
Re: Ariadne's thread
Posted:
Dec 4, 2011 2:53 AM


The Venus calendar in the Codex Dresden deviates from the astronomical cycle up to four days in the short range but is accurate to one day in 500 years on the large scale. This means that the Mayan astronomers had a very good formula for the Venus year (synodic orbit) allowing them to shift dates on the small scale without losing overall accuracy. I don't know of any successful attempt to explain the Venus calendar of the Maya. Observation alone can't explain it. Careful observations over long periods of time could have led to the knowledge that one synodic Venus orbit is longer than 583 days and a little shorter than 584 days. If you wish to get further from here you need a mathematical tool, a number sequence generating good values from such a pair. Begin with 583 days for one Venus year and add continuously 584 days for each more Venus year:
583/1 (plus 584/1) 1167/2 1751/3 2335/4 2919/5 3509/6 4087/7 4671/8 5255/9 5839/10 6423/11 7007/12 7591/13 ...
Now you can check on these values. A demanding task if you got no optical instruments. Another way to select a value from this sequence is to assume that several values not very far from the begin are fine, so you can choose the one that comes handy and fits into the numerical system of your calendar, in this case the 260day count, 'spine' of the Mayan calendar. 7007 days are 27 Tzolkin of 260 days minus 1 trecena of 13 days for 12 Venus years. Multiply the numbers by a factor of 20 and you get 540 Tzolkin minus 13 x 20 days or 1 Tzolkin for 240 Venus years
240 Venus years are 539 Tzolkin
accurate to 1.045 or simply one day in 500 years. Luckily, the handy value is also the most accurate one.
If you accept number patterns and sequences as tool of early mathematics you can look the astronomers and mathematicians of ancient Egypt and Mesopotamia and Mesoamerica over the shoulders.
Remembering what I have been told regarding my number columns fourteen years ago I wonder how mathematicians who ponder the most complicated problems can fail when it comes to early mathematics. I go on dreaming of a mathematical subdiscipline that cares about the simplest solution to a given problem.

