The Maya Number of Time: Intervalic Time Reckoning in the Maya Codices,Part 1

Mathews P. , Maya Hieroglyphic Weekend Oct 26–27, 1991 (Cleveland, 1991), 160.

Verb-object-subject is the common reading order in Maya codical grammar; however, there are several other writing formats (cf. Bricker, 1986).

The exception is the terminal abbreviated sequence in the table which may have been intended to be attached to the intial (also abbreviated) sequence via a recycling mechanism; e.g. the terminal picture many not have represented an eclipse.

To understand the nature of the problem, suppose we wished to set up a similar structure in the 7-day week pattern in our own calendar (i.e. modulo 7 instead of 13). Oddly enough, the solution would be the same; that is, the sequence would be, starting arbitrarily: 7, 3, 6, 2, 5, 1, 4, finally returning to 7. (Thus, beginning with Sunday: Sun — Sun — Wed — Tue — Thur — Tue — Wed — Sun.) No other Maya almanac seems to exhibit this constant difference property across the interval set. However there does exist a short stretch in the other set of distance numbers in the same table that does reflect the slightest hint of it. The second differences in this run are −11, −2, −10, −6, −2, −2, −2, −2, −7, 0, −11, −6. Could the short span of −2's be all that remains of a constant difference sequence that, for unknown reasons, had later been altered?.

Our resources for Table 2 (as well as Table 5) include Förstemann (1902, 1906), Thompson (1972) and Vail (p.c). We have generally, except where noted, adopted the values of the intervals given by the latter two authors.

Note that the sum of both the first two and of the last two numbers is 13.

Vail (n.d.) believes this applies to a secondary almanac embedded in the third frame of the main almanac. The intervals are not stated explicitly but must be inferred.

For a discussion of this point see Aveni 1980, pp. 67–83, 173–83. Basically there are far too many eclipses preceded by shorter groups of intervals than those given in the table.

Possible variations occurring in the Madrid Codex appear on pp. 2c (20 17 15), 11c (20 20 5 (7)), 3a–6a (20 20 (6) (19)), 99d (20 10 10 (12)), and 22a–23a (10 10 10 10 10 10 5).

A similar, though not quite perfect, mirror symmetry is evident in the example from D4b–5b (Table 2(a), Category IV) if one starts from the 8th entry in the sequence and moves both ways; the 6, however, would be anomalous.

For a full description see Tedlock 1982, chap. 7, pp. 153–71.

We cannot be sure how the codices were actually used. Landa (Tozzer 1941) says they were never employed publicly (p. 29); that priests conducted certain rituals in which they read prognostications for the New Year (pp. 153–4); that they published the festival days (p. 111); and that some cast lots to determine their duties for the future (p. 112).

In some instances, such as example #58, we were able to recover only the vague hint of a 13 18 13 18 rhythm at the end of an 18-term sequence that, according to the Brickers (1992), may have been affected by the later inclusion of movable astronomical events.

We expended much effort charting out runs of lucky and unlucky days and numbers in Burner Almanacs and day lists in the post-Conquest Books of Chilam Balam of Mani and Tizimin, but we found no intervalic correspondences or likenesses whatever with the almanacs, save for the sequences listed in Table 4.

Our acknowledgements will be found at the close of Part 2.

Aveni A. . 1980 Skywatchers of Ancient Mexico (University of Texas Press, Austin).

Aveni A. Hartung H. Buckingham B. . 1978 ‘The Pecked Cross Symbol in Ancient Mesoamerica’, Science, ccii, 267–79.

Bill C. n.d. In Papers on the Madrid Codex, ms. ed. by Bricker V. Vail G. (Publication (in press) of the Middle American Research Institute, Tulane University, New Orleans).

Bricker V. 1986 A grammar of Mayan hieroglyphs (Publication no. 56, Middle American Research Institute, Tulane University, New Orleans).

Bricker V. Bricker H. 1988 ‘The seasonal table in the Dresden Codex and related almanacs’, Archaeoastronomy (supplement to Journal for the history of astronomy, no. 12, S1–62.

