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Almanaque

Alexandre Cherman

Recurrences…

Last week I wrote about an impertinent hoax that is being spread on the internet [LINK] (a little bit redundant, I know, since the very definition of internet hoax requires it to be spread…). Writing about the immeasurability of the year and the week made me think about what would be the real recurrence of the “day of the month/day of the week” combination. In other words: when will a year be identical to another one?

Our calendar is the Gregorian Calendar, but I’ll address this matter under the light of the Julian Calendar. Not because it is simpler (and it is!), but because I don’t want to jump the gun on some issues that will come naturally if we just follow the course of history, especially about the real rule for leap years (and no, it is not “one leap year every four years”).

In the Julian Calendar, the year has 365 days and the week, 7. 365 days is not a multiple of 7! That is what we call immeasurability. The closest multiple of 7 is 364. 364 is 52 x 7. So the year has 52 weeks and 1 day. Hence, if this year began on a Thursday, next year will begin on a Friday. And this simple rule applies to all regular years.

On leap years, with 366 days, there are 2 days in excess. 2016, a leap year, begins on a Friday, and 2017 will begin not on a Saturday, but on a Sunday. To concoct a general rule, we need to work with these blocks of 4 years (3 regular, 1 leap), totaling 1461 days. Which is not a multiple of 7 either!

The first multiple of 7 we will find, to no one’s surprise, is the sum of 7 blocks of 4 years each. In other words, the recurrence happens, in the Julian Calendar, every 28 years! 2043 will be identical to 2015. And then 2071. And then 2099…

(It doesn’t mean it won’t happen sooner, as for example, 2026…)

Curiously, this rule only applies til 2099! 2100 is a crucial year regarding the differences between the Julian and the Gregorian calendars. But I’ll get to that in due time… ■