I got a message the other day informing me of an appointment on Monday 02/Sep/15.  Corrected swiftly to Wednesday 02/Sep/15.  Which got me to wondering how far in the future it would take before 02/Sep/15 was a Monday.  (It turns out that it'll only take 100 years, until 2115.  Isn't it nice how two-digit years have slid back into common usage as memory of the Y2K panic fades?)

But I noticed something as I was checking through the centuries, and that is that September 1st ??15 will never be a Monday, and it's all because of Pope Gregory.  Moving forward 100 years from 2015 to 2115 moves us back two days in the week, because 100 years = 100 * 365 + 24 leap days (which would be 25 if not for the Gregorian calendar rule where 2100 doesn't get one), or 36524 days total.  36524 days is 5217 weeks plus five extra days, or 5218 weeks minus two days, so the weekday moves back by two (or forward by five, which equivalent in modulo-7 arithmetic).  So the same thing happens going from 2115 to 2215, and 2215 to 2315.  We've now gone back six days.

And then we go from 2315 to 2415.  This time, though we have our full 25 leap days, because of the 400-year rule from the Gregorian calendar, so we only go back one day.  So now we've gone back seven days, or a full week.  If we started on a Tuesday in 2015 (as September 1st will be), we'll go back to Sunday in 2115, Friday in 2215, Wednesday in 2315, and back to Tuesday in 2415.  And 01/Sep/15 will never be on any other days of the week.

The Julian calendar didn't have this problem (problem?  Maybe that's a bit strong; it's really more of a characteristic), because it always had 36525 days per century, and always went back one weekday in the same interval.  So any given date would hit every day of the week for a given two-digit year suffix.

Who is it we have to blame for the seven-day week again?  Babylonians?  Wonder if we'll ever be able to get rid of it...