Calculating the Date of Easter

The God Plays Dice blog has an entertaining post on how the date of Easter is calculated. Wikipedia has all the messy details of course, but the blog makes a good introduction to the topic. "Easter is the date of the first Sunday after the first full moon on or after March 21... [T]he cycle of Easter dates repeat themselves every 5,700,000 years. The cycle of epacts (which encode the date of the full moon) in the Julian calendar repeat every nineteen years. There are two corrections made to the epact, each of which depend[s] only on the century; one repeats (modulo 30, which is what matters) every 120 centuries, the other every 375 centuries, so the [p]air of them repeat every 300,000 years. The days of the week are on a 400-year cycle, which doesn't matter because that's a factor of 300,000. So the Easter cycle has length the least common multiple of 19 and 300,000, which is 5,700,000 [years]."

Re:Huh.

[sonicdevo]

"Easter is termed a moveable feast because it is not fixed in relation to the civil calendar. Easter falls at some point between late March and late April each year (early April to early May in Eastern Christianity), following the cycle of the moon. After several centuries of disagreement, all churches accepted the computation of the Alexandrian Church (now the Coptic Church) that Easter is the first Sunday after the first fourteenth day of the moon (the Paschal Full Moon) that is on or after the ecclesiastical vernal equinox. Easter is linked to the Jewish Passover not only for much of its symbolism but also for its position in the calendar. The Last Supper shared by Jesus and his disciples before his crucifixion is generally thought of as a Passover meal, based on the chronology in the Synoptic Gospels..."

http://en.wikipedia.org/wiki/Easter [wikipedia.org]Wikipedia

Re:So what is the calculation for Eastern Orthodox

[johnw]

The same, except they use the Julian calendar where the western Christian churches use the Gregorian calendar. The calculation of the Jewish passover uses actual observations of the moon so that may be different again.

You'll find it all on Wikepedia.

Re:Metric School Terms

[26199]

In the UK school is split into three terms ... in the middle of each, you get a week off, and between them, you get two weeks off. Except over the summer when it's six weeks.

So there's more holiday through the year, but the summer vacation is shorter.

(This is probably because we don't have as much summer.)

Re:So what day did Jesus die on?

[Anonymous Coward]

The day of his birth is very much not set in stone, certainly not if you ask people of two distinct denominations.

Religious scholars believe Jesus was born some time between 7-4 BC. The date of Christmas, December 25th, was chosen as was a day used by pagans to celebrate their various gods and goddesses, thus allowing Christians to celebrate without drawing too much attention to themselves. Candles and the ubiquitous fish symbol (the one without the feet;-)) are also left-overs of early Christianity's secrecy.

It's not like they kept extensive birth records on the children of peasants.

Why do computer geeks celebrate Halloween on Christmas? Because OCT 31 = DEC 25.

Re:Spring equinox

[AndrewRUK]

Only problem is, your way isn't always right, because the date of Easter is always calculated from March 21st even if (as this year) the northern hemisphere spring equinox doesn't fall on that date.

The date IS set in stone.

[raehl]

It's the first Sunday after the vernal equinox.

The problem isn't that the date is not consistent; it's that the date is set using a DIFFERENT CALENDAR SYSTEM.

In Perl

[Phroggy]

sub GetEasterDate {
  my($year)=@_;
  # http://www.smart.net/~mmontes/nature1876.html
  my $a=$year%19;
  my $b=int($year/100);
  my $c=$year%100;
  my $d=int($b/4);
  my $e=$b%4;
  my $f=int(($b+8)/25);
  my $g=int(($b-$f+1)/3);
  my $h=(19*$a+$b-$d-$g+15)%30;
  my $i=int($c/4);
  my $k=$c%4;
  my $l=(32+2*$e+2*$i-$h-$k)%7;
  my $m=int(($a+11*$h+22*$l)/451);
  my $month=int(($h+$l-7*$m+114)/31);
  my $p=($h+$l-7*$m+114)%31;
  my $day=$p+1;
  return (0,0,0,$day,$month-1,$year-1900);
};

Re:Metric School Terms

[Anonymous Coward]

Yeah, those of us above school age also get a statutory 28 days paid holiday. Which seems a lot compared to the US 11 or 12(?) but if you think that's good I believe the Dutch get 35 days and every 2nd Friday. To take it to the extreme the French are forced to work at most on 35 hours [thedailymash.co.uk] and get four weeks but have to take them in August. Hurrah for the EU!

