Astronomy in the Mexican Codex Borgia

Elizabeth Hill Boone's essay ‘Pictorial codices of ancient Mexico’ in The ancient Americas: Art from sacred landscapes, ed. by Richard Townsend (Chicago, 1992), 197–209, from which this quote (p. 197) was taken, offers an excellent overview of the basic form and content of these texts.

For a discussion of the many hypotheses concerning the origin of this ubiquitous cycle of Mesoamerican calendrics, see the summary in Aveni A. , Empires of time (New York, 1989), 200–2.

The commensuration principle is well known, especially in Maya calendrics, cf. Lounsbury F. , “Maya numeration, computation, and calendrical astronomy” in Dictionary of scientific biography, xv (1978), 759–818. The largest commensurate number to date that has surfaced in the codices includes common multiples of the Maya haab (Aztec = xiuhmolpilli) or 365-day year, the synodic periods of Mars and Venus along with other important calendrical numbers. The motive in creating such long periods seems to have been to discover a ‘like-in-kind’ to the historical date counted from it, via a pattern of backward projection of current events to prior events of some sort that fell in the same point in various cycles (ibid. 787). For example, the birth date of a ruler would be thought to share common attributes with those personages, e.g. the founder of the dynasty or gods of the previous era, born on the same date in an earlier cycle. The goal of such calculations was to lend legitimacy to the authority of the contemporary personage.

For a discussion of the purely numerological cycles often permuted with astronomical time periods, see the two-part article by Aveni A. Morandi S. Peterson P. , ‘The Maya number of time’, Archaeastranomy, no. 20 (1995), S1–28 and no. 21 (1996), S1–32.

As Thompson J. E. S. (A commentary on the Dresden Codex: A Maya hieroglyphic book (Philadelphia, 1972), 27) once put it: ‘The intention seems to be to take whatever periods in nature are involved and to keep on multiplying them until they are divisible by 260.’.

See e.g., Bricker V. , ‘The relationship between the Venus Table and an almanac in the Dresden Codex’, in New directions in American archaeoastronomy, ed. by Aveni A. (British archaeological reports, International Series no. 454; Oxford, 1988), 81–103 (D30c–33c; 25–28); Bricker V. Bricker H. , ‘Archaeoastronomícal implications of an agricultural almanac in the Dresden Codex’, Mexicon, viii (1986), 29–35; idem, ‘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 (Tulane: Middle American Research Institute Publ. no. 57; New Orleans, 1986), 51–80 (M43b–45b); idem, ‘The Seasonal Table in the Dresden Codex and related almanacs’, Archaeoastronomy, no. 12 (1988), S1–62 (D65b–69b); idem, ‘A method for cross-dating almanacs with tables in the Dresden Codex’ in The sky in Mayan literature, ed. by Aveni A. (Oxford, 1992), 43–86 (D65–69, 29b–30b, 40c–41c); idem, ‘Zodiacal references in the Maya codices’, ibid., 148–83.

Usually painted on animal hide, as opposed to bark paper for the Maya codices, these are considerably more numerous (numbering perhaps two dozen) than the mere three (or possibly four) Maya codices.

‘Maya almanacs focus on the specific activity being performed, while the Mexican ones focus on periods of time’ ( Boone , op. cit. (ref. 1), 201). See also Furst J. L. (‘The year 1 Reed, day 1 Alligator: A Mixtec metaphor’, Journal of Latin American lore, iv/1 (1978), 93–128, p. 97): ‘In fact, the Mixtec calendrical system is not set up to measure with any precision, long, or even short, intervals.’ Until recently the division of sections of the Maya codices into ‘almanacs’ or endless rounds of time (even if specific starting points are indicated) and ‘tables’ or ephemerides in the chronological sense (attributable to Thompson, op. cit. (ref. 5)) has been blurred by the discovery of almanacs that include embedded astronomical events such as heliacal risings of Venus and eclipses, cf. e.g. Bricker V. H. , op. cit. (ref. 6, 1998).

