working on Venus almanac to decode Floyd numbers in the form 1.5.5.0 The table of Venus apparitions Ernst Forstemann discovered the Venus content of the table in 1901, when he noticed that the red numbers across the bottom of each of pages 46 to 50 are identical, and sum to 584(8). This is very close to the mean synodic period of Venus (583.92 days). The sequence of numbers making up the sum is 236, 90, 250, and 8. These divisions in the synodic period are almost certainly intended to mark the four principal apparitions of Venus - visibility as morning star, invisibility at superior conjunction, visibility as evening star, and invisibility at inferior conjunction. The apparitions of Venus Venus period of visibility as morning star begins with its heliacal rise--- the date on which it rises with the sun. It rises earlier, and thus rides higher in the sky at sunrise until it reaches maximum western elongation, about half way through its apparition as morning star. Thereafter, it rises progressively closer to sunrise, finally rising after the sun so that it is lost from sight. At this time, Venus lies between the earth and sun. The midpoint of this period of invisibility is the moment of superior conjunction. It re-emerges from the suns glare when it rises at sunset (cosmic rise). It then rises progressively later as evening star until it reaches maximum eastern elongation. When it rises at sunset once again, it is lost behind the earths shadow at inferior conjunction before re-appearing again as morning star. The synodic period is the time required to complete a full set of apparitions, e.g. from heliacal rise to heliacal rise. See Michielbs Maya Astronomy page for a description of Venus apparitions. Above the red numbers (separated from them by a block of text) are black numbers that record a running total from page 46 to page 50. A single pass through the five pages of the almanac tracks Venus over 5 synodic periods. At the upper left of each page, there are 13 rows of tzolkin dates. The tzolkin is cycle of 260 days, each designated by one 20 day name glyphs and 13 numbers. Each row of tzolkin dates corresponds to a pass through the table. Although many of the day signs have been obliterated, the structure of the table makes it possible to restore them. On the first page of the table, the first date in first row is 3 Kib. This corresponds to superior conjunction of Venus, when Venus disappears after its apparition as morning star. The second date in the row is 2 Kimi, 90 days after superior conjunction, corresponding to cosmic rise as evening star. The next date is 5 Kib, 250 days later still, when Venus again disappeared at inferior conjunction. The last date in the row on this page is 13 Kan, 8 days later, marking heliacal rise. The next page begins 236 days later, with superior conjunction again, on a day 2 Ahaw. After a complete pass through the table, it is re-entered again at the beginning, but on the second row of tzolkin day signs. Although the first station listed in the table is a superior conjunction date, the first total (recorded above it) is 236. This suggests that the table is intended to be entered 236 days before superior conjunction, at heliacal rise. The table thus appears to begin and end at heliacal rise. Since 3 Kib marks the first superior conjunction, the true entry date, found by counting back 236 days to heliacal rise, is 1 Ahaw. Since 13 passes through the table are required to track through all 13 rows of tzolkin dates, the table covers 5 x 13 = 65 Venus periods = 37960 days. The table is no doubt carried out this far to make it commensurate with the Calendar Round: 65 Venus periods = 146 tzolkin = 104 haab = 2 calendar round cycles. Thus the table recovers the initial tzolkin date on which table was entered after a complete cycle of 65 Venus periods. The last date listed in the table is 1 Ahaw, the same tzolkin date on which the table is entered. Lounsbury suggests that 1 Ahaw was chosen as the entry date because of the association of Venus with the hero twin Hun Ahaw.(9) Note that between the 1 Ahaw heliacal rise dates at the beginning and end of the table, heliacal rise is recorded every 584 days. Because 584 is a whole multiple of 20 + 4, the day sign advances by four places at each heliacal rise through the table. Thus five day signs can correspond with heliacal rise, Ahaw, Kan, Lamat, Eb and Kib. Codex Actual Morning star 236 263 Sup. Conj. 90 50 Evening star 250 263 Inf. conj. 8 8 Total 584 584 The 584 day period between heliacal rises is within one day of the average value of the true synodic period. As will be explained below, even greater accuracy was achieved by applying a correction on successive passes through the table. But the times allotted to the apparitions of the planet between heliacal rises are much less accurate. For example, Venus is morning star for an average of 263 days, rather than the 236 days allotted in the table. In practice, the discrepancy is perhaps not as great as it may seem because of the difficulty in observing the planet when it rises or sets shortly before or after the sun, and because the actual synodic period varies from 581 to 587 days. In addition, the most important station, the time of heliacal rise, will be close to correct, occurring at 584 day intervals. Nevertheless, the accuracy with which the scribes determined the mean synodic period proves they were competent Venusian observers, and leads to the conclusion that they deliberately altered the length of apparitions for ritualistic purposes. Gibbs suggests that the almanac distorts observation so that the auguries associated with the beginning of each apparition