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Re: Ariadne's thread
Posted:
Dec 4, 2011 2:53 AM
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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
260-day 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.
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