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013-The Calendar: Leap Years

posted Feb 29, 2012, 3:29 AM by Gregory Taylor   [ updated Feb 29, 2012, 3:31 AM ]
(For Feb 29/12)


Para: Think you know when February 29th, 1600 was?

Cubi: Hey, think again! Hey, it depended on what country you were living in!

QT: On this February 29th, we will take a look at the evolution of the calendar.

Sexi: To fully understand, know that the Earth takes about 365.242199 days (not 365) to go around the sun.


Para: First, ever find it odd that SEPTember, OCTober, NOVember and DECember aren't the seventh, eighth, ninth and tenth months?

Sexi: Well, they used to be. The Roman Calendar (from 753 BC, or 1 Ab Urbe Condita) was ten months of 304 days. They had an eight day week.

Quinn: Sometime around 700 BC(??) they added two months to the end(?), Januarius and Februarius, to make 355 days. Some time later, there was an extra month added on top of that about every other year, since they noticed their March 1st was drifting.

Cubi: Hey, records are kind of vague from back then.

QT: This wound up creating an average of 366.25 days per year... and given 400 years, that's 146,500 days.... not the 146,096.9 days it should have been.

Para: They were getting ahead of themselves.

Cubi: Hey, so around 153 BC(?), they just decided to start the year in January instead of March. Hey, but by the end of 47 BC (about 708 AUC), things were so messed up that Julius Caesar made a decree.

Sexi: 46 BC lasted 445 days to bring the calendar back in line, and from 45 BC onwards the year would have ten more days, to total 365, except an extra "leap" day would be added every four years.

QT: Which was somehow interpreted after his death as every three years. Augustus corrected things in 8 BC, and removed leap days until after(?) 4 AD, to fix the alignment problem. Note, there is no year 0.

Quinn: Oh, and the months Quintilus and Sextilis were renamed to Julius and Augustus. The Caesars were popular. Or a little full of themselves. Or both.

Para: Of course, we now name that entire calendar after Julius too. Even though he only lived to see it for two years.


Para: We now have 365.25 days in a year. Close enough to 365.242199 days?

QT: Well, no. Exact values matter. Because after 400 years (365 by 400 = 146,000) we will have added 100 days (so 146,100)... but 365.2422 by 400 is 146,096.9 and thus we've still overshot by 3 days.

Cubi: Hey, three days per 400 years no big deal, right? Hey, wait, jump ahead 1600 years, and you'll be out of whack by (3 x 4) or 12 days. Easter's moved!

Sexi: Enter Pope Gregory XIII who, in 1582, decreed that October 4th would be followed by October 15th, to pull things back in line. This went over about as well as you'd expect.

Para: Hey, Greg, you're stealing ten days from us!

Cubi: Hey, who says we have to abide by Catholic inventions!

Quinn: Hey, the Pope is trying to keep true Christians from worshiping on the correct days!

Sexi: Gregory XIII further said that century markers would NOT be leap years, unless they were divisible by 400, to prevent this problem from reoccurring for another 3,000 years.

QT: That correction is why 2100, 2200 and 2300 will NOT be leap years... but why 2000 - and 1600 for that matter - WERE leap years.

Cubi: Hey, and the Pope died three years after declaring the change... reforming the calendar's a bit of a jinx.

Para: So I say again, think you know when February 29th, 1600 was?


Sexi: If you lived in Italy, Spain, Portugal, or Poland/Lithuania, you bought into the October shift of 1582.

Quinn: France jumped in later that same year, shifting from December 9th to December 20th, 1582, and the Netherlands followed suit.

QT: However, it took *until the 20th century* for EVERYONE to buy in, the Protestant countries being particularly reluctant...

Para: So you could celebrate February 29th, 1600, in France, then cross over the English Channel, since everyone there thought it wouldn't be February 29th for another 10 days!

Cubi: Hey, and certain calendar conversion cases are particularly interesting. Hey, jump to 1700, the first time a leap year (divisible by 4) was NOT supposed to be a leap year (NOT divisible by 400), according to the new calendar. Hey, Norway converts, Sweden, well...

QT: Sweden (including Finland) tried to bridge the date gap gradually, saying they would exclude all leap days over the next 40 years. But after excluding the 29th in 1700, they then had it anyway in 1704 and 1708... leading to giving up and using February 30th, 1712, to pull them back in line with the Julian calendar.

Quinn: Eventually, Sweden's (now eleven day) correction occurred in 1753, jumping from February 17th to March 1st. This less than a year after the British Empire (including America) finally caved, via the British Calendar Act of 1751. Their days went from September 2 to September 14, 1752.

Sexi: When Alaska was bought by the US (Gregorian) from Russia (Julian), the state jumped from October 6 to October 18, 1867. The Russians themselves didn't convert until 1918, after the October Revolution. Well, end of October for them, November according to most everyone else.

Cubi: Hey, don't forget about Asian countries either, most of whom accepted the system in the late nineteenth century (1800s), while still retaining their own non-Western methods. Hey, not everyone counts time via Anno Domini!

Para: The last conversion, at least according to Wikipedia, was Turkey in 1926, dropping 13 days. A parallel battle in the early twentieth century was time zones, but that's another story.

Quinn: Indeed, the year 2000 is notable as being the first time a century marker was "leaped" by the world consistently. A fact overshadowed by new problems, like Y2K. Still, these alignment issues are a problem for historians... and what of time travelers?

Sexi: As a final note, the day of the week for February 29th is reverse cyclical, running Monday, Saturday, Thursday, Tuesday, Sunday, Friday, Wednesday... meaning (if nothing changes) MathTans (aka Taylor's Polynomials) won't be leaping on a publishing day again until 2032. When we will most likely no longer be publishing.

Cubi: Hey, stop being so genre savvy...

QT: Want to create yourself some calendars? Try it at home!
Prefer to stick to math using our seven day week? Try it at home too!

Quinn: That's it then... so where's Lyn been through all this?!

Para: Oh, I figured she was too young to be a calendar girl.

*collective stare*

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