Loreto:
> Actually it probably is that the oldest calendars have several-
> numbered days in a week. Four and seven are not the favourites.
?? Let's get this right. The time it takes for the moon to go around
the earth is said to take 27.321661 days, no? Most people don't deal
well with fractions and certainly not hunter-gatherers. They may
have had time to carry the two, but seriously! So the overwhelming
chances are that people at that time favoured _whole_ numbers. Ancient
people didn't need to know with extreme exactitude how long it took
for the new moon to come about again. As long as they knew that it
was approximately 27 days, that was enough.
You say that "four" and "seven" are not the favourites? Well with
what other numbers may we divide the lunar cycle to give the optimal
accuracy? ... Um, well... We have:
3 * 9 = 27 (off by a small fraction)
4 * 7 = 28 (off by a larger fraction)
5 * 6 = 30 (off by a couple of days)
Now yes, it would seem like "nine" and "three" are the favourites
because it's most optimal. So why favour "four" and "seven"?
The year is approximately 365 days long, for one thing. When you take
the lunar cycle in _combination_ with the solar cycle, "seven" is
really great. The solar year can be approximated using 7 and 52
(a multiple of 13). So we can approximate 13 lunar cycles in such
a rounded-off year, or rather 13 monthes... all using nice whole
numbers. Sweet!
Now take "9" and "3" from your optimalized lunar cycle and try to
coordinate it with the approximate year. By dividing the year by
"9", the only whole numbers you can use are "40" (yielding a 360-day
year that's off by five whole days) or an ugly prime "41" (a 369-day
year that's off by about four... ick!!). Let's use "3" instead. We
then need to use 3*122 = 366 days. This is bad for two reasons:
1) What am I gonna do with an ugly number like 122 (61*2)??
2) 366 days is a worse approximation than 365 (7*52)
since the actual year is about 365.25 days
Get it now? The point is that we're not talking about the calculation
of a lunar cycle or the calculation of a solar year in isolation. It's
the _combined_ calculation of these cycles using whole numbers as the
restriction. In that way, "four" and "seven" appear to me to be
favourites with "seven" being the "divine" whole number to tie in both
the lunar cycle and the solar year with the greatest amount of
accuracy without using fractions.
Playing with the Mayan calendar recently in order to program my website
to display the date for today made me realize all this. In fact, we
could tie in the Venutian cycle too using "seven". Seven times thirty-two
is the best way to approximate the revolution of Venus, if I were an
ancient hunter-gatherer turned astronomer. Since 32 is a nice multiple
of 2, 4, 8 and 16, I could have a mathematical hayday. Granted, you
could use nine if you were only concerned with just a sun-venus thing
since 9*25 is 225 days. That's ok I guess but how can you ignore
what the moon is doing and yet be so star-struck for tiny Venus?
Here's the cool part. If you were interested in a sun-venus-moon combo,
I'm thinkin' "seven" is a very handy whole number at your disposal. But
then a relationship between the sun, Venus and the moon would only
describe the entire origins of Near Eastern religion, that's all.
Remember the goddess and the two guys that always hang around her,
whether it be two suitors or father & son? It's all astronomy and
mathematics being deified.
= gLeN