What do Computers and Easter have in Common?

easter-lily

The word computer is derived from computus, a Latin term literally meaning computation. Originally, computus had a very narrow meaning, describing the calculation of the date on which Easter falls each year.

Within Christianity, Easter is a moveable feast, meaning that its celebration day is not based on a fixed calendar date, but is variable each year based on the application of a set of rules. And the rules for computing the date in which Easter is celebrated are a bit complex. In fact, it’s ironic that computus is so closely related to computer, as you might feel the need for a computer after reading the rules for determining Easter.

Early Christians knew from the Gospels of the association in time between the Jewish Passover and Christ’s crucifixion and resurrection. Because of this, early celebrations of Easter were held on the Sunday falling within the seven-day celebration of Passover, also known as the Feast of the Unleavened Bread. Passover begins on the 15th day of the Jewish month of Nisan. The Hebrew calendar consists of lunar-based 30-day months with an extra lunar month (an intercalary month) added every 2nd or 3rd year. Because the month of Nisan could vary widely, often occurring before the vernal equinox, and because the Hebrew calendar itself varied by geographic location, the computation of Easter came under pressure to be codified by early Christian religious leaders.

The First Council of Nicaea in 325 called by Constantine I, which determined so much of the Church’s rules still in use today, tried to establish a consistent methodology for Easter. It still took several centuries for the rules for calculating Easter to become established, and even today the Eastern Orthodox Church calculates the date in a slightly different manner than the western Church. The most important point to remember about the computus is that it is a completely man-made construct, and that while it uses terms like full moon and months in its calculation, these are of its own making and have nothing to do with real astronomical full moons or months that tie to any other calendar in use.

So, hold on to your Easter bonnet, here’s the way in which we compute Easter day. First, we have to begin with understanding something about lunar and solar years. The computus is based on a lunar year which consists of alternating 29 and 30 day months. Therefore, a lunar year of 12 lunar months consists of 354 days and is 11 days shorter than a solar year, which consists of 365 days. As the differences between lunar years and solar years mount, the days are called epacts. When the epacts accumulate to 30, an extra lunar month is inserted into the year, bringing the solar and lunar years back into harmony. By adding one extra day every 19 years, called the saltus lunae or moon’s leap, this cycle of lunar additions and solar years repeats itself. This is known as the Metonic cycle. According to the Easter tables established by Dionysius Exiguus in 525, each year in the 19-year cycle is assigned a number from 1 to 19, known as the Golden Number, and each Golden Number has an associated date which is called the Paschal full moon. But before we talk about how the Golden Number is calculated, we need to know a bit more about the computus, the Easter month, and Paschal full moons.

In a calendar year (beginning on January 1st), the lunar month in which the 14th day falls on or after the vernal equinox is designated as the Easter month (in this case, the vernal equinox is always defined as March 21st regardless of when it occurs in the heavens).  And remember that the March 21st vernal equinox date is based on the lunar calendar, not our modern calendar.  The Easter month is also called the Paschal month. Why the 14th day?  The 14th day in a lunar month is traditionally considered the day of the full moon, even though astronomically speaking, the lunar month under computus is not directly related to the actual phases of the moon.  Since this “full moon” is really just a virtual full moon and not real in any astronomical sense, it is called an ecclesiastical full moon, or Paschal full moon. One additional note, astronomically speaking again, the vernal equinox can fall on March 19th, 20th, or 21st, but is fixed to March 21st for purposes of the computus.  Still with me?

Once you determine the date on which the Paschal month begins, it is relatively easy to compute the date of Easter – it’s the first Sunday that falls after the 14th day of the Paschal month. Using this logic, Easter never falls before the vernal equinox and can fall within the range of March 22 to April 25. If all this isn’t confusing enough, the Eastern Orthodox Church calculates Easter based on the Julian calendar, even though most countries under the Eastern Orthodox Church have adopted the Gregorian calendar for civil purposes. But I digress.

To determine Easter day we need first to calculate the Golden Number. The Golden Number is a, sort of, translation tool that connects the lunar calendar to the Gregorian calendar. It’s pretty easy to use – just take the remainder after dividing the current year by 19, then add one. Now, look up the that number, the Golden Number, on the Easter tables (see below) and the corresponding date is the Paschal full moon date (also called the ecclesiastical full moon).  Look at a current calendar for that month and year and the first Sunday falling after the Paschal full moon date is Easter.

I know, it’s confusing, so let’s use 2017 as an example.  Divide 2017 by 19 and you have 106.158 (rounded to three digits, which works for our purposes here). Determine the remainder by dividing 0.158 (106.158 minus 106) into 1/19; or 0.158/0.526, which equals 3. Now add 1 to the remainder of 3, equaling 4 and look up the date corresponding to the Golden Number 4 on the Easter tables (below). The corresponding date is April 11th.  Now look at the calendar for April 2017 and the first Sunday after April 11th is April 16th – this year’s Easter. By using the Golden Number, you avoid having to have a full understanding of the lunar calendar and the other artificial constructs baked into the Easter calculation.

Easter Table

Remainder      Paschal Full Moon Date
1                                  14 April
2                                    3 April
3                                23 March
4                                  11 April
5                                31 March
6                                  18 April
7                                    8 April
8                                28 March
9                                  16 April
10                                  5 April
11                              25 March
12                                13 April
13                                  2 April
14                              22 March
15                                10 April
16                              30 March
17                                17 April
18                                  7 April
19                             27 March

Now, if you don’t have an Easter table handy, there are still ways to compute Easter Day, but you’re going to need a computer, and programming and math skills beyond my reckoning…

Advertisements

,

  1. Leave a comment

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: