The Calculation of Easter

In his Ecclesiastical History of the English, the eighth-century historian Bede repeatedly mentions the controversy between the Irish and the Roman churches over the correct calculation of Easter. As Bede sees it, the culminating moment in this battle comes at the synod of Whitby when both sides present their arguments before king Oswy, who decided in favor of the Roman method. From our distance, the argument may seem rather silly—an argument over how many angels can dance on the head of a pin. (The standard answer to that question, by the way, is "as many as God wants.") Looking more closely, we might notice that beneath the surface debate is really a question of power—who gets to define the rules for the most important Christian celebration. In any event, for the historian interested in establishing a chronology of the Middle Ages, the debate over how to calculate Easter is invaluable. We owe the AD system of counting years to an early Easter calculator, and the Church's continuing concern that Easter be celebrated correctly ensured that various regions all adopted the same count of years—the one we still use today.

Easter in the Early Church

From at least the 2nd century CE, there was prolonged controversy over what date upon which the passion of Jesus ought to be celebrated. Much of the confusion stems from ambiguity in the biblical account. All four gospels clearly state that Jesus rose from the grave on the first day of the week (now called Sunday), three days after the crucifixion. They also, however, refer to the Last Supper with relation to Passover, which begins on Nisan 15 (see the Jewish calendar). The synoptic gospels imply it was a Passover meal, but John says it was on the day before Passover (Nisan 14).

I won't go into the doctrinal disputes to which these ambiguities gave rise. The interested reader should consult the "Easter" entry in a good encyclopedia of theology (e.g., the Dictionnaire de Théologie Catholique). The generally favored solution was that Easter should always be on a Sunday, and that there should be some rule for determining a time fairly close to Passover. Just what this rule should be took a long time to hammer out. Relying upon the Jewish definition of Passover was uncongenial to many Christians, and as the Jewish calendar was not yet fixed by rule there was also the practical problem of waiting for the determination of the Sanhedrin in Jerusalem for a date which then had to be transmitted to widely separated churches throughout the Roman empire. To calculate Easter, then, Christians needed to find a lunar month in spring, which required both a definition exactly when spring began and a method of computing lunar months (i.e., a lunar calendar) that could be converted into the Julian calendar.

The rule eventually agreed upon was that Easter should be celebrated on the Sunday after the 14th day of the "Paschal" month. That Paschal, or Easter, month (essentially a Christian version of Nisan) is the one where the 14th day is on or next after the vernal equinox.

Even after this definition was generally accepted, there were still problems. When, exactly is the vernal equinox, and what sort of lunar calendar does one keep to track the Paschal month?

The Romans took the vernal equinox to be on March 25, a traditional date, to which they clung stubbornly for many years. Many of the eastern churches, however, took March 21 as the equinox. This measurement was fixed by direct observation of astronomers in Alexandria in the early third century. During that time, Alexandria was famous as a center of astronomic knowledge, and it was a natural place to go for expert consultation.

The lunar calendar used to track the new moons was also a subject of debate. The earliest surviving Easter tables show that the approximation 8 years = 99 months was used. This approximation results in an error of 1 day every 5.2 years. Clearly, for any long-term calculation of the moon, this rule will very quickly accumulate significant errors. In the early third century, a Roman named Augustalis introduced a new approximation: 84 years = 1039 months. This equation leads to an error of 1 day every 64.6 years—a significant improvement. Meanwhile the eastern churches, undoubtedly advised by Alexandrian astronomers, had found an even more accurate cycle: the familiar Metonic equation of 19 years = 235 months. This approximation has an error of only 1 day in 316.6 years.

Alexandrian Easter

In 325 CE, the Council of Nicaea met. One of its primary tasks was to ensure a uniformity of observation in liturgical matters, particularly with respect to the observation of Easter. The council decreed that Easter should be kept on the same day everywhere, and from the evidence of a surviving letter, it seems that the Alexandrian church was to make the standard calculations. Just because the Alexandrian church was tasked with calculating Easter does not mean they continued to rely upon astronomers to supply them with the actual date of the vernal equinox. Rather, they seem to have taken a number from the astronomers sometime in the 3rd century, and simply used it from then on. In 325 CE, for example, the equinox fell on March 20 (in Alexandria).

Rome did not actually abandon the 84-year cycle or March 25th equinox (which, of course, led to periodic differences in date between the Alexandrian and Roman churches), but often Rome seems to have accepted Alexandrian calculations. Not always, however. From time to time, the Roman church expressed its unhappiness with dates that it considered unsatisfactory. Ironically, every time the Romans consulted experts, they were essentially told that their way was inaccurate, and that they should adopt the Alexandrian computation.

