## The Dresden Codex Venus Table

The most fully discussed and best known of all the literary material on astronomy from Mesoamerica is probably the Venus table of the Dresden codex. This is a table of mean motion covering 104 years. An introduction gives a calculation involving 12.19.13.16.0 1 Ahau 18 Kayab (a Ring Number) and a later date 9.9.9.16.0 1 Ahau 18 Kayab. In the interval of 1,366,560 days (72 CRs) represented by the difference between these dates, there is about a half-year shift, both of the tropical year and of the Venus synodic period.4 The calculations in the Venus table show clearly that the Maya would have known that this was a gross error on both

Venus and the Sun, and no one has yet suggested a good reason why they should count back to a base that they knew to be incorrect. Kelley (1976, p. 256) has suggested that the initial date was calculated as a rising of Venus (probably at or near one of the equinoxes or solstices) four days after inferior conjunction and that the table provided a constant measure of the amount by which observation was off from reality. At any given time, it would be easy to see how many days of error had accumulated in a given number of formal repetitions of the basic 584-day mean interval. Everyone else has assumed that the terminal date was fairly closely in step with reality. It has also been assumed that the introductory calculations were used to "reset" the (late) table base to new positions, but that the table was not adjusted.

Besides the introductory page, there are five additional pages, each containing the set of month names for a period of 584 days, with the month names repeating after 5 x 584 (2920), which equals 8 x 365. There is also a table of the 13 repetitions of the day names in each of the month positions. These are accompanied by glyphs for cardinal directions and glyphs for a series of 20 deities. Besides this, there are pictures of three sets of deities, associated with the different table positions. The month names mark intervals of 236 days, 90 days, 250 days, and 8 days.5 It has been assumed that inferior conjunction lay in the middle of the 8-day period. Because of the asymmetry of the 236- and 250-day periods, the structural or mean superior conjunction is at day 52 of the 90-day period rather than at day 45. The 90-day period seems far too long for invisibility at superior conjunction but

4 For the tropical year, modulo 365.24220 yields 3741 cycles and a remainder of 188.9299 days;for Venus, modulo 583.92166 yields 2340 cycles and a remainder of 183.3158 days.

5 Modern rounded values are closer to 8,263,50, and 263 days for these synodic intervals (Gibbs 1977). Cf. §7.1.4.4 for their meanings.

was also used by the Babylonians (see §7.1) and is substantially less than that used in China (§10.1.4).

There are actually three sets of month names, the middle one beginning with 18 Kayab, corresponding to the introductory date, the top one with 13 Mac, and the bottom with 3 Xul. The date at 13 Mac and those on the same line on p. 46 are the only ones in the table that lack the past tense suffix, which, in Kelley's opinion, should imply that 13 Mac was the current date when the table was first written. It is widely assumed that 3 Xul and 13 Mac serve as correction positions for alternative table bases, but it seems equally likely that they were of primary importance in interlocking Venus with eclipses, as 1st suggested by Spinden (1928, pp. 44-45; 1930, pp. 91-92), and then amplified by Smiley (1961) and Kelley and Kerr (1973, pp. 182, 188). The minimal interval between a given name on 18 Kayab and the same day name on 13 Mac is 11,960 days, precisely the length of the eclipse table, as Spinden noted. The minimal interval between the same day name on 3 Xul and 18 Kayab is 9360 days, a major eclipse interval (the Thix, cf. §5.2.2) of particular Maya interest because it also restores the same day of the 260-day period. These figures mean that if there is an eclipse at or near any date in the 3 Xul line, there is a high probability that there will also be eclipses on the equivalent dates of the 18 Kayab and 13 Mac lines. These positions are diagrammed in Figure 12.10.

Spinden (1924, pp. 184, 193) was the first to draw attention to the relationship between the date 1.18.5.4.0 1 Ahau 13 Mac given at Palenque and now recognized as the birth-date of a Maya god, and 1 Ahau 13 Mac, a major base of the Dresden Venus tables. As Spinden pointed out, the next occurrence of the date 1 Ahau 13 Mac following 9.9.9.16.0 1 Ahau 18 Kayab, the primary base of the Dresden Venus table, is at 9.11.3.2.0 1 Ahau 13 Mac. We now know that this date fell within the lifetime of Chan Bahlum, ruler of Palenque, in whose reign the tablets relating to the birth of the gods were executed. The two dates 1 Ahau 13 Mac are separated by 2 x 1508 Mesoamerican years or 2 x 1507 tropical years, so that Maya calendar dates were at the same seasons for four years at both ends of the interval. The period of 1508 Mesoamerican years may be called the great solar round. It is surely no coincidence that 1.18.5.4.0 1 Ahau 13 Mac is half a great solar round after the four-year period in which the normal Maya era base (13.0.0.0.0 4 Ahau 8 Cumku) fell.

Stela C at Copan shows a similar back calculation to 10.19.14.17.0 6 Ahau 18 Kayab, one short Venus period of eight years before 11.0.3.1.0 1 Ahau 18 Kayab,6 which is three great solar rounds before 9.9.9.16.0 1 Ahau 18 Kayab, the central base of the Dresden Venus table (slightly corrected from Spinden 1924, p. 174).

Figure 12.11 shows the emergence of various deities from a water lily vine with star glyphs, the two-headed serpent, the Bird of Heaven, and a brief text opening with a date 13 Muluc 8 Zotz. The principal god is identified in the text as One Ahau, the equivalent of Quiche Hun Hunahpu.

6 These dates precede the usual era base at 13.0.0.0.0 4 Ahau 8 Cumku.

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