The periodic affinities are succinctly tabulated in the Ecological Linguistics summation sheet ‘Codices, attempted reconstruction of common prototype’ (Washington, D.C., 1995). The most thorough study of the Borgia Group is by Nowotny K. A. , ‘Tlacuilolli: Die Mexicanische Bilderschriften’, Iberoamerikanische Bibliothek, Monumento Americana 3 (Berlin, 1961); that of the Borgia itself, idem, Codex Borgia (Graz, 1976). Recent scholarship on the Borgia includes Diaz G. Rogers A. , The Codex Borgia: A full color restoration of the ancient Mexican manuscript (New York, 1995), with commentary by Byland B. Anders F. Jansen M. Reyes L. , Los templos del cielo y de la oscuridad: Oráculos y liturgia libro explicativo del llamado Codice Borgia (Madrid, Mexico City and Graz, 1993); and Sisson E. , ‘Recent Work on the Borgia Group of Codices’ Current anthropology, xxiv (1983), 653–6.

Seler E. , ‘Venus period in the picture writings of the Borgian Codex group’, Bureau of American Ethnology bulletin, no. 28 (1904), 355–91. There is some disagreement among scholars regarding the assignment of directions to the deities on B28. According to Seler, op. cit., and Byland (see ref. 9), the directions are: Lower right, north; upper right, west; upper left, east; lower left, east; and centre, centre. According to Anders (op. cit. (ref. 9)), they are east, north, west, south and centre, respectively.

Seler , op. cit. (ref. 10), 384–5.

See e.g. Thompson , op. cit. (ref. 5) and Aveni A. , Skywatchers of ancient Mexico (Austin, 1980), 184–95. The most recent glyphic decipherment associated with these pages appears in Scheie L. Grube N. , Notebook for the XXIst Maya Hieroglyphic Workshop, Mar. 8–9, 1997 (University of Texas at Austin, Department of Art and Art History, the College of Fine Arts and the Institute of Latin American Studies, 1997), 138–57. See also Davoust M. , Un nouveau commentaire du Codex de Dresde (Paris, 1997).

Canonic as opposed to actual. The mean synodic period of Venus, 583^d.92, produces a shortfall of 0^d.08 per canonic Venus period (hereinafter VP) or approximately 5^d.2 per 65 VP of the Dresden Table; however, this shortfall is remedied via the correction table on p. 24 of the codex, wherein one is instructed to deduct 4 (or occasionally 8) days from the tabulations at a point close to the completion of the 65 VP run (e.g. on the 57^th or 61^st VP), thus bringing the canonic Venus in closer temporal proximity to Venus in the sky; thus at 8 Ahau on p. 50 9D, one deducts 4 days and proceeds to the next line of the table, or p. 46 A10. The literature on proposed correction mechanisms is both vast and contentious. For an unbiased summary consult Lounsbury, op. cit. (ref. 3), 184–95. Lounsbury used the best accepted form of the correction scheme to derive the date of installation of the original version of the table (a.d. 934 Nov. 20), from which the extant (probably fourteenth-fifteenth century) updated copy was fashioned. Cf. F. Lounsbury, ‘The base of the Venus Table of the Dresden Codex and its significance for the calendar correlation’, in Calendars in Mesoamerica and Peru: Native computations of time, ed. by Aveni A. Brotherston G. (British archaeological reports, S 174; Oxford, 1983), 1–26. Correction tables/mechanisms apparently are absent in the Borgia Venus references.

Mesoamerican calendrical novices who wish to follow the course of argumentation can employ the table of day sequences for the 260-day calendar given in Table 6.

Anders , op. cit. (ref. 9), 289–95.

Throughout I employ the standard abbreviation mfirst = first appearance in the east in the morning sky; mlast = last appearance in the east in the morning sky; efirst = first appearance in the west in the evening sky; elast = last appearance in the west in the evening sky. Unlike the Dresden, the Borgia does not tabulate the subintervals of Venus (intervals of disappearance and appearance).

Interestingly, in the Vaticanus B (p. 70) version of the table the coefficient is 11, which signifies a day 40 + 260n (where n is an integer) from 10 Movement. Whether this implies a different use for the calendar or is simply a scribal error I cannot say.

