The Calendar, Part I

Happy New Year, everyone! Here is an abbreviated history of the Julian and Gregorian Calendars that we all know and love! I’ll be coming back to it later this week to talk about this fascinating subject. But for now, I thought a little history is in order:

The calendar is a fascinating mechanism. It’s full of history, politics, religion, intrigue, assassination, science, and yes, mathematics.

We begin with the idea that how we define a year is not simply a whole number of days, and certainly not 365 of them. A day is defined as the amount of time it takes the Earth to make a complete rotation on its axis. A solar (or tropical) year is defined as the amount of time it takes the Earth to make a complete orbit of the sun. And that doesn’t come out to an even number of days; it’s 365.2422 days.  This causes all kinds of problems and has for centuries!

We’re not going to go all the way back here, just to slightly before the Julian calendar, because that was the first standard solar calendar. Before that, it took a committee to decide when to add and subtract days based on moon phases and such. That sounds like no fun!

Before the Julian calendar, there were 10 months in the year: Martius, Aprilius, Maius, Iunius, Quintilis, Sextilis, September, October, November, and December. Each month had either 30 or 31 days. Since 304 days wasn’t enough to have a full year, things were rough. That’s not important to us, though. I just wanted to include it as background to explain why October isn’t the eighth month like the prefix suggests it should be. King Numa Pompilius added Ianuarius and Februarius to the end of the year, and tried to balance out the days so that it worked out. It didn’t, and that’s another story. They used to have a leap month!

The Romans were getting closer to having a working calendar, though, and they had 12 months, and finally Julius Caesar fixed things up. By then, they had 365 days in the calendar, and only one leap day every three years (SO close!) to compensate. Now they were getting somewhere! Then on the Ides of Martius (actually the first month of the year) one year after his calendar went into effect, Julius was betrayed and murdered. It was actually Augustus, Julius’s great-nephew (by blood, adopted as his son), who completed the work. He bounced Ianiuarius and Februarius to the beginning of the calendar, renamed Quintilus to Iulius to honor his father, and changed Sextilus to Augustus. Hey, he earned it, right? He had to jiggle the days of the months a bit so that his own month wasn’t shorter than Julius’s, but you know, to the victors go the spoils (Marc Antony would agree, I’m sure). So, when you think that December should be the tenth month and isn’t, blame Augustus Caesar!

By this time, then, the Julian calendar had the months in the same familiar order we know, with the appropriate number of days and leap year occurring every four years instead of every three! This worked for almost 16 centuries! Just one small problem: The math was all predicated on the idea that the solar year was 365.25 days long. As discussed earlier, it’s actually 365.2422. So, even though we had leap years occurring every four years, the Julian calendar was overcorrecting by a smidge, 0.0078 of a day (a little over 11 minutes) every four years. That’s pretty good, until you do it for 16 centuries! The calendar that had served humanity so well was not working again. In 1582 Pope Gregory XIII saw that the calendar was off by no fewer than 10 days, when comparing to the measurable solstice and equinox days! Mass hysteria, dogs and cats living together! Okay, so planting and holidays were off a bit. But when you have an agrarian society, that can be the difference between life and death!

Pope Gregory decided not only to take 10 days off the calendar (October 5-14, 1582 to be precise) for a reset, he also made the necessary corrections so that it wouldn’t happen again. He decreed the following: Leap year would occur when the year is divisible by 4, with the exception of years that also divide evenly by 100. But to this exception there would also be an exception. Years divisible by 400 would be reinstated as leap years! Got all that? Yeah, lots of people didn’t agree with his new Gregorian Calendar. Neither did the whole world agree with the whole “skipping 10 days” thing.  Probably a lot of people with early October birthdays. Anyway, this led to chaos throughout the world of trade. From 1582 to as late as 1927, many countries, even some states and territories within the US, didn’t necessarily agree on what day of the year it was! Eventually everyone came on board, because as time went on, the roundoff error got even worse. Sometimes, being stubborn doesn’t pay!

The worse news was about the disagreement over when to change the calendar. But we’re really not getting into that now. We now live in a safe, comfortable world, where at least we can agree on what day and year it is!

Believe it or not, we’re going to do more with the calendar later. It’s a deep subject, deserving of more study.

For a much more detailed history on this phenomenon, see Stephen P. Morse’s amazing webpage!