Resumen:

Pages 24 and 46-50 of the Dresden Codex have long been recognized as an astronomical table which was used by the pre-Hispanic Maya of Yucatán to predict appearances and disappearances of Venus. This presentation extends understanding of the Dresden Venus table by establishing the solar significance of some of the iconography and dates incorporated in it.

I. VENUS CONTENT AND STRUCTURE

The Venus table is comprised of an introductory page (page 24; fig. 1) and, in the main body (pages 46-50; fig. 2), a compilation of the appearances of Venus as morning and evening star. On the right sides of each of the five pages of the main table, there are three vertically stacked illustrations. The subject of the top panels is a series of celestial regents, widely recognized as such on account of the sky symbols clearly painted on four of the five thrones. The middle panels show Venus incarnated as a spear-throwing warrior, and the bottom panels present wounded victims. The hieroglyphic text of the main table is divided vertically on each page, with captions for the illustrations on the right side and the data pertaining to the visibility of Venus on the left side.

The prominent numerical intervals in the catalog of visibility of the planet (fig. 3a,b) show that its 584-day synodic period was of fundamental interest. The top line of each of the five pages of the main Venus table presents one 584-day synodic period which has been divided into sub-intervals of 236 days, 90 days, 250 days, and 8 days. Although three of the sub-intervals do not precisely reflect the observed behavior of Venus (Aveni 1980:86; Gibbs 1977:33), these lengths were selected to convey the periods of appearance as morning star, disappearance at superior conjunction, appearance as evening star, and disappearance at inferior conjunction. The Venus data was formatted to be read horizontally across all five pages, so that each complete line in the top section represents five synodic periods, or 2,920 days. This top section (lines 1-13) lists the tzolkin positions of the sub-intervals. The second section of the main part of the Venus table, marked on page 46 by a prominent red outline, consists of lines 14-19. Line 14 completes the listing of Calendar Round dates of Venus events by providing the haab positions corresponding to the tzolkin entries listed above in lines 1-13. Line 15 consists entirely of repetitions of a single verb. Line 16 lists the succession of four cosmic directions corresponding to the sub-intervals, followed on line 17 by twenty glyphs referring to deities. Line 18 mentions the Maya name for Venus, Chac Ek (red or great star), and the last line of the second section sums the number of days which transpire while the progression of sub-intervals builds the five synodic periods.

The bottom part of the Venus table, separated on pages 46 and 47 by a heavy red line, consists of lines 20-26. This portion of the table relates, on line 20, a second set of haab positions which can be read with

Fig. 1. The Venus Table of the Dresden Codex, Page 24

a Transcription, based on Lounsbury (1978:fig. 2).

b Drawing, based on Codex Dresden (1972), Codex Dresdensis (1975), and Códices Mayas (1976).

Fig. 2. The Venus Table of the Dresden Codex, Pages 46-50

Based on Codex Dresden (1972), Codex Dresdensis (1975), Códices Mayas (1976), and Kingsborough (1831-48, vol. 3).

Fig. 3a. Venus Cycles of the Dresden Codex, Pages 46-50

Drawing based on fig. 2.

Fig. 3b. Venus Cycles of the Dresden Codex, Pages 46-50

Restored transcription based on Thompson (1950:222); square brackets indicate corrections of mathematical errors.

the tzolkin dates of lines 1-13 to form the record of a different set of pre-Conquest appearances of Venus. With some variation in their vertical arrangement, lines 21 and 22 generally list the same sequence of twenty

deities as is seen in line 17 (but shifted horizontally one position) and another verb. On most pages, line 23 again names Venus, and the four perimeter directions of the cosmos (shifted horizontally one position) are restated on line 24. Line 25 provides yet a third set of haab dates which can be used with the tzolkin dates of lines 1-13 to constitute another record of historical positions of Venus, while line 26 states the lengths of the sub-intervals of the 584-day synodic period of the planet.

In three columns of hieroglyphic text painted along its left side, the page 24 introduction to the Dresden Venus table (fig. 1) summarizes the information conveyed by the illustrations for the main table. This passage mentions east (A4), Venus (A5-9, B3), all of the celestial regents (B5-9), some of the incarnations of Venus as a spear-throwing warrior (C4-7), and all of the speared victims (C8-12). The right side of the page lists multiples of the synodic period of Venus, and provides other numbers which can be used to construct substitute bases for entering the main table on pages 46-50. Information on the historical development of the Dresden table is entered at the bottoms of the three left columns of the page.