The year bearer is the name of the last day, less the 5 unlucky days (nemontemi), of the year or, in effect, the 360^th day of a given year. Of the 20-day names five and only five can occupy this position because 365 ÷ 20 yields a remainder of 5. On the other hand 365 ÷ 13 yields a remainder of 1 with each advancing year; therefore following Table 5, advancing by five in day name and one in coefficient we would write a sequence of years: 1 Reed, 2 Flint, 3 House, 4 Rabbit, 5 Reed, etc. Thanks to the Aztec chroniclers we know for sure, at least in the calendar system operating in Tenochtitlan at the time of the conquest, that the aforementioned set corresponds to the years 1519, 1520, 1521, 1522, 1523 (±52n for other sets).

No date accompanies the fifth panel, which is located at the centre.

For a discussion see Aveni A. , op. cit. (ref. 2), 124–7.

Seler's first reading of this partially effaced date as 4 Movement (op. cit. (ref. 10), 390) was likely influenced by the fact that it is the central date on the Aztec sun stone, the day of the fifth creation. Seler's choice was influenced not only by the seminal nature of 4 Movement (= Maya 4 Ahau) in the calendar but also by the fact that such a choice would result in there being a whole number (3) of Venus periods between that date and the 1 Water date (A5 in the table). But Anders hold the opinion that the coefficient was five, which, after careful examination of the Graz facsimile, I have adopted. (On the facsimile the discerning eye will note that three yellow dots appear to the left and two red dots appear to the right of the sign for Movement).

As very little is visible in this date panel it is difficult to understand the basis for the tentative assignment of 8 or 3, Rabbit or Wind, by Anders , op. cit. (ref. 9), 173. Having examined the facsimile I think it best to leave this entry as uncertain.

Seler has it as 4[3], that is 4 or 3. Since I can see 4 dots in the panel I have decided to adopt that value.

Seler's uncertain 6 is countered by the puzzling 13 of Anders , op. cit. (ref. 9), 172. Though I remain uncertain about the value of the coefficient I doubt that any eye could detect so many dots in this date panel as Anders suggest.

The Caso correlation for Christian and Aztec years is fully explicated in A Caso, ‘Calendrical systems of Central Mexico’, in Handbook of Middle American Indians, x, ed. by Wauchope R. (Austin, 1971), 333–48.

Oddly enough this is the very year of contact, the year 1 Reed during which Quetzacoatl was prophesied to return to claim his throne.

In each instance I have consulted Tuckerman's tables ( Tuckerman B. , Planetary, lunar & solar positions, A.D. 2 to A.D. 1649 at five-day and ten-day intervals (Philadelphia, 1962)) for the more exact calculations, while I have employed the Voyager program (Voyager 1.2 Interactive Desktop Planetarium, San Leandro, CA: Carina Software) for graphic depictions, some of which are presented here.

See the bottom line, column D on each of the Venus pages of the Dresden codex. I have shown ( Aveni A. , ‘The Moon and the Venus Table: An example of commensuration in the Maya calendar’, in Aveni (ed.), The sky in Mayan literature (ref. 6), 87–101) that the disappearance intervals of Venus vary with the seasons and I have argued that not only were the Maya aware of this variation but also they employed it in setting up weather and maize crop predictions. See also Aveni A. Closs M. Crowley B. , ‘The planet Venus and Temple 22 at Copan’, Indiana, ix (1984), 221–47; and Sprajc I. , ‘The Venus-Rain-Maize complex in the Mesoamerican world view’, Journal for the history of astronomy, xxiv (1993), 17–70 (Part I) and Archaeoastronomy, no. 18, S27–53 (Part II).

The Annales de Quauhtitlan ‘at the time when the planet was visible in the sky (as evening star) Quetzalcoatl died. And when Quetzalcoatl was dead he was not seen for 4 days; they say then that he dwelt in the underworld, and for 4 more days he was bone (emaciated, weak); not until 8 days had passed did the great star appear; that is, as the morning star. They say that then Quetzalcoatl ascended the throne as God.’ (Quoted in Seler , op. cit. (ref. 10), 364–5).

