The Calendar

Does anybody really know what time (it) is?

All of us Mazatlecos know that Carnival is a pretty big deal around here. What few people know though, is when Carnival is. Of course we know that this year it is on Feb 21st, but when is it next year? Like most things in life, the real answer is a little more complicated than "next Wednesday." To get to the answer we have to understand a little more about our calendar. First I'll start with an easy question.

The Basics

We all know that there are 365 days in year, and that every fourth year, for some strange reason called a "leap" year, we have 366 days. These leap years occur during years which are divisible by four, and which happen to have US presidential elections. I think they did that so they could have one extra day of campaigning. Now the question: Is the year 2000, (which by the way is not the first year of the next millennium) a leap year? If you answered "yes," you are not only correct, but probably also lucky, because only once every four hundred years is a century a leap year. That means that while the year 2000 is a leap year, the years 2100, 2200, and 2300 will not be leap years, even though they are divisible by four. How did we get into this mess?

Why do we care?

It all started a very long time ago, when people started getting organized and wanted to know things like "Should I start planting my crops now?" Needless to say, this was a very important question, and getting it wrong could mean starvation and death. Thus people started to create something called a calendar, and since Issac Newton hadn't been born for a few thousand years yet, coming up with a calendar that works was no small feat. I'll skip over the Egyptians, Babylonians, and Phoenicians, and I mean no offense to the Hebrews, Muslims, and Mayans, but in order to keep this article to a reasonable length, we'll start out with the Roman calendar.

Mr. Caesar's Calendar

About one century BC, our old friend Julius Caesar decided to get serious about this calendar problem. Up until then they were using a lunar calendar, based on the phases of the moon, which was getting seriously out of step with the seasons. It was so far out of step that in 46 BC they stuck an extra 23 days into February, and added two months between November and December to get back in sync. Talk about a long year! Anyway, Mr. Caesar hired the best astronomer in the business to come up with a calendar, and henceforth decreed that the year was 365.25 days long. This was a huge improvement over the Egyptian 365 day year, and things were going along pretty smoothly for a while, but there was still a problem. To see what the problem was, let's look at what exactly a day, month, and year really are.

The Day

How long is a day? Well, first we should ask what is a day? The answer is, it depends. If you mean the time it takes for the sun to go from sunrise to sunrise, or high noon to high noon, the answer is slightly different each day, as the Earth goes around the sun, but the average value is 24 hours 3 minutes, and 56.55 seconds. This day is called a solar day. On the other hand, if you measure the amount of time it takes for a certain star to get exactly back into its former position, then the day is only 23 hours 56 minutes and 4.10 seconds long, and is called a sidereal day. Well, let's split the difference and call a day exactly 24 hours. What the heck. The reason they are different is because the Earth is revolving around the sun while it is spinning on its own axis. Since it is revolving in the same direction as it is spinning, it has to go a little further to line up exactly with the sun each day. Just to add a little to the upcoming confusion, I'll throw in at this point that in early times people made a big deal about the moon. Religion dictated that the moon was really important, and should be involved in the calendar somehow. That is how months came about, but the problem there is that the moon orbits around the earth every 29.53059 days, and really has absolutely nothing to do with the timing of the seasons. (Though it does have some influence on the tides - see the January Pacific Pearl for that story.)

The Year

Now back to the year. Using modern instruments a year is exactly 365.242199 solar days. Astronomically, a year is the amount of time it takes for the Earth to make one complete revolution around the sun. This is the important number, if we want to know when to plant the corn. We expect the seasons to repeat themselves every 365.242199 days. You might wonder why none of the numbers come out even. The answer to this is why should they? How long it takes for the Earth to spin around its axis has absolutely nothing to do with how long it takes the Earth to travel around the sun. The numbers are what they are. So lets get back to the Romans.

A bunch of years

Julius had a good thing going for a while, but his year was long by 11 minutes and 14 seconds. You see .242199 is not .25, even though it is close. Julius didn't notice this problem while he was alive, but it adds up. It comes to about three quarters of a day per century, or about 7 days in a thousand years. Fast forward to 1582, when things were getting very serious. Famine, plague, war, pestilence you ask? No, but the date to celebrate Easter was getting all messed up and something had to be done. Pope Gregory stepped in, and decreed that people going to sleep on Oct 5th would wake up on Oct 15th. Boy talk about a good nights rest! But after about 1600 years, that is how far the old Roman calendar had gotten out of sync with the seasons again. His calendar, which is based on a year that is 365.2422 days long, is the one we use today. His new rule for leap years was that every fourth year is a leap year, except for centuries which are not leap years, except for every fourth century. Thus 2000 will be a leap year, while 1900 was not. Just to tie up a loose end, they are called leap years because normally each year a festival date moves forward one weekday, but every fourth year festival dates leap forward two days. (365 = 52 * 7 + 1 and 366 = 52 * 7 + 1 + 1)

Easter

So, when is Easter? It is complicated enough that really only the pope knows for sure. (Just kidding.) When I tell you the answer, you will have no doubt that it was decided by a committee, and you are right. It was decided by the Council of Nicaea in 325 and they came up with this. Easter falls on the first Sunday following the first full moon that falls on or after the vernal equinox. This isn't so bad, but the problem is it isn't true. Well, it is true but it depends on what you mean by full moon and vernal equinox. What the Council of Nicaea meant was the official vernal equinox, which is March 21st, and the official full moon, which might differ from the real full moon by one or two days. So, when is Easter? The actual formula is too complicated to write down here, but if you are really interested, you can find out at http://forum.swarthmore.edu/dr.math/problems/john.6.12.99.html If that's too much trouble, I suggest you ask the pope.

When is the Leap Day?

One last thing, just for your amusement. A simple question: Which day in a leap year is the "leap day?" If you said February 29, then bbbbrrrrrrrrrppppp - that's the buzzer that says you should have taken what was behind door number 2. The real answer is February 24th. I can hear you say, come on, get real. Well, our old friend Mr. Caesar decreed that "the 6th day before Kalendae of March" should be doubled. The corresponding day in our calendar is February 24th, and in Caesar's time there would have been two February 24ths rather than adding a February 29th to the calendar. This legacy still goes on today, for example there is a festival of St. Leander that in regular years takes place on February 27th, and in leap years it is moved to February 28th. Now that you know all of this valuable information, I should tell you that our wise church elders and government leaders are still hard at work trying to get this Easter mess straightened out. Just last March, there was a meeting of the World Council of Churches and the Middle East Council of Churches, to try to settle this Easter issue. The great new idea that came out of this committee is to define Easter as the first Sunday on or after the first full moon after the vernal equinox. Sound familiar? The difference is that this time they want to use the "real" full moon and the "real" vernal equinox. To get around the problem that date the "real" full moon might depend on where you are in the world, they have settled on using Jerusalem as the location for monitoring the astronomical events. This is supposed to take effect at the beginning of the next century, in 2001.

So Easter is...

So, when is Easter? Well, all I can tell you is that this year(1998) it is on April 12th, and no, I don't have the pope's email address.

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