Our article has just published in the latest issue of Science (Vol. 336 no. 6082 pp. 714-717), co-authored by William Saturno, David Stuart, Anthony Aveni and Franco Rossi.
Article Abstract
Maya astronomical tables are recognized in bark-paper books from the Late Postclassic period (1300 to 1521 C.E.), but Classic period (200 to 900 C.E.) precursors have not been found. In 2011, a small painted room was excavated at the extensive ancient Maya ruins of Xultun, Guatemala, dating to the early 9th century C.E. The walls and ceiling of the room are painted with several human figures. Two walls also display a large number of delicate black, red, and incised hieroglyphs. Many of these hieroglyphs are calendrical in nature and relate astronomical computations, including at least two tables concerning the movement of the Moon, and perhaps Mars and Venus. These apparently represent early astronomical tables and may shed light on the later books.
A few years ago I proposed that some of the most celebrated Maya vases were commissioned for young men in Classic society (Houston 2009: 166). My thoughts at the time: “pots with such labels could have been bestowed in the setting of age-grade rituals or promotions, a recognition of feasting and expensive drinks as markers of adult status, even trophies and material honours while in page service, ballplay or war.” The notion appealed to me on behalf of all those ungainly, ever-changing youth in past and present times—as a set, the boys and young men could be seen as an unexpected aesthetic locus, a target for what was arguably the summit of ceramic painting in the ancient New World. But this idea involved a second, very specific expectation. The painted vessels so-named and so-possessed would involve not only young men but youths at times of change, on transit through the rites of passage so familiar to comparative anthropology.
A fresh piece of evidence lends weight to this conjecture. An eroded and shattered cylindrical vessel in the Juan Antonio Valdés Museum in Uaxactun, Guatemala, contains the usual Primary Standard Sequence. The glyphs have a cadenced coloration of two red-painted glyphs followed by one left uncolored. This scheme recalls the Primary Standard Sequences on such luminous vessels as a bowl from the area of Tikal, now in the Museo Popol Vuh (Kerr #3395; the presence of Jasaw Chan K’awiil’s name on the bowl brackets it temporally to AD 682 ~ 734; see also K #595). The vessel in Uaxactun has the following sequence, somewhat occluded by the darkness of the photographs I have seen: ….u-tz’i ba-IL yu-k’i-bi ti-YAX-CH’AHB ch’o-ko AJ-?BAHLAM che-he-na SAK-MO’-‘o ?-?…., the final glyphs surely the name of the painter. Figure 1 reproduces a key passage, the name of the drinking vessel (yuk’ib), just before an expression ti yax ch’ahb, “for the first fast/penance(?).” Then, crucially, the name of the owner, a ch’ok or “youth.”
Figure 1. Passage on a vessel in the Juan Antonio Valdés Museum (drawing by author).
As Stuart and others have noted, the yax ch’ahb refers to a rite of passage for young males, perhaps most eloquently in a text from Caracol Stela 3 (Stuart 2008; also Houston et al. 2006: 131-132, fig. 3.30). There, a young prince, only a few months beyond 5 years of age, underwent this arduous rite. It formed part of his first bloodletting but probably involved much other pain besides, including the denial of food. The import is clear: the vessel at Uaxactun was intended specifically for an age-grade ritual, the first (presumably) of many sacrificial offerings from a noble youth. Did it offer a filling and restorative draft of liquid after penance? Was it a gift to others who might witness his ascent to adult duty? Of these matters we cannot be certain. But the likelihood is now stronger that most such vessels marked and materialized shifts of status: a liquid passage from boyhood to the obligations of elite men.
REFERENCES CITED
Houston, Stephen. 2009. A Splendid Predicament: Young Men in Classic Maya Society. Cambridge Archaeological Journal 19 (2): 149-178.
Houston, Stephen, David Stuart, and Karl Taube. 2006. The Memory of Bones: Body, Being, and Experience among the Classic Maya. Austin: University of Texas Press.