For a discussion of the arcus visionis, or the angle of the sun below the horizon on which an object at the horizon is barely visible, a very important factor in these calculations, see Schaefer B. , ‘Heliacal rise phenomena’, Archaeoastronomy, no. 11 (1987), S19–34. Also see Aveni A. Hotaling L. , ‘Monumental inscriptions and the observational basis of Maya planetary astronomy’, Archaeoastronomy, no. 19 (1994), S21–54, esp. the appendix. The mfirst event, evidently not tabulated, would have occurred 6 days after 1 Reed 1 Alligator (or 1 Reed 7 Deer), thus yielding the total disappearance interval of 7 days in this particular instance. In Figures 6–9 the sun is placed on the horizon to enhance the figure (scale 1cm ≈ 6°).

efirst actually occurred on 10 April 1519, synchronic evening set on 13 Mar and mlast on 10 Feb for a disappearance interval of 59 days. As suggested above, similar Venus phenomena would relate Dates IIIA and IVA that relate IA and IIA; therefore one ought to examine the other possible pairs; thus: IIIA = 13 Mar 1415 (mlast + 2d = efirst — 58d), VA= 15 Feb 1311 (mlast — 57d). Clearly the earlier dates offer little concordance with mfirst Venus events.

Assuming an arcus visionis of 6°, the event in question would have taken place on 11 Feb. Of the 1 Reed 5 Movement dates in the previous calendar round, 8 May 1415 offers a satisfactory fit and therefore cannot be ruled out; however, as one extrapolates backwards through sets V, VII, …, the drift between the real and canonic Venus elast results in ever greater discordance.

Many of these events are transient phenomena. Among those listed by Keber Quiñones E. in her Codex Telleriano Remensis: Ritual, divination, and art in a pictorial Aztec manuscript (Austin, 1995) are the aurora borealis, comets, eclipses, and the zodiacal light. See also Köhler U. , ‘Comets and falling stars in the perception of Mesoamerican Indians’, in World archaeoastronomy, ed. by Aveni A. (Cambridge, 1989), 289–99. He attributes much of the imagery to comets and meteors.

There is at least one monumental text (the tablet of the 96 Glyphs at Palenque) that refers to a lunar conjunction. Peter Mathews (private comm.) translates the glyph block, which shows a Venus glyph conflated with a lunar crescent, as ‘It Venus mooned’. On the date to which the statement applies the crescent had indeed just passed (evening) star Venus. Thus the translation is an apt description of what actually happened to Venus in the sky.

Victoria R. Bricker's recent analysis of real-time Venus events on B-53-54, using an entirely different method from that employed here, also indicates a best fit of heliacal rise phenomena with dates that fall within the temporal provenience of the codex. See ‘The Venus Almanac on pages 53 and 54 of the Borgia Codex’ (unpublished manuscript).

The 1 Ahau starting date of the Dresden Table actually follows the 1 Alligator starting date of B53–54 by 39 days.

Cf. Justeson J. , ‘Ancient Maya ethnoastronomy’, in World archaeoastronomy, ed. by Aveni (ref. 33), 76–129. Thus the first of the four stations in the Dresden specifies the last date on which the morning star is still visible when the moon is at the same phase as it rose heliacally; the next specifies the first date on which the evening star is visible when the moon is again at that phase; the next station specifies the expected date of heliacal setting of the evening star, one half lunar phase offset from the previous three dates; and the last station specifies heliacal rising of morning star eight days later (p. 94).

Our study of eclipses in the Aztec record, for example, reveals that only those sky events were chosen that marked seminal social events, such as conquests and accessions. Moreover like-in-kind events deliberately pegged at multiples of 52-year cycles played a dominant role in the Aztec construction of history. Cf. Aveni A. Calnek E. , ‘Astronomical events in the Aztec expression of history: Eclipse data’, in Ancient Mesoamerica (in press).

Much has been written on the idea that the future is contained in the past. For example, the tangled verses in the Mayan Book of Chilam Balam of Tizimin (The ancient future of the Itzá, translated and edited by Edmonson M. (Norman, Okla., 1982)) combine past and future tenses. See also Farriss N. , ‘Remembering the future, anticipating the past: History, time and cosmology among the Maya of Yucatan’, Comparative studies in society and history, xxix (1987), 566–93.