1992 ‘A method for cross-dating almanacs with tables in the Dresden Codex’, in The sky in Mayan literature, ed. by Aveni A. (Oxford University Press, New York), 43–86.

Bricker V. Vail G. (eds). n.d. Papers on the Madrid Codex (Tulane University Press, New Orleans).

Codex Dresdensis.

1975 Codex Dresdensis: Sächsische Landesbibliothek Dresden, Mscr. Dresd. R310 (Faksimile-Ausgabe des Codex mit Kommentar von Helmut Deckert und Ferdinand Anders) (Codices Selecti, liv; Akademische Druck- und Verlagsanstalt, Graz).

1988 Un Comentario al Códice de Dresde: Libro de Jeroglifos Mayas (Fondo de Cultura Económica, Mexico).

Codex Peresianus.

1968 Codex Peresianus (Codex Paris): Bibliothéque Nationale Paris (mit Einleitung und Summary von Ferdinand Anders) (Codices Selecti, ix; Akademische Druck- und Verlagsanstalt, Graz).

Codex Tro-Cortesianus.

1967 Codex Tro-Crotesianus (Codex Madrid): Museo de América Madrid (mit Einleitung und Summary von Ferdinand Anders) (Codices Selecti, vii; Akademische Druck- und Verlagsanstalt, Graz).

Craine E. Reindorp R. (ed). 1978 The Codex Peréz and the Book of Chilam Balam of Máni (University of Oklahoma Press, Norman).

Crawfurd J. . 1867 The history of the Indian archipelago (Cass, London).

Förstemann E. . 1902 Commentar zur Madrider Handschrift (Codex Tro-Cortesianus) (Sauneirs, Danzig).

1906 ‘Commentary on the Maya Manuscript in the Royal Public Library of Dresden’ (Papers of the Peabody Museum of American Archaeology and Ethnology, Harvard, iv/2).

Hofling C. O'Neil T. . 1992 ‘Eclipse cycles in the moon goddess almanacs in the Dresden Codex’, in The sky in Mayan literature, ed. by Aveni Anthony F. (Oxford University Press, New York), 102–32.

Justeson J. . 1989 ‘Ancient Maya ethnoastronomy: An overview of hieroglyphic sources’, in World archeaoastronomy, ed. by Aveni A. (Cambridge University Press, Cambridge), 76–129.

Lattimore R. . 1959 Hesiod (University of Michigan Press, Ann Arbor).

Lounsbury F. . 1978 ‘Maya numeration, computation, and calendrical astronomy’, in Dictionary of scientific biography, xv, 759–818.

Love B. . 1994 The Paris Codex: Handbook for a Maya priest (University of Texas Press, Austin).

n.d. ‘A Dresden Codex Mars table?’, Latin American antiquity, in press.

Maass A. . 1924 Tydschrift Indische Taal-, Land Volkerkunde, lxi/1, 103.

Seler E. . 1902–23 Gesammelte Abhandlungen zur Amerikanischen Sprach- und Altertumskunde (5 vols, Akademische Druck- und Verlagsanstalt, Graz).

Tedlock B. . 1982 Time and the Highland Maya (University of New Mexico Press, Albuquerque).

Thomas R. B. . 1994 The Old Farmer's Almanac, 1995 (Yankee Publications, Dublin, N.H.).

Thompson J. E. S. . 1950 Maya hieroglyphic writing: An introduction (Publication 589, Carnegie Instititute of Washington, Washington, D.C.).

1972 A Commentary on the Dresden Codex (Memoirs of the American Philosophical Society, xcii).

Tozzer A. . 1941 Landa's Relación de las Cosas de Yucatan (Papers of the Peabody Museum, xviii; Cambridge, Mass.).

Vail G. n.d. ‘Starting dates and intervals for the Madrid almanacs’ (ms).

Zuidema R. T. . 1977 ‘The Inca calendar’, in Native American astronomy, ed. by Aveni A. (University of Texas Press, Austin), 219–59.