The greatest festival in the Christian Church is Easter, a movable feast celebrating the resurrection of Jesus Christ. I have always wondered about the Byzantine blend of mathematics, astronomy, and folklore that are used to set the date for this holiest of days. Especially intriguing is the variation from one tradition to another of the date on which Easter is observed; Eastern Orthodox churches, for instance, typically use a different date for Easter than Catholic or Protestant churches. Why this difference?

In the beginning, Christians of Jewish origin commemorated Easter immediately after Passover, which occurs on the evening of a full moon and corresponds to a fixed date according to the Jewish (lunar) calendar. Hence, Easter could fall on any day of the week. However, gentile Christians wanted Sunday to be the day for celebrating the resurrection, which required that the feast occur on a moveable date.

In 325 A.D., the Council of Nicaea decided that Easter should be commemorated on the first Sunday after the first full moon on or after March 21st which was the date of the vernal equinox in that year. Thus Easter was bound to fall between March 22 and April 25. For each annual celebration, they thought to maintain the same day of the week (Sunday), the same season of the year, (Spring, shortly after the equinox), and the same relationship to the astronomical full moon (a few days following the full moon) that occurred at the time of Jesus¹ resurrection.

Since the time of Julius Caesar, the western world had functioned according to the Julian calendar, whose errors were becoming apparent even in the 4th century. Also, because the actual astronomical equinox could occur several days away from the 21st of March, additional error was introduced since the Easter calculation as decreed by the Council would still proceed assuming an equinox on March 21st.

By the 16th century, the accumulated error had reached ten days, enough to be noticeable even to the non-astronomically inclined. In 1582, Pope Gregory XIII reformed the calendar and approved the use of the system that bears his name. Also, to bring the calendar into conformance with astronomical observations, ten days in October were skipped. Most Catholic countries switched to the Gregorian calendar in that year, but Protestant Europe took almost another two centuries to be convinced. Once the British Isles began using the Gregorian calendar in 1752, all the western churches celebrated Easter on the same day. Russia, the Balkans, and the Middle East did not switch to the Gregorian calendar until the late 19th or early 20th century.

However, while virtually all secular institutions today are using the Gregorian calendar, certain parts of the Eastern Orthodox Church (including the Russian Orthodox) have not accepted it and are using the Julian calendar to this day in calculating the dates of Easter and all their feasts. And thanks to the Nicene fathers, since the Easter calculation is dependent on an arbitrary date on the calendar (March 21st), Orthodox Easter differs from the other churches because that date falls on a different day depending on whether one uses the Gregorian or Julian calendar. Had the definition been tied to an astronomical event (the equinox) which was independent of the calendar, the calendric differences would have been inconsequential.

In 1920, Soviet Armenia began using the Gregorian calendar. The Armenian Apostolic Church waited three more years to establish its use in calculating feast dates, making it one of the first Eastern Churches to have adopted it. Nevertheless, the Armenian Patriarchate of Jerusalem is the lone exception, still adhering to the Julian calendar because of concerns relating to the established system of sharing rights over key Holy Land shrines. As a result, Jesus¹ birth is celebrated in Jerusalem every year on January 19th, which is January 6th on the Julian calendar.

The current discrepancy between the two systems is 13 days, but because of the more complex rules used to define Easter (the Sunday after the first full moon after the equinox), there is no methodical pattern between the Julian and Gregorian Easter. Orthodox Easter occasionally coincides with the western Easter, but most often it comes later by either 4 or 5 weeks. In the 200 years between 1900 and 2099, Easter will coincide 57 times (28% of the years). In the Julian calendar, the sequence of Easter dates is repeated every 532 years; in the Gregorian, the cycle repeats but once every 5,700,000 years.

This year, the date of Easter according to both calendars falls on the same day: April 15th (April 2nd in the Julian system). Many saw this coincidence, coupled with the fact that it would be the first Easter of a new millennium, as an opportunity to try and convince the world¹s various churches to agree on a common method of calculation. The intent was to offer the world a more unified witness and not allow divisions over arcane matters to dilute the Christian message. Talks were sponsored by the World Council of Churches aiming towards a reconciliation of systems. Unfortunately, these discussions are taking longer than expected to reach fruition.

Below are reproduced two of the many L) existing algorithms for calculating the date of Easter; both of these are for the Gregorian calendar, but others are available for the Julian as well. Julian algorithms are shorter and simpler. All are variations on the same theme.

Note: Ardem Tajerian is a librarian with the Los Angeles Public Library.

Resources for Further Inquiry:

A great deal of information exists on the World Wide Web regarding calendar systems and methods for calculating Easter and other holidays. One good introduction with links to many useful tables of data can be found at:

http://www.smart.net/~mmontes/ec-cal.html

The World Council of Churches¹ press release on the talks over unification of the dating system is found at:

http://www.wcc-coe.org/wcc/news/press/99/0lfeat.html

A more technical and thorough discussion of calendar systems in general is found at:

http://www.tondering.dk/claus/cal/node3.html

Numerical Algorithms for Calculating the Date of Easter

Y%X is an integer remainder when Y is divided by X; Y/X is an integer division where the remainder is discarded. For example, 18%7=4 and 18/7=2.

Oudin¹s Method

century = year/l00
G = year % 19
K = (century - 17)/25
I = (century - century/4 - (century-K)/3 + 19*G + 15)%30 I = I- (I/28)*(1-(I/28)* (29/(I + 1))*((21- G)/11))
J = (year + year/4+ I+ 2-century + century/4)%7
L = I-J
Easter Month = 3+(L+40)/44
Easter Day L + 28 - 31*(EasterMonth/4)

Butcher¹s Method

a=year%19
b=year/100
c=year%100
d=b/4
e=b%4
f=(b+8) /25
g=(b-f+1)/3
h=(19*a+b-d-g+15)%30
i=c/4
k=c%4
1=(32+2*e+2*i-h-k)%7
m=(a+11*h+22*l)/451
Easter Month = (h+1-7*m+114)/31 [3=Mar, 4=Apr]
p=(h+1-7*m+114) %31
Easter Date=p+1 (date in Easter Month)

1. According to Ex. 12:2-6, Passover is to occur at dusk on the 14th day of the first month of the year. Because the months are based on the lunar cycle and the first of the month begins at the new moon, Passover always occurs at the time of the full moon, but on varying days of the week.
2. The date in spring when morning and evening occupy equal lengths of time, generally around March 23rd, plus or minus a few days.
3. These result from an inaccurate addition of leap days relative to the actual solar year. The Julian calendar falls behind the actual calendar by one day in 128 years.
4. There are, in fact, a number of other more subtle differences, such as the meridian at which one observes the new moon (traditionally Jerusalem, but Greenwich is another possible standard).
5. The proposal involved the abandonment of the arbitrary March 21 equinox in favor of accurate astronomical observations of the equinox and full moon (at the meridian of Jerusalem), as well as the agreed use of the Gregorian calendar. Naturally, the impact on Eastern Orthodox churches would be much more significant than on western churches.