The Start of Anno Domini Dating

In one of these periodic reexaminations of the issue, the problem was handed over to one Dionysius Exiguus (Denis the Little, or as I like to call him, Denis the Scrawny). Dionysius reported back reaffirming the Alexandrian method of calculation, and since the tables currently in use were about to expire, he also took the opportunity to calculate the dates of Easter for the next 532 years. The tables he produced and the introductory letter have survived. To the beginning of his tables he prefaced the last 19 years of the old tables. Those tables identified the year in the year of Diocletian (sometimes called the Era of the Martyrs, for the great persecutions of Christians that took place under that emperor), years 228-247 to be precise. When Dionysius continues his table, however, he dates the years in the cycle from the incarnation of Christ (anno domini is Latin for "year of the lord"), as he believed them to be. In his letter, he explains that he preferred that Jesus, not a persecutor of Christians, be remembered in his tables. The first year in his continuation is 532, which is thus equated with the year of Diolcetian 248. To provide another correlation to a known count of years, Dionysius also indicates the year of the indiction, a 15-year cycle used in the late Roman empire for purposes of taxation. AD 532 was the 10th year of the indiction, according to Dionysius.

A Medieval Easter Table

To get some sense of how Easter was calculated after Dionysius by people who lacked computers (or even Arabic numerals), I here transcribe an actual table from a manuscript written in 1004. I will reproduce it as exactly as I can, including abbreviations.
B M iiii ii xxvi vi xiii v id aprl xvi kl aprl xxi
  M v iii vii vii xv iiii kl aprl kl aprl xvii
END M vi iiii xviii i xvi xv kl mai xi kl mai xviii
  M vii v Nvlla ii xvii Non aprl xvii id Aprl xv
B M viii vi xi iiii xviii viii kl aprl v kl aprl xvii
  M viiii vii xxi v xviiii Id april xx kl mai xviii
  M x viii iii vi i iiii non aprl v id aprl xxi
  M xi viiii xiiii vii ii xi kl aprl viii kl aprl xvii
B M xii x xxv ii iii iiii id aprl id aprl xvii
  M xiii xi vi iii iiii iii klaprilis non aprl xx
OGD M xiiii xii xvii iiii v xiiii kl mai vii kl mai xii
from Berne Stadtbibliothek, Cod. 87, fol. 18.

So, what does it all mean? Let's start with the column headings, which in this case actually come in the middle of the table. Expanding the abbreviations, the headings mean: anni domini (years of the lord); indictiones (indictions); epactæ (epacts); concurrentes; cicli lunae (lunar cycles), 14ma Luna (the 14th moon); dies dominica post (the Sunday afterwards); luna ipsius (this moon).

The indiction we have already seen. It plays no direct role in the calculation of Easter, but note that the cycle remains consistent with that given by Dionysius. The epacts indicate the age of the moon (i.e. days into the lunar month) on March 22, the earliest possible date of Easter Sunday. The concurrentes give the day of the week (the so-called ferial numbers) of March 24th. The lunar cycles track the Metonic, 19-year cycle. Later in the Middle Ages, this cycle will be determined by the numerus aureus, the golden number, so called because it is the key to figuring out the date of Easter. Note, however, that this lunar cycle, while it has the same practical effect as the golden number, is not exactly the same. For example, 1010, which has a golden number 4, is listed as the first year of the lunar cycle. The 14th moon is the 14th day of the lunar month, i.e., the full moon. The Sunday afterwards is Easter. The "moon itself" is the age of the moon, i.e., the day of the lunar month, on Easter.

Apart from the numbers and dates, the other abbreviations in the margin are B, for bisextilis, i.e. a leap-year; END for endecadas and OGD for ogdoadas mark the subdivisions of the Metonic cycle. The first is a period of 11 years, the second of 8. They coordinate the insertion of lunar leap.

Translated Medieval Easter Table
  Year Indct Epct 3/24 Gldn# Full Moon Easter Moon on Easter
L 1004 2 26 6 14 April 9 March 17 21
  1005 3 7 7 15 March 29 April 1 17
  1006 4 18 1 16 April 17 April 21 18
  1007 5 0 2 17 April 5 April 6 15
L 1008 6 11 4 18 March 25 March 28 17
  1009 7 22 5 19 April 13 April 17 18
  1010 8 3 6 1 April 2 April 9 21
  1011 9 14 7 2 March 22 March 25 17
L 1012 10 25 2 3 April 10 April 13 17
  1013 11 6 3 4 March 29 April 5 20
  1014 12 17 4 5 April 18 April 25 21

If you check these years (for example with the ChurchCalendar applet) you will find only one (March 17) is wrong. This one is an obvious scribal blunder. Easter must come after the full moon. The scribe wrote 16 Kalends of April when he should have written 16 Kalends of May, which is April 16, the correct date. Further, if you calculate the week day of the 24th, you will find that all of them match up correctly (1 = Sunday, etc.).