Förstemann (1906:185) and other scholars working during the first half of the twentieth century (Teeple 1930:94-98; Thompson 1950:217-227) showed how the pre-Hispanic Maya used the Venus table to predict the rise of the planet as morning star. Entering the table on the date written at the right ends of lines 13 and 14, 1 Ahau 13 Mac, the reader would theoretically have been at the place of an appearance of Venus as morning star following an 8-day disappearance of Venus at inferior conjunction. Working from information in the page 24 introduction to the main table ), modern students of the manuscript have unanimously recognized the specific base date referred to in lines 13 and 14 of the table as 11.0.3.1.0 1 Ahau 13 Mac (June 15, 1227 by the 584285 conversion constant). This date was quite close to an actual heliacal rise of Venus as morning star (Aveni 1992:94-96).

The continuation of the Dresden Venus table from the 1 Ahau 13 Mac heliacal rise as morning star occurs on page 46, at column 1 of line 1 and column 1 of line 14, where the date 3 Cib 4 Yaxkin is written. This date, linked with the long count position 11.0.3.12.16 3 Cib 4 Yaxkin (February 6, 1228; see Table 1), represents the end of the visibility of Venus as morning star. It was derived by adding the number of days (236) written in column 1 of line 26 of the table to the 11.0.3.1.0 base date. To reach the next station of the Dresden table, the Maya reader added the period of disappearance at superior conjunction (90 days, written in column 2 of line 26) to the 3 Cib 4 Yaxkin date. The result, 11.0.3.17.6 2 Cimi 14 Zac (May 6, 1228), is the first date of Venus's appearance as evening star. The

TABLE 1

VENUS CYCLES OF THE DRESDEN CODEX, PAGES 46-50

11.0.3.1.0 1 Ahau 13 Mac base= June 15, 1227 (584285 conversion constant)

1229) was reached by adding the 250-day period of visibility (line 26, column 3) to the 2 Cimi 14 Zac date. Following an 8-day disappearance at inferior conjunction (line 26, column 4), Venus once again rose as morning star on 11.0.4.12.4 13 Kan 7 Xul (January 19, 1229). With the completion of the first synodic period on that date, the reader of the Venus table moved through the first line of pages 47 and succeeding pages until the end of the first line was reached after a total of 2,920 days (page 50; line 1, column 20 of the table) on 11.0.11.3.0 9 Ahau 13 Mac (June 13, 1235). As that was a date of rise as morning star appearance, 236 days (line 26, column 1) were added to reach the last date of visibility as morning star on 11.0.11.14.16 11 Cib 4 Yaxkin (February 4, 1236). The latter date is written at the beginning of the second line of the Venus table. This reading method was applied to successive lines until the appropriate place for correcting error was reached.

As their mathematical system did not incorporate fractions, the 584-day value used in the Dresden table for the synodic period of Venus was the most accurate figure available to the pre-Hispanic Maya. The observationally determined average length of this period is now known to be 583.92 days. Hence the 0.08 day discrepancy per synodic period would eventually have caused predictions of Venus events to move ahead of the actual occurrences. This error would have amounted to 0.4 days per 2,920-day line, and to 5.2 days for each 13-line reading of the complete table. The cumulative error was not immediately problematic, because there is short-term fluctuation in the duration of the synodic period of the planet. Also, as was mentioned above, some of the sub-intervals used by the Maya to characterize the visibility of Venus were inherently inaccurate. However, one of the sub-intervals, the period of disappearance during inferior conjunction, is in conformance with average behavior. Accordingly, a scheme for correcting the cumulative astronomical error would have been desirable.

It was John Teeple (1930:94-98) who first recognized that some of the numbers written in the page 24 introduction can be used to generate error-correcting bases for the Venus table. He added these numbers, found in the second row of the top right side of the page, to the Long Count date near the bottom of column C (9.9.9.16.0) to develop bases which could be used to indicate when the reader should omit the final section of the table. This reduced the accumulated error by either four or eight days. The base-shifting procedure also enabled Teeple to explain the three sets of month dates found in lines 14, 20, and 26 of pages 46-50, as well as another base date (1 Ahau 18 Uo) that appears at the bottom of column C on page 24.

Modifications to Teeple's method for calculating re-entry dates for the table have been proposed in recent years (Closs 1977; Lounsbury 1983; reviewed in Justeson 1989:79-81 and Paxton 1986:41-54, and this has resulted in suggestions for revision of his sequence of shifted bases.