are consistent with established auguries for days in the tzolkin. He suggests that the almanac is contrived to bring the apparition dates as close to observation as possible while retaining the required links with the tzolkin. Aveni has suggested that the dates of Venus apparitions may have been chosen in an effort to make the Venus cycle and the eclipse cycle commensurate. He noted that the length of apparitions recorded in the Codex are nearly multiples of lunar months (236 days = 8 lunar months - 0.24 days; 90 days = 3 lunar months +1.41 days; and 250 days = 8.5 lunar months -1.25 days). (11) Entering and using the table Heliacal rise will fall on a day 1 Ahaw only rarely. If tzolkin dates are ignored, the table could be used to track the apparitions of Venus if entered on any heliacal rise date. In practice, it is possible that the table was used in this way, as a computational aide for finding the number of days between rituals to be performed at stations in the planets path through the heavens. However, the mythological significance of rise on the day named for Hun Ahaw likely made entry into the table on such a day particularly significant. In fact, page 24 supplies long count dates that are days 1 Ahaw on which the table could have been entered. The entry dates are listed on the lower left hand side of page 24. The first column of the page contains the number 6.2.0. The kin coefficient is circled in red and tied up with a bow knot. This indicates what has been called a ring number, which appears to be used to count back to a date prior to creation. The calendar round date of creation, 4 Ahaw 8 Kumku, is written below the ring number. The number in the second column is 9.9.16.0.0. Below it, 1 Ahaw 18 Kayeb is written, but this is not the correct tzolkin date if this is an ordinary long count number. It is, instead, what Thompson called a long reckoning, counted forward from the date reached by the ring number.(12) Transformed into a standard long count, it is 9.9.9.16.0 1 Ahaw 18 Kayeb. The number in the next column is also 9.9.9.16.0. This date is likely intended to be an entry into the table. 9.9.9.16.0 corresponds to 9 Feb 623 AD (Gregorian) if the 85 version of the GMT correlation is adopted. This should be a heliacal rise date , but in fact at this time Venus was 13-16 days from heliacal rise. Thus, 9.9.9.16.0 does not appear to be a practical entry date into the Venus table. However, it is six centuries before the Dresden Codex was compiled. It is likely a throw-back, calculated by subtracting multiples of the length of the Venus table from a later 1 Ahaw that was close to heliacal rise. 9.9.9.16.0 fails to mark an actual date of heliacal rise because of the error that accumulates when the table is re-cycled. It was probably included in the Venus pages because of ritual or augural significance. Lounsbury has called 9.9.16.0, the long reckoning used to reach the entry date, the super-number of the codex because it is a multiple of so many cycles-- 5,256 tzolkins, 3,744 haabs, 2,320 Venus periods, 72 calendar Rounds. The date before creation reached by the ring number is also a day 1 Ahaw 18 Kayeb, and thus another throw-back entry date.(13) This may have been regarded as the date when Venus first rose in the prelude to creation. For a fuller discussion of ring numbers, see Gregory Reddick, Ring and Serpent Numbers in the Dresden Codex -------------------------------------------------------------------------------- If 9.9.9.16.0 is a calculated entry date, the practical base of the table must have been a later 1 Ahaw. Identification of a plausible date depends on the correlation constant used to match long count positions with the Gregorian calendar, and thus with modern calculations of heliacal rise dates. Lounsbury notes that if the 85 constant is adopted, as exceptionally good match occurred on 10.5.6.4.0 1 Ahaw 18 Kayeb = 25 November 934 AD, which was within 0.1 day of heliacal rise. Moreover, the 9.9.9.16.0 heliacal rise date recorded in the Codex is an exact multiple of 584 day Venus periods earlier than 10.5.6.4.0, suggesting that the Codex rise date was calculated from the rise date discovered by Lounsbury. He identifies 10.5.6.4.0 as a unique event in historical time. He believes it is both strong evidence for the 85 correlation constant, and the probable date on which the Venus table was inaugurated.(14) Lounsburys argument has been accepted as definitive by many Mayanists, but it has not escaped criticism. Dennis Tedlock notes that the birth of God GI, father of the hero twins, is recorded at Palenque 780 days (3 tzolkin cycles or 1 synodic period of Mars) before the date given in the Dresden as the first rising of Venus. This suggests that a Venus table with 1 Ahaw 18 Kayeba s base date must have been in use at Palenque two centuries before 10.5.6.4.0. Although no 1 Ahaw 18 Kayeb date can be closely matched with heliacal rise if the 83 constant is employed, several 1 Ahaw dates are available. Both 10.15.4.2.0 1 Ahaw 18 Wo (11 December 1129 AD) and 11.0.3.1.0 1 Ahaw13Mak (20 June 1227 AD) are heliacal rise dates if the 83 constant is correct. 11.5.2.0.0 1 Ahaw 3 Xul (28 December 1324 AD) is one day after heliacal rise. Tedlock noted that 1 Ahaw 18 Wo, 1 Ahaw 18Mak,and 1 Ahaw 3 Xul are dates on which the table can be adjusted if the correction scheme described below is applied. He suggests that this is evidence of revision of the table on one of these dates.(15) See also The Correlation Question. See the on-line Catalog of Venus heliacal risings and setting in the Yucatan
Posted on: Mon, 05 Jan 2015 17:23:03 +0000
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