Math Mutation 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 course, if you're a Biblical literalist, you already know the answer: 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 must be something special about this number. 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. References:
  • Days of the Week at Wikipedia
  • The Week at Wikipedia
  • The 7-Day Week at webexhibits.org