Nevertheless, there is unanimity of opinion in the acceptance of most of

Teeple's tenth- and eleventh-cycle bases. These universally accepted bases are:

10.10.11.12.0 1 Ahau 18 Kayab

10.15.4.2.0 1 Ahau 18 Uo

11.0.3.1.0 1 Ahau 13 Mac

11.5.2.0.0 1 Ahau 3 Xul

It is generally recognized that the Dresden Codex was copied from earlier sources, and that it is likely to have been revised as it was recopied (Thompson 1972:15; Paxton 1986). It has also been proposed that at least two of the correction bases listed above, 10.10.11.12.0 1 Ahau 18 Kayab (October 25, 1038) and 10.15.4.2.0 1 Ahau 18 Uo (December 6, 1129), were already obsolete when the present version of Codex Dresden was painted (Lounsbury 1983:11, Paxton 1986:57).

II. SOLAR ORIENTATION OF SHIFTED BASE DATES

Since the appearances and disappearances of Venus are caused by the position of the planet with respect to the sun, the Dresden table necessarily incorporates solar intervals. Förstemann (1906:182) realized that the 2,920-day lines of the Venus table are approximately commensurate with the solar year. The general ratio expressed by each of these thirteen lines is that five synodic periods of Venus (5´584=2,920) are equal to eight solar years (8´365=2,920). As Aveni (1980:94) has noted, Venus events follow a general pattern of seasonal repetition at eight-year intervals. However, the absence of fractions from the Maya number system would have resulted in gradual drifting of these events from their initial positions in the Dresden table. The length of the tropical year, the period required for the orbiting earth to return to the vernal equinox, is 365.2422 days (Aveni 1980:100). As eight tropical years is 2,921.9376 days, the 2,920-day lines of the table move ahead of the seasonal year at the rate of 1.94 days per line. This cumulative error amounts to a 25.2-day difference by the end of the thirteenth line of the Venus table (37,960 days = 104 haab = 2 Calendar Rounds = 65 Venus Rounds).

The two latest bases for correcting cumulative error in the predictions of the appearances of Venus which are actually written in the table are 1 Ahau 13 Mac (line 14, column 20) and 1 Ahau 3 Xul (line 26, column 20), respectively linked to the Long Count dates 11.0.3.1.0 (June 15, 1227) and 11.5.2.0.0 (December 22, 1324). A fact not previously considered in analysis of the Dresden table is that these bases also realign Venus predictions with the seasons and Maya directions. The base shift to 1 Ahau 13 Mac links the heliacal rise of the planet with the summer solstice, and the shift to 1 Ahau 13 Mac associates the event with the winter solstice. The summer solstice of 1227 occurred on June 15, at 6 hours, 44 minutes, and 45 seconds Universal Time (Meeus 1995:131), which can be adjusted to local Yucatec time by subtracting six hours. Hence the summer solstice and the canonical rise of Venus as morning star coincided exactly on the date of the 1 Ahau 13 Mac base shift. According to Meeus (1995:134), the winter solstice of 1324 fell on December 13, at 10 hours, 33 minutes, 14 seconds Universal Time (4 hours, 33 minutes, 14 seconds Yucatec Time). The 1 Ahau 3 Xul base missed by nine days in correlating the rise of Venus as morning star with the winter solstice. Considering the complexity of the orbits involved, this approximation would appear to be reasonably accurate. Moreover, since each successive 2,920-day line of the table shifts predictions two days in the earlier direction, the alignment of this Venus event with the winter solstice would have become closer as the 1 Ahau 3 Xul table was used. When the end of the fourth line was reached, the predicted rise of Venus as morning star fell on December 14, 1356, and the winter solstice occurred on the night of December 12/13 (December 13 at 5 h 3 m 51 s UT, which was shortly before midnight on December 12 YT; see Meeus [1995:134]). The greatest discrepancy occurred at the end of the thirteenth line, when the canonical heliacal rise of Venus fell on November 26, 1428, and the winter solstice was on December 12 at 16 h 37 m 34 s UT (Meeus 1995:136). Thus if users of the Dresden Venus table relied only on information actually written there, the greatest difference in predictions derived from the alignment of the 1 Ahau 3 Xul base with the winter solstice would have been 16 days. Realignment of Venus predictions with the tropical year brings the table into conformance with the standard Maya directional system. As shown on pages 75-76 of the pre-Hispanic Madrid Codex (fig. 4), east and west are defined as sunrise and sunset. In annual terms, these directions are the segments of the horizons limited at the north by the summer solstice sunrise and sunset and at the south by the winter sunrise and sunset positions. Use of the shifted bases for the correction of cumulative Venus error in the Dresden table respectively places the 1 Ahau 13 Mac and 1 Ahau 3 Xul bases at the northeast/northwest and southeast/southwest corners of the Maya cosmos (fig 5).

