Re: I Should've Been Asleep Two Hours Ago...

On Sat, Apr 24, 2004 at 05:23:30PM -0500, Iain E. Davis wrote:
> > From: David Peterson [mailto:ThatBlueCat@AOL.COM]
>
> > What would be even cooler is if someone who was math savvy
> > could figure out how to manipulate the code so that it could
> > be applied to different calendrical (?) systems.  So, for
>
> ...different calendar systems... (I believe that's the way it would be
> said.)
"Calendrical" is a perfectly valid word, and is in fact part of the title
an excellent book on how different calendars work and how to convert
dates among them: _Calendrical_Calculations_ by Reingold and Dershovitz.


> > a way to manipulate it so you could get 14.  But even that
> > should be easier than, say, a system where each week was
> > composed of four days, or maybe each year was composed of
> > five weeks.  If there's anybody who knows how to do this kind
> > of thing, I'd love to see it done.
The easiest thing is to start by throwing away everything except the
day, and then build up from there. Calendars amount to a system for
providing a name for each day.  Most of them do so by grouping days into
larger units, and those units are determined by astronomy: a week is 7
days because of the 7 visible planets; a month was originally the time
for the moon to go through all of its phases and come back to where it
started; and of course, a year is the time it takes to go through the
cycle of seasons.

So if your conculture is based on Earth, it would probably have similar
units.  If it's on another planet, however, then you have to decide
what cyclic phenomena they would base their calendrical system(s) on.

The historical development is something like this: first days are
counted, and grouped into somewhat arbitrary divisions.  The 7-day week
originated in Babylonia and was, as I said, due to the 7 visible
"planets" in the night sky; other cultures used different numbers of
days (the Romans had an 8-day cycle, for instance).

The next thing that happens is the recognition that the moon takes
29 or 30 days to go from new moon to new moon (or full to full or
first quarter to first quarter).  So the culture starts counting moons.

Once they have conceptualized the moon as a chunk of time, they have the
tools to notice that the seasons return after 12 moons, giving rise to
the 12-month year.

Unfortunately, a true lunar month is only about 29.5 days, so 12 of them
only add up to 354 days, which isn't quite a full year.  Dealing with
this discrepancy is where calendar inventors start getting creative.

Once you get to the point where the discrepancy is noticed, you have
basically three types of calendar systems:

1. Purely lunar, in which months are based on the moon and years are 12
   such months long.  Since the calendar year is shorter than the
   tropical year by about 11 days, the seasons migrate through the
   calendar, taking about 33 years to come full circle.  If we had
   such a calendar and spring began in March this year, then in
   three years it'd begin in April, then in three more years it'd begin
   in May, etc.  However, you'd never need to mark the phases of the
   moon on the calendar because the new moon would always be on the
   1st of the month, the full moon on the 15th.  The Islamic calendar
   is of this type.

2. Purely solar, in which the year is based on the seasons and the
   month is just 1/12 of the solar year.  Our calendar is of this type.

3. Lunisolar, in which months are lunar and years are solar; the
   difference is made up by adding extra months ("leap months")
   periodically.  The Chinese and Hebrew calendars are of this type.

Orthogonal to the above classification is another one: calendars can be
"arithmetic", which means they're based on a simple rules governing
repeating cycles that approximate the astronomical phenomena, or
"observational", which means that the calendar is tied to the actual
astronomical events.  Our calendar is arithmetic.  If it were
observational, then instead of having a leap year every 4 years, we'd
have one whenever we needed to in order to keep the March equinox on the
20th of the month.  That would be *about* every 4 years, but every once
in a while it'd be 3 or 5 years instead, and the only way to know for
sure if a given year were a leap year would be to look in an almanac (or
do some fairly computationally intense math to calculate the time between
equinoxes yourself).

The Hebrew calendar is arithmetic, although it's one of the more complex
arithmetic calendars.  The Chinese calendar is observational - the month
begins on the date of the new moon in Beijing, and leap years happen
whenever there are 13 lunar months between winter solstices.

The Islamic calendar is also observational - but literally; a month only
ends after 29 days if the appointed religious official actually sees the
new crescent moon in the sky at sunset.  Otherwise the month is 30 days
long.  Since crescent visibility depends on a lot of factors that are
not completely predictable, like weather, Islamic calendars prepared in
advance are only approximate.

-Mark

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