Maddenation

Finding Easter

Recently, my golfing buddies started thinking seriously about planning our annual outing to Myrtle Beach. We quickly identified some times in March that might be suitable. Then someone mentioned that Easter is early this year, and that we should check that out before going further. No one knew when Easter was exactly, although the consensus was that it was probably in March. Indeed, Easter next year comes on March 27. How do we know that? Well, somebody (the Pope?) figures it out for us based on obscure rules established as part of the Gregorian calendar reform in 1582. Of course, the basis for the Easter date is the Jewish Passover, which is celebrated after the first full moon following the vernal equinox. This sets all the other dates. For example, Ash Wednesday is 46 days before Easter Sunday. What? You thought it was 40 days? Well, it is 40 days if you exclude Sundays, the days traditionally excluded from fasting rules.

I got interested in the date of Easter a few years ago, when I read an article called Easter is a Quasicrystal in Scientific American (March 2001, Mathematical Recreations column, p. 82). The article was interested in the pattern produced by plotting the Easter date vs. year. I’d show you the pattern, but the webmaster has still not instructed me in how to include a graph (or picture) in an entry. That notwithstanding, the really amazing part of the article was the set of instructions for determining Easter. Holy quasicrystal! Take a look.

The ecclesiastical rules are:

 Easter falls on the first Sunday following the first ecclesiastical full moon that occurs on or after the day of the vernal equinox;
 this particular ecclesiastical full moon is the 14th day of a tabular lunation (new moon); and
 the vernal equinox is fixed as March 21.
 resulting in that Easter can never occur before March 22 or later than April 25.

Choose any year of the Gregorian calendar and call it x. To determine the date of Easter, carry out the following 10 calculations (it�s easy to program them on a computer):

1. Divide x by 19 to get a quotient (which we ignore) and a remainder A. This is the year’s position in the 19-year lunar cycle. (A + 1 is the year’s Golden Number.)
2. Divide x by 100 to get a quotient B and a remainder C.
3. Divide B by 4 to get a quotient D and a remainder E.
4. Divide 8B + 13 by 25 to get a quotient G and a remainder (which we ignore).
5. Divide 19A + B - D - G + 15 by 30 to get a quotient (which we ignore) and a remainder H. (The year’s Epact is 23 - H when H is less than 24 and 53 - H otherwise.)
6. Divide A + 11H by 319 to get a quotient M and a remainder (which we ignore).
7. Divide C by 4 to get a quotient J and a remainder K.
8. Divide 2E + 2J - K - H + M + 32 by 7 to get a quotient (which we ignore) and a remainder L.
9. Divide H - M + L + 90 by 25 to get a quotient N and a remainder (which we ignore).
10. Divide H - M + L + N + 19 by 32 to get a quotient (which we ignore) and a remainder P.

Easter Sunday is the Pth day of the Nth month (N can be either 3 for March or 4 for April).

Now, far be it from me to criticism the church, but isn’t it time we fixed Easter? I mean, sure they didn’t know as much about astronomy five thousand years ago when they were deciding on the Passover date. But now we do. If you’re going to commemorate the Resurrection, why not do it at (roughly) the same time each year rather than at some quasi-random date between 3/22 and 4/25? Make it the first Sunday after the vernal equinox (which the church fixes as 3/21). Or better yet, make it the first Sunday in April. Forget the moon, full or not. What does the moon have to do with it anyway?

So that’s my rant for today. I don’t think the Pope is going to change Easter anytime soon. But he should, he really should.

DadExplanations12/02/04 5 comments

Comments

Kathleen • 12/06/04 4:12 PM:

This is quite interesting, if I do say so myself. I read most of the formula steps, but not them all. It gets pretty involved. Do you think they will change the date of Easter? I don’t think many people care about this, and I don’t think that it is a high priority. I am wondering: do you really think it needs to be changed? Or are you just making a point?

So, are we not supposed to fast on the Sundays of Lent? I thought we were supposed to fast on Fridays anyway, not Sundays. Does that mean that we can have whatever we gave up on those Sundays? I’m holding steady with my abstinence of chocolate and sweets during Lent. I’m hoping that one day it will stick. :0)

Dad • 12/07/04 11:28 AM:

Yes, I really think it should be changed, but I’m not going to start a crusade about it. I suppose the current system adds a bit of mystery and ancient tradition to the feast. However, we have moved several holidays to Mondays (at least in the USA) to create 3-day weekends. So moving Easter to a “fixed” date (albeit, always a Sunday) may not be so far-fetched.

Regarding Lent, in the olde days (pre-Vatican II), we used to fast every day except Sunday. However, I never noticed that it wasn’t really 40 days until now.

David • 12/07/04 5:07 PM:

Seriously Kath, Dad’s too busy ‘crusading’ for his Universal Time Campaign & Lobby to worry about such trivialities. Come on now.

Dad • 12/07/04 11:44 PM:

David, next time someone asks you what time it it in Kuala Lumpur, tell them, “It’s the same time it is here. It’s right now. “

David • 03/23/07 3:51 PM:

The Tilted Earth at its ‘Equal Night of Spring’ is a cool article about astronomy and the seasons and universal time. Dad, I thought you’d be interested. The article also discusses the timing of Easter (a bit). Here’s a cool quote:

“It seems wonderfully appropriate that you would anchor the timing of your planting season directly to the source of it” - Dr. Paul Doherty.

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