveni A. , “The real Venus-Kukulcan in the Maya inscriptions and alignments”, Sixth Palenque Round Table, 1986, ed. by Robertson Greene M. Fields V. M. (Norman, Okla., 1991), 301–21). We apologize for this oversight. A reply to his interpretation is in press ( Aveni A. Closs M. Hartung H. , “A reply to Baudez' ‘Archaeoastronomy at Copan and elsewhere: An appraisal’”, Archaeoastronomy [bulletin], to appear).

The sum of the averages was 584^d.80, surprisingly close to the long term average of 583^d.92. The average interval of AM/PM appearance was 267^d.3, PM Last to AM First 7^d.2, and AM Last to PM First 43^d.0. Cf. 263^d, 8^d, 50^d respectively (cf. ref. 8 above).

Freedman D. Pisani R. Purves R. Adhikari A. , Statistics, 2nd edn (New York, 1991), 475–92; Studies in statistics, xix (1978), ed. by Hogg Robert V. , Preface, 66–106.

Biometrika tables for statisticians, ii, ed. by Pearson E. S. Hartley H. O. (Cambridge, 1976).

The standard deviation for GE to the other station intervals is much less than for MA to station intervals. This leads to a different set of Canonic Venus day numbers for MA and GE.

Table 1 dates: 1, 3, 5, 7, 14, 16, 20, 32, 36, 37, 42, 44d, 63, 65, 78, 86.

Add Table 1 dates: 2, 22, 43, 47, 73, 80, 82, 87.

Add Table 1 dates: 6, 17, 60, 62, 69, 96, 98.

One MA value of 34° was deleted from the calculation for its high level of deviation from the other values. The next highest level for GE or MA in any of these groupings was 10°.

Table 1 dates 3, 5, 7, 14, 32, 36, 37, 42, 44d, 63, 65, 78, 86.

Bricker H. , “Nightly variation in Venus' position near times of greatest eastern elongation”, Paper read at Katun Mesa Redonda de Palenque, Palenque, Mexico, June 1993.

See ref. 8.

For the range of observable apparent magnitude (-2 to +6), the computed AV would range between 7° and 25°.

These positions were determined approximately on the Voyager Interactive Desktop Planetarium (TM), Version 1.2 (Carina Software, San Leandro, Calif.) and rechecked on a celestial globe using Tuckerman's tables (ref. 26).

For example, Lounsbury F. , “A Palenque king and the planet Jupiter”, in Aveni (ed.), World archaeoastronomy (ref. 10), 246–60.

Pages 43b-45b of the Dresden Codex have been interpreted as a Mars table (see most recently, Bricker V. Bricker H. , “The Mars Table in the Dresden Codex”, in Research and reflections in archaeology and history: Essays in honor of Doris Stone, ed. by Andrews E. W. , v (Middle American Research Institute, Tulane University, Publication no. 57 (1986)), 51–80), though the text follows a format quite different from the Venus Table and has not been as generally accepted as an astronomical device as its more famous counterpart. The synodic period, 780^d, is segmented into 10 station intervals of 78 days pivoted about the average number of days between conjunctions and stationary points of Mars on its orbit.

What are the observational limits for the detection of retrograde motion? For Saturn, the slowest moving planet, around opposition it is easy in our view to detect a motion of 0°.35. It takes an average of 20 days for the planet to move this far; but detection would be extremely difficult at about 0°.05 (about 1/10 of a lunar disk — Average about 3 days). For faster Jupiter, motion near the stationary points is easily detectable over a 15-day period, but becomes extremely difficult at about 2 days. For Mars, motions as large as 0°.35 can occur in less than 10 days and a careful observer would hardly pass a night, or two at the very most, without being able to see the planet move noticeably among the stars.

We determined that there is only a 2% probability that this could have occurred by chance. Extracting the tun and katun ending dates from the sample elevates Mars visible all night to 29% and invisibility to 10%; it leaves the figures for Jupiter and Saturn unchanged.

Aveni A. , Empires of time (New York, 1989), 127–35.

Dütting D. Aveni A. , “The 2 Cib 14 Mol event in the inscriptions of Palenque, Chiapas, Mexico”, Zeitschrift für Ethnologie, cvii/2 (1982), 233–58.

Schele Miller , op. cit. (ref. 19), 122.

MacLeod B. , “The crossing triplet: A reading for the Triad Introductory Glyph”, paper presented at 7th Mesa Redonda de Palenque, 1988.