A great many descriptions of ancient Maya mathematical notation read something like this:
The Maya made use of a base-20 (vigesimal) system with the units of 1, 20, 400, 8,000, 160,000, etc.. To write a number, a scribe would show multiples of these units in a set columnar order, moving down from highest to lowest, and add them accordingly. “32” for example would be written as single dot for 1, representing one unit of 20, above the two bars and two dots for 12, corresponding to the “ones” unit (1×20 + 12×1 = 32). A larger number such as 823 would be written in three places as two dots followed by one dot followed in turn by three dots, standing for the necessary multiples of 400, 20, and 1 respectively (2×400 + 1×20 + 3×1 = 823).
Similar descriptions of Maya math pervade the literature, textbooks and the internet. For example Michael Coe writes in the latest edition of The Maya (p. 232):
Unlike our system adopted from the Hindus, which is decimal and increasing in value from right to left, the Maya was vigesimal and increased from bottom to top in vertical columns. Thus, the first and lowest place has the value of one; the next above it the value of twenty; then 400; and so on. It is immediately apparent that “twenty” would be written with a nought in the lowest place and a dot in the second.
The illustration accompanying this text provides many examples of this purely vigesimal system:
Maya number notation from Coe’s The Maya (8th edition, p. 233)
Maya mathematical notation is described the same way in a number of other influential books widely read in classrooms and seminars, such as The Ancient Maya: New Perspectives (McKillop 2004:277) or the venerable The Ancient Maya (Sharer and Traxler 2006:101). In the latter work, two types of counts are represented (see below) – the purely vigesimal or base-20 count (with units of 1, 20, 400, and 8,000) alongside what’s called the “chronological count” (with units of 1, 20, 360, 7,200). The second is of course the basis for the familiar Long Count system.
Maya number notation as shown in The Ancient Maya (6th edition, p. 101).
A big problem exists with all of these seemingly straightforward descriptions of Maya mathematical notation. As far as I am aware no purely vigesemal place-notation system was ever written this way. It’s true that in Mayan languages numbers are base-20 in their overall structure, just as in most Mesoamerican languages. In Colonial Yukatek, for example, we have familiar terms for these units: k’al (20), bak’ (400), pik (8,000), and so on. However, ancient scribes never represented these units in a columnar place notation system, as is so commonly described in the textbooks. That format was instead always reserved for a for the count of time, in what we know as the Long Count. That system is mostly vigesimal, but it is skewed in one of its units (the Tun, of 360 days) in order to conform as much as possible to the number of days in the solar year (365). To reiterate: the columns of numbers we find in the pages of the Dresden Codex or painted on the walls of Xultun (stay tuned, folks…) are all day counts; the positional notation system was never used for reckoning anything else.
In the ancient inscriptions non-calendrical counts using large numbers are quite rare, mostly found in connection to tribute tallies, such as the counting of bundled cacao beans. But in those settings the scribes always seem to show nice rounded numbers (as in ho’ pik kakaw, “5×8,000 [40,000] cacao beans,” shown in the murals of Bonampak) without all the place units we know from the Long Count. In the Dresden and Madrid codices, counts of food offerings are given as groupings of WINIK (20) signs with accompanying bars and dots for 1-19. In this way a cluster of four such elements (4×20) with 19 writes 96 (See Love 1994:58-59; Stuart, in press).
There is a good deal we still don’t know about the ways the Maya wrote quantities, especially of non-calendrical things. The pattern nonetheless seems clear that the place notation system of the Long Count was restricted to time reckoning, and never applied to the purely vigesimal counting structure we see reflected in Mayan languages. The descriptions of written numbers found in the many texts about the ancient Maya therefore need to be corrected.
Sources Cited:
Coe, Michael. 2011. The Maya (8th edition). Thames and Hudson, New York.
Love, Bruce. 1994. The Paris Codex: Handbook for a Maya Priest. University of Texas Press, Austin.
McKillop, Heather. 2006. The Ancient Maya: New Perspectives. W.W. Norton, New York.
Sharer, Robert, and Loa Traxler. 2005. The Ancient Maya (6th edition). Stanford University Press, Stanford.
Stuart, David. In press. The Varieties of Ancient Maya Numeration and Value. To appear in The Construction of Value in the Ancient World, ed. by J. Papadopolous and G. Urton. Cotsen Institute of Archaeology, UCLA, Los Angeles.
You must be logged in to post a comment.