Posts Tagged ‘19’
Tuesday, March 23rd, 2010
… or, “How to Make a Simple Definition Really Complicated”
Today I was chatting with a friend of mine about when Easter is this year, and he cited the well-known (and incorrect) formula: “Easter is the first Sunday after the first full moon after the spring equinox.”
Although this is a pretty good approximation, and it is correct most years, the actual calculation of Easter is surprisingly complicated. The correct definition is that Easter occurs on the first Sunday after the paschal full moon. This is an artificially calculated date that actually does not correspond to any astronomical event. The best description of the paschal full moon is that it is pretty close to a full moon that is usually the first one after the spring equinox!
How did we get into this mess? Why don’t we just celebrate Easter on the same every day each year, as we do with Christmas? And why does the moon have anything to do with it? That is actually a pretty good story that goes way back in time … back before Christ was even born.
[By the way, let me interject that I am not a practicing member of any religious faith. My main reason for being interested in the date of Easter is that I am interested in the ways in which the moon affects our culture. If you are bothered by sentences like "Christ was born," you should mentally add, "according to the Christian religion."]
Let’s start with what the Bible says about Christ’s death. Depending on the book you read, he was either crucified on the date of the Jewish Passover, or the following day. In any case, his resurrection occurred on the Sunday after Passover. Hence, in the early years of Christianity, the practice was to observe Easter on that day.
But determining the date of Passover is itself no easy matter, and that is where the moon comes in. The Jews, like many other ancient civilizations (such as the Babylonians, from whom they borrowed their month names), used a combination lunar-solar calendar. These calendars have the advantage that the new moon always falls on the same day each month; day 1 is the first day after the new moon, and day 14 is (usually) the day of the full moon. Passover was defined as the 14th day of the month of Nisan.
The mischief starts because the lunar cycle is not synchronized to the solar cycle; 365 days is a little bit more than 12 lunar cycles. So if you want the same months to occur at the same time each year (as the Jews did; Nisan was supposed to be the first month of spring, when the barley ripens), you need to insert extra months now and then. In order to prevent your calendar from becoming completely chaotic, it’s nice to have a rule for when to do it.
Fortunately, the lunar and solar cycles do match up very closely every 19 years. Earth takes 19 trips around the sun in almost exactly the time that the moon takes 235 trips around Earth. (The difference is about two hours.) This means that your lunisolar calendar needs to have 12 normal years of 12 months, and 7 long years of 13 months, in each 19-year cycle. (12 x 12 + 7 x 13 = 144 + 91 = 235.) This fact was discovered by the ancient Babylonians and the ancient Greeks; the 19-year cycle is called the Metonic cycle after Meton of Athens. In the Hebrew calendar, it became a standard practice to have long years in years 3, 6, 8, 11, 14, 17, and 19 of the cycle.
This procedure kept the month of Nisan in the spring, where it was supposed to be. However, the Hebrews fiddled with their calendar quite a bit over the centuries; in the early days, the month of Nisan was often determined simply by observing when the barley ripened (a non-astronomical definition if there ever was one!). A controversy arose among early Christians over the facts that (a) the methods used for determining Passover had changed over the years, and (b) in some versions, Passover could occur before the spring equinox. The Nicean council in 325 AD resolved the controversy by adopting the definition that my friend (remember him? See the first paragraph) learned in school.
But that isn’t the end of the story! They didn’t have high-tech computers back then, so Christians continued to use the Metonic cycle of 19 years to compute when full moons would occur. Not only that, they used March 21 as the date of the equinox, which is not always astronomically correct. (For example, this year the equinox fell on March 20.) In other words, they tied the definition of Easter to an approximation of when the full moon occurs and an approximation of when the equinox occurs. This double approximation can result in a date for Easter that is completely different from “astronomical Easter.” The discrepancy arises, in particular, when the full moon occurs very close to the equinox. For example, in 2019 there will be a full moon on March 21, which is not “after the equinox” according to the church but is “after the equinox” according to Earth and the sun. The official paschal full moon that year will be April 20, not March 21, and Easter will be celebrated on April 21 instead of March 24.
But hold on! There are even more complications to the story! Notice that the church defines the spring equinox as occurring on March 21. But which calendar are you using? The Catholic church, and most Western churches, uses the Gregorian calendar, which first went into effect in 1583. However, the Orthodox Christian church uses the Julian calendar, which differs from the Gregorian calendar by 13 days. Why do they do that? Well, because they’re orthodox. Remember that one of the points of the Nicean council was to base Easter on the way that Passover used to be determined in the time of Christ, not the way it is determined now. Similarly, if we’re using a purely solar calendar to determine the equinox, then we should use the solar calendar that was in use during Christ’s lifetime and during the Nicean council — the Julian calendar, not the Gregorian one. That’s what orthodoxy means. You don’t let things like contemporary customs or the contemporary state of science keep you from doing things the right way, i.e., the way that they have always been done.
Thus, Orthodox Easter (or Pascha) frequently differs from the Roman Catholic Easter. This year, and next year, they are the same. But in 2012 Orthodox Easter will be one week later, and in 2013 it will be a whopping five weeks later (on May 5 instead of March 31).
Interestingly, there has been a move afoot in recent years to bring the Western and Eastern customs into alignment. The problem is especially acute in parts of the world (e.g., the Middle East) where Christianity is not the majority religion and where there are also different forms of Christianity in close proximity. The World Council of Churches has proposed what seems like a sensible compromise: to stick to the Nicean definition of Easter, using the true astronomical full moon and the true astronomical equinox. In other words, to adopt the definition that my friend told me. The nice thing about this definition is that nobody has to learn anything new! And it’s not a complete win for either side. The Orthodox churches would have to change more, but the Catholic church would have to change, too (for example, in the year 2019, as explained above).
However, disputes over matters of faith take a long, long time to resolve, and so I don’t expect to see this one resolved any time soon. I expect that Catholic Easter, Orthodox Easter, and astronomical Easter will remain three different things.
But finally, getting back to the question, “What does the moon have to do with Easter?” I thought the following sentence from the World Council of Churches document answered it very nicely:
“Easter/Pascha has a cosmic dimension. Through Christ’s resurrection, the sun, the moon, and all the elements are restored to their primordial capacity for declaring God’s glory. … Easter/Pascha reveals the close link between creation and redemption, as inseparable aspects of God’s revelation. The Nicene principles for calculating the date of Easter/Pascha, based as they are on the cycles of the sun and moon, reflect this cosmic dimension much more fully than a fixed-date system.”
I hope I have managed not to offend anybody; if you are interested, here are some other sites that discuss the timing of Easter.
The World Council of Churches paper, from 1997, is here.
Apparently they’re still talking about it. Here is a pastor’s blog that says (as of 2009) they are getting closer to an agreement.
Here is a page that explains the computation in terms of a formula. Note the prominent appearance of the numbers 19 (the length of the Metonic cycle), 7 (the number of days in a week), 4 (adjusting for leap years?) and 100 (adjusting for the Gregorian calendar). And note a couple of bizarre fudge steps that have no readily apparent explanation.
I find this explanation in tabular format to be much easier to follow. Note that within any given century, the date of the paschal full moon is completely determined by the Metonic cycle.
And what if you just want to know, “When is Easter in 2010?” The answer is that the actual full moon and the paschal full moon are on March 30, and Easter is on April 4.