## Tuesday, December 27, 2011

### 51: Why The Week?

With the New Year approaching, I've been thinking about calendars
again lately.  One issue has always bothered me:  why do we have 7-day
weeks?  7 is kind of an ugly number-- it's a prime number, it's
not a factor of the basis of our number system, 10, and doesn't
directly divide into the length of most months or of the year.
Wouldn't a 10-day cycle be more convenient to calculate with?  Or how
about 6 days, which we could also easily divide in half when needed?
5 days might be nice too,  enabling easy counting on your fingers.  Of
the Bible says the Earth was created in 7 days, and it was dictated
directly by God, so I'm destined for eternal punishment for
questioning God's math.  But the rest of you are probably aware that
the Bible has relationships to other ancient religious texts, and some
non-Judeo-Christian societies have developed 7-day weeks as well, so
there must be more to it.
Why do we have weeks anyway?  The concepts of the month, related
to the lunar cycles, and year, related to the solar cycle, are pretty
obvious.  But humans have a natural need to periodically congregate,
to exchange goods and news of their neighbors:  in many societies, the
word 'week' is related to that for 'market day'.  A full month is
apparently too long to wait for a market day, so most societies have
created some shorter intervals.  The 7-day week is not fully
universal:  there are records of early societies having 3 to 10 day
market intervals, such as the 9-day market period in early Rome.  But
eventually societies as diverse as Hindu, Babylonian, Chinese,
Japanese, and Judeo-Christians ended up using the 7-day week, so there
Not surprisingly, the best explanations again turn to the cycles
of the heavens.  The simplest one is that the week is about 1/4 of a
month, and corresponds to the intervals between the main phases of the
moon: the new moon, full moon, and two half-moons.  A more interesting
version is that it comes from the fact that there are precisely 7
non-fixed celestial bodies that were visible to ancient societies:
the sun, the moon, Mercury, Venus, Mars, Jupiter, and Saturn.  This is
supported by the fact that in some Eastern cultures, the 7-day week
was used primarily by astrologers, and not a controlling factor in
civil life until interaction with the West made it convenient later
on.
Another interesting explanation I found online, at
webexhibits.org, relates to geometry.  This seemed kind of surprising
at first, since 7 doesn't seem to be a very geometrical number.  It
does not correspond to sides or angles of any regular solid, or of any
very interesting planar figure, other than things like stars and
polygons that work for any number anyway.  But here's how it works:
Try to tie a tight string or rubber band around a set of round
objects, such as soda cans.  If you have more than 3, most
configurations will be unstable, easily shifting around if you apply
pressure.  But 7 cans forming a hexagon with one in the center will be
much more stable, and tend to stay in that configuration.  Perhaps for
ancient people transporting bushels of grain or tent poles, this was
significant, and bore a connection to the market day.
Whatever its origins, the 7-day week is probably here to stay.
You can actually think of it as one of our few direct links to ancient
history:  because the weekdays repeat cyclically regardless of changes
to the other aspects of the calendar, we are still tracking an
unbroken chain of 7-day weeks that began at least as far back as Roman
times, if we can trust the Wikipedia entry.  Apparently, this has been
confirmed through examination of an early Ethiopian document
describing Easter Sunday of 311, as well as another first century
Roman document that mentions a day of the week along with its Julian
date.  This cycle may have started as early as 1400 B.C., according to
some sources.  It's kind of amazing to think that we still maintain
this link to our early history, after all the political and social
upheavals over the years.
And this has been your math mutation for today.

• Days of the Week at Wikipedia
• The Week at Wikipedia
• The 7-Day Week at webexhibits.org