The Naranjo Stela 23 event (#54 in Table 1), which has not been studied from an inscriptional/iconographic viewpoint in nearly as much detail as 2 Cib 14 Mol, was even more spectacular. On the night of 24 Jun 710 (the very date of an inscription in which Naranjo was said to have undertaken a military (?) action against one of its neighbours), Mercury, Venus, Mars, Jupiter and Saturn lay within a 6° circle and four of them (excluding Jupiter) were positioned inside a circle of radius 1°! Furthermore, this date was five days past June solstice (see Schele Freidel , A forest of kings (ref. 17), 191 and 460 for details). Also, no one has offered any inscriptional material to fit another spectacular planetary lineup that occurred in a.d. 828.

Justeson J. Kaufman T. , “A chronological framework for the decipherment of Epi-Olmec hieroglyphic writing” (unpublished ms., 1993).

Lounsbury F. , “Astronomical knowledge and its uses at Bonampak”, in Archaeoastronomy in the New World, ed. by Aveni A. (Cambridge, 1982), 143–68.

See for example Schele Miller , The blood of kings (ref. 19), 112.

Urrutia E. (ed.), Atlas climatológico de Guatemala (Guatemala City, 1964); World Weather Disc (Worldwide Airfield Summaries, Seattle, 1988).

One may reason that, because of the 5:8 commensuration between the Venus and seasonal years, Venus events ought to be fixed quite naturally within the seasons; however, over long periods of time Venus phenomena undergo a gradual backslide, about 4 days per century, through the seasons. Moreover, sizeable variations in the time of occurrence of Venus phenomena within a cycle, along with minor variations in celestial latitude, and terrestrial atmospheric and twilight conditions, play a profound role in altering precisely when the planet can appear, disappear or reach MA or GE. The result is that through time these events would meld into a general seasonal continuum. Therefore, we would attribute any skew in the seasonal histogram to culture rather than nature.

Justeson , op. cit. (ref. 10), 107 and 123, note 20.

Justeson , op. cit. (ref. 10).

Schele Freidel , A forest of kings (ref. 17).

Lounsbury , op. cit. (ref. 58).

Closs , op. cit. (ref. 6), 146.

While the precise predictive v. general arithmetic aspects of astronomical tables is not directly at issue in the present context, the debate about the function of astronomical tables in the codices is worth reviewing briefly. That the tables aim to predict an observable phenomenon is indicated in (a) Aveni's study (op. cit. (ref. 10)) in which it is shown that the Venus Table could have been used to forecast eclipses that were actually visible in real time between the seventh and the thirteenth century in Yucatan, (b) several works by the Backers in which iconographic parallels are employed to connect particular almanacs to the long count and thence directly to the Gregorian calendar (the icons refer to particular solstices, eclipses, haab stations, meteorological and agricultural events (for a summary see Bricker and Bricker, op. cit. (ref. 7)), and (c) the existence of aberrant numbers, in the codices which can be demonstrated to generate specific predictions. On the other hand the purely arithmetic nature of the tables can (but need not) be supported by (a) the fact that the eclipse table predicts eclipse stations, only a small percentage of which correspond to visible eclipses, and (b) the existence of interval sets that do not manifest reality but seem instead to be based upon purely numerological considerations, e.g. the grouping of lunar phase sets into 177, 177, 177, …, 148-day periods, the 5-month period (nearly) always coming before the picture (event) in the lunar table or the similar 19, 19, 19, 21-day grouping in the Mars table. A study of the numerical characteristics of all the interval sets (astronomical and non-astronomical) is currently under way by the first author.

Lounsbury , op. cit. (ref. 48).

Bricker Bricker , op. cit. (ref. 49).

Cf. Aveni , Skywatchers of ancient Mexico (ref. 8), chap. 5.

Aveni , Skywatchers of ancient Mexico (ref. 8), 85–86.

For a more detailed discussion of this term, see: Schoch , op. cit. (ref. 31); Huber P. , “Astronomical dating of Babylon I and Ur III”, Monographic journals of the Near East: Occasional papers, i/4; Weir J. D. , “The Venus tablets: A fresh approach”, Journal for the history of astronomy, xiii (1982), 23–49; Schaefer , op. cit. (ref. 8); and Purrington R. D. , “Heliacal rising and setting: Quantitative aspects”, Archaeoastronomy (supplement to Journal for the history of astronomy), no. 12 (1988), S72–85.