The Mathematics of Calendar Reform

The Gregorian Calendar is inconsistent, and there is only so much we can do about it. The earth takes about 365.24 days to go around the sun. The number of days in the year are nicely controlled with leap years and leap seconds, to make this work out.

We have a tradition of the 7-day week. We have a tradition of months which are 28 or 30 or 31 days long. But worst of all, each year starts on a different day of the week, forcing us all to have new calendars each year.

So, can we do better? Sure we can. Let's look at the numbers:

First, every number can be expressed as a series of primes multiplied together, called a "prime factorization".

365 = 5*73

Yuck. Well, if we want 5 seasons of 73 days each, we are all set. I don't think so :)

364 = 2*2*7*13

This has potential. We could have 7 day weeks, 4 weeks in a month, and 13 months. Plus one day every year which is outside the "days of the week". A kind of yearly holiday for the 365th day. And on leap years, we need one more day like this. Then, every year would have the same pattern. Indeed, these kinds of 13-month systems have been proposed, and even used occasionally. The most recent version is probably this one:

http://en.wikipedia.org/wiki/International_Fixed_Calendar

I admit they are probably the most elegant, but I think the world will not readily switch to 13-month calendars.

So, we have two other choices. Give up months altogether, and go with 7*13 = 91 day quarters. This has also been proposed:

http://en.wikipedia.org/wiki/World_Season_Calendar

The other choice is to stick with three months in a quarter, with one month getting 31 days and the other 2 getting 30 days. I tend to think this is the most reasonable course of action. Here is a calendar system that works this way:

http://en.wikipedia.org/wiki/World_Calendar

Now, so others have proposed that, instead of having a day or two each year outside of the week, we should stick with 7-day weeks all year, but change the number of weeks per year to keep the calendar with the right "average days per year". These so-called "leap-week" calendars are interesting, but I think they would tend to drift a little too far from the astronomical events for my tastes. The first day of each season would drift around by a few days each year.

Anyways, for more info on this subject, look up "Calendar Reform"

Two good sources are wikipedia:
http://en.wikipedia.org/wiki/Calendar_reform
and this one:
http://personal.ecu.edu/mccartyr/calendar-reform.html

I'm in favor of The World Calendar, how about you?