Raphael  Resurrection of Christ 
The first
Ecumenical Council was held in Nicaea, Asia Minor, in 325, convened by Emperor
Constantine. Ecumenical councils could not be held before that date, for Christians
were persecuted and had to meet in secret. This first Council had very
important consequences: Aryanism, which denied the divinity of Christ, was
condemned; the version of the creed still recited in mass today was defined;
and the Council established the algorithm to calculate the
date of Easter, which is still in use. This algorithm is so
complicated that Donald Knuth included a program to perform it in his famous
and classic computer encyclopedia, The Art of Computer
Programming.
Easter was
fixed on the first Sunday after the first full moon after the spring equinox,
which that year fell in March 21st. To calculate the exact date one must take
into account that the solar cycle (the year) contains 365.2421988 days, while
the lunar cycle (the phases of the moon) lasts 29.530588 days, two numbers with
many figures that do not have a simple relationship with one another, so the
calculation is quite complex.
The astronomers
of the ancient civilizations were deeply disturbed because the cycle of the sun
is not an exact multiple of the cycle of the moon. The quotient of the two
numbers is 12.368267, which means that a year lasts for 12 lunar months plus
over a third. In Babylon they divided the year into 12 months and chose 12 as
the basis of their numbering system, but every three years or so they had to
introduce an extra month, so that the sun would not be left behind. The years with
13 months were considered abnormal, weird, bad luck. Number 13 still drags that
disreputable character.
By the
sixth century B.C., Babylonian astronomers discovered that every 19 years the
sun and the moon are back in almost the same relative positions. Indeed, 19
solar years have 19´365.2421988
= 6939.60 days, while 235 lunar months have 235´29.530588 = 6939.69 days. In other
words, if 235 lunar months are distributed between 19 years, the resulting
cycle introduces an error of 0.09 days, one day per 220 years. Around 432 B.C.,
the Greek astronomer Meton rediscovered the cycle of 19 years (we call it the Metonic cycle), and even improved it a bit, reducing
the error to about one day every 300 years.
As the date
of Easter depends on the full moon, the algorithm to calculate that date
depends on 19, the number of years in the Metonic cycle. I will not insert the
full algorithm here, just a table that helps to calculate the date with very
little effort.
0

1

2

3

4

5

6

7

8

9


Up
to 1582

5/4

25/3

13/4

2/4

22/3

10/4

30/3

18/4

7/4

27/3


15831699

12/4

1/4

21/3

9/4

29/3

17/4

6/4

26/3

14/4

3/4


17001899

13/4

2/4

22/3

10/4

30/3

18/4

7/4

27/3

15/4

4/4


19002199

14/4

3/4

23/3

11/4

31/3

18/4

8/4

28/3

16/4

5/4


10

11

12

13

14

15

16

17

18


Up
to 1582

15/4

4/4

24/3

12/4

1/4

21/3

9/4

29/3

17/4


15831699

23/3

11/4

31/3

18/4

8/4

28/3

16/4

5/4

25/3


17001899

24/3

12/4

1/4

21/3

9/4

29/3

17/4

6/4

26/3


19002199

25/3

13/4

2/4

22/3

10/4

30/3

17/4

7/4

27/3


To compute the
date of Easter in a given year using the
table, just find the remainder of the year in question when divided by 19,
which is always a number between 0 and 18. Then look at the corresponding
column in the table, in the row corresponding to the year. The table gives the
date of the first full moon after the spring equinox, in the day/month format.
There is
just one thing missing: the date thus obtained can fall on any day of the week.
Easter will be the next Sunday. This last rule applies even if the date on the
table falls on a Sunday, to prevent the Christian Easter to fall on the same
day as the Jewish Passover.
Manuel Alfonseca
this calculation only applies to the western churches, not the Eastern Orthodox (Greek, Russian, Serbian, Bulgarian, etc.)
ReplyDeleteThe Eastern Orthodox church applies the same calculation and algorithm. What changes is that they still use the Julian Calendar, and therefore March 21st falls in a different day, which means that some years (not all) the date of Easter falls a lunar month later for them.
DeleteI like the table better.... All those long numbers and the algorrilla (oops! algorithm!) make for massive headaches....
DeleteCool! I never knew that about the number 13. And I always wondered exactly what the formula was for Easter.
ReplyDelete