III. DEITIES OF THE DRESDEN VENUS TABLE IN THE CONTEXTS OF THE TROPICAL YEAR AND WORLD DIRECTIONS

The linking of the corrected 1 Ahau 13 Mac (11.0.3.1.0) and 1 Ahau 3 Xul (11.5.2.0.0) bases for the Dresden Venus table with the corners of the Maya universe furthers understanding of the twenty deities listed in lines 17 and 21-22. Because these deities are associated with directions and specific intervals of time, which can be calculated from the corrected bases (as in Table 1), it is possible to identify some celestial members of Maya pantheon. As mentioned earlier, these dates are associated in lines 15-19 with a verb

Fig. 4 Directions of the Maya Cosmos, Pages 75-76 of the Madrid Codex

North is shown at the top of the page; based on Codex Tro-Cortesianus (Codex Madrid) (1967) and Códices Mayas (1976).

Fig. 5. Two Realignments of the Dresden Venus Table with the Tropical Year and the World Directions

which evidently means "appear" (or something similar), glyphs for the four perimeter directions, the sequence of the twenty deity positions, glyphs for Venus, and a number which registers the place of the interval in the 2,920-day cycle. The sense of the statements is that the Venus appearance (or disappearance) on a certain Calendar Round date is linked with a particular direction and with one of the twenty deities. Thus this Dresden Codex characterization of Venus motion in terms of deities can be diagramed to follow the Codex Madrid 75-76 illustration of the apparent motion of the sun (fig. 6). According to this system, the twenty deities of the Dresden Venus table demarcate the cosmic directions. As was shown earlier in Table 1, the dates of the subintervals of the 1 Ahau 18 Kayab (10.10.11.12.0, or October 25, 1038), 1 Ahau 13 Mac (11.0.3.1.0, or June 15, 1227), and 1 Ahau 3 Xul (11.5.2.0.0, or December 22, 1324) tables can easily be computed. The general orientations of all three tables are shown in Table 2.

Comparison of the dates for the subintervals of the first 2,920-day cycles of the 10.10.11.12.0 1 Ahau 18 Kayab and the 11.0.3.1.0 1 Ahau 13 Mac tables provides a possible explanation for the shift of one position toward the right in the second listing of the twenty Dresden Venus table deities (lines 21, 22). The dates of the beginnings of the morning star periods for Venus during the 1 Ahau 13 Mac table correlate almost exactly with the ends of these intervals during the 1 Ahau 18 Kayab table. The line 21/22 list of twenty deities and directions is adjacent to the Calendar Round positions for the 10.10.11.12.0 1 Ahau 18 Kayab table, suggesting that the 1 Ahau 13 Mac table was being compared with this 1 Ahau 18 Kayab predecessor. It appears that the date of the most current revision of the Venus table was for the 1 Ahau 13 Mac base. The shifted positions of the deities are evidently an indication of the historical context of that date. The information is a comparison of the present with the past and a general statement that, with the 1 Ahau 3 Xul table (lines 1, 25, 26), the system would continue in the future.

IV. THE 1 AHAU 13 MAC BASE AND SOLAR REGENTS

The pattern underlying the illustration of the celestial regents of the Dresden Venus table (fig. 7) is, as I understand it, similar to that of picture selection for modern Western calendars. The chosen scene pertains to an important event which can occur at any time during the period under consideration. Such a system is consistent with the definition of east and west in the Madrid 75-76 diagram of the cosmos as a position which may occur on either solstice date, or on any intermediate date. As Lounsbury (1978:777-778) has also noticed, the regents occupying the celestial thrones at the tops of pages 46-50 are named in the positions corresponding to the dates of rise of Venus as morning star for the 1 Ahau 13 Mac table (deity positions D, H, L, P, and T of line 17). In each instance, the heliacal rise date is given on the page preceding that where the illustration and morning star interval are found. This associates the celestial regents of east

Fig. 6. Positions of The Twenty Dresden Venus Table Deities, the Synodic Periods of Venus, and the World Directions Following the 11.0.3.1.0 1 Ahau 13 Mac Base

Table 2. Orientations in the Tropical Year of Three Sections of the Dresden Codex Venus Table

Fig. 7. Celestial Regents of the Dresden Venus Table

with the entire 236-day period of visiblility as morning star, not merely the date of heliacal rise. I would argue for interpretation of two of the celestial regents (fig. 7a,c) as the sun at the solstice corners of the Maya universe. The first solstice regent, shown at the top of page 46, was named as the holder of that throne on the summer solstice that coincided with the date of the 11.0.3.1.0 1 Ahau 13 Mac (June 15, 1227) base shift for correcting cumulative error in Venus predictions. This regent has previously been referred to by Kelley (1976:82) as simply "the deity who wears the headdress of the long-snouted monster with crossbands in his eyes."

Thompson (1972:67) noted that the name glyph of the page 46 regent is the T792 monster with upturned snout and Bacab insignia as prefix. To him, the most impressive features of the image of the enthroned god were advanced age and a headdress in the form of a grotesque serpent. Thompson also remarked that the throne of the regent is a celestial band with the head of God K at the end. I would propose interpretation of the page 46 regent as the sun at summer solstice to explain this grouping of iconographic motifs.

Characterization of the summer solstice sun as an aged figure is apt because the sun moves very slowly around the dates of the solstices. Inclusion of the knotted loop headdress of the Bacabs (fig. 7a, glyph from page 24) further supports the interpretation, as these gods also seem to represent solstice suns. The Bacabs have been classified according to the system of Schellhas (1904) as God N. In a recent re-examination of the attributes of God N, Taube (1992:92-99) commented that the divinity is strongly quadripartite, and also cited Diego de Landa's statement (in Tozzer

1941:136-137) that the Pauahtuns, the Bacabs, and the Xib Chacs are different names for the same deities. All of these gods have four aspects oriented to the four directions and their respective colors. Since the Maya directional system is defined by the solstice rise and set positons of the sun, this feature should indeed be fundamental to God N if he is a sun god. Landa's information on the Bacabs (in Tozzer 1941:135) includes the statement that "They said they were the four brothers whom God placed, when he created the world, at the four points of it, holding up the sky so that it should not fall." These placements are the solstice sunrise and sunset positions.

The personification of the sun as the winter solstice, again effected through the use of the bacab God N, is seen at the top of page 48 of the Dresden Venus table (fig. 7c, deity position H). Thompson (1972:68) based his identification of the page 48 regent as a bacab on age and the inclusion of a tun sign in the deity's headdress. As in the page 46 solstice example, this advanced age is shown by the toothless mouth of the figure. The name glyph of the page 48a bacab (fig. 7, lower section) includes the same looped headdress as was used to identify the page 46a bacab regent. A pair of glyphs in the text painted above, which name the sun god Itzamna as Lord of the dawn, evidently also refer to the page 48 regent. The position of the winter solstice in the Dresden Venus table, counted from the

initiation of the 1 Ahau 13 Mac table on the summer solstice of June 15, 1227, is consistent with interpretation of this regent as the sun.

Further study of the page 47 and 50 celestial regents may establish that some of the remaining figures represent the sun, as well. According to the diagram of zenith and nadir dates provided by B. J. Isbell (1982:fig.1), the 1 Ahau 13 Mac table approximately aligns celestial regents and the rise of Venus as morning star with the first solar nadir (deity position D, column 4, January 19) around the latitude of Uxmal (January 18±2 days) and with the second solar nadir (deity position P, column 16, November 6) at the base of the Yucatán peninsula (November 7±2 days).

V. SUMMARY AND CONCLUSIONS

The Maya representation of celestial motion found on pages 75-76 of the Madrid Codex has been applied to study of the Venus table on pages 24 and 46-50 of the Dresden Codex. It has been shown that the shifted base dates used to recycle the Venus table by correcting cumulative error in the predictions of the appearances and disappearances of the planet also serve to realign the table with the corners of the cosmos as depicted in the Madrid illustration. According to the 584,285 constant for conversion of Long Count dates, the 11.0.3.1.0 1 Ahau 13 Mac (June 15, 1227 in the Julian calendar) base corresponds exactly with the date of the summer solstice. This date forms the northeast and northwest corners of the Maya universe. The 11.5.2.0.0 1 Ahau 3 Xul (December 22, 1324) base falls nine days after the winter solstice, with the alignment becoming closer as reading of the table continued. Hence the 1 Ahau 3 Xul base coincides with the southeast and southwest corners of the Madrid diagram of the cosmos.

The system of celestial motion diagramed on pages 75-76 of the Madrid Codex also explains functions of members of the Maya pantheon found in the Venus table of the Dresden Codex. The main section of the table includes a listing of twenty deities, some of whom are the celestial regents illustrated at the tops of pages 46-50 and named on page 24. Each of the twenty name glyphs in the main table is associated with one of the perimeter directions of the Maya universe and a specific interval for the appearance or disappearance of Venus. This information can also be charted in terms of the directional system of the Madrid illustration. The celestial regents shown on pages 46 and 48 can be recognized respectively as incarnations of the sun at the summer and winter solstices. The bacabs of the Maya religion, named with these illustrations, can similarly be identified as the solstice suns.

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