Re:Why would

[GvG]

In my part of the world the Monday after Easter is a national holiday. I've actually implemented the Gaus algorithm to compute the date of Easter in multiple programs, to check if people working on a given date were entitled to extra compensation for working on a holiday.

Re:leap days?

[the_other_chewey]

now, does all that fancy mathematics and statements about the repetition cycle of days include the Leap Year's Lead Day, as well as the fact that it didn't exist the last time this cycle started?

Yes, the formula by Gauß does. That's one of the reasons the mathematics have to be so fancy.

Re:Metric School Terms

[psychodelicacy]

Absolutely - the Anglo-Saxons had a lot to say about the dating of Easter. See http://faculty.virginia.edu/OldEnglish/aelfric/detemp.html [virginia.edu] for an original text on the subject if you're wildly interested. Melvyn Bragg's novel "Credo" dramatises the Synod of Whitby and gives a sense of exactly how serious an issue this was for people. Since Easter is the major Christian feast, it was a matter of orthodoxy to date it correctly. Interesting to think that being bad at math could make you a heretic!

Re:666 !!!

[Daniel Dvorkin]

the way he would have had to if this were a Muslim story

Or, you know, a Jewish or Christian one. The penalty of death by stoning for adultery is straight out of the Old Testament.

Re:how is it...

[psychodelicacy]

Even worse... there are Christian women on /.

Seriously, do you assume that all Christians are no-brain idiots who think dinosaur skeletons are an atheist conspiracy? Donald Knuth is a Lutheran, Gregor Mendel was an Augustinian monk, Copernicus was a priest, as was Georges Lemaitre. Lord Kelvin and Max Planck were committed Christians, Arthur Stanley Eddington was a Quaker... There are more here: http://en.wikipedia.org/wiki/List_of_Christian_thinkers_in_science [wikipedia.org] (Not all of those in this list were Christians throughout their lives, but the ones I've named were/are.)

Re:It's not even accurate ...

[MikeBabcock]

Ironically you're trying to show the illogical nature of one who professes to dislike Fundamentalists (presumably because of their illogical nature).

Of course, the person in question probably has no idea where the term Fundamentalist comes from in modern Christian terms, so their Worldview on the issue is most likely to be entirely based in the media. Yes, the very media from which science should not be learned either.

Or, "Fundamentalism ... I don't think that word means what you think it means."

Re:Curious

[magicchex]

In 1 Kings 7:23: 'And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about.'

Now of course you have to assume the bible is giving accurate measurements, which is doubtful, so this argument is fairly bunk (even to an atheist such as myself).

Re:Jewish, not Pagan, and especially not Druid

[bkaul01]

The date of Easter is approximately "The Sunday in Passover"

Absolutely correct regarding the origins. Unfortunately, we don't calculate the date based on the Jewish Calendar, so some years (like this one), their observances are separated from each other by up to a month. Passover doesn't begin until April 20 in 2008.

Re:Birth and death

[Wuhao]

The date IS fixed -- it's all a matter of perspective. Dates are divisions of a calendar, and a calendar tracks time using periodic and regular astronomical events. Obviously, the easiest of these is the day, since it's easy to tell when the sun rises, and our body clocks (and therefore the work day) are tuned to it. Unfortunately, days are too granular: to really organize a civilization, you need larger logical units (such as weeks, months and years). Nowadays, we use a calendar which tracks the sidereal year -- the time it takes for the earth to complete one full orbit. For agricultural purposes, this is ideal, since it will tell you when to grow your crops. Unfortunately, it was a tricky one to calculate: even if you know that the earth orbits the sun, you're stuck dealing with the fact that the orbit is nearly circular so you can't find a visible difference in size in the sun, and the stars are so incredibly distant that there's no appreciable parallax. One cue that you CAN watch for is the equinox, and this is exactly what early calendars did to track the seasons. Your typical farmer isn't going to have the time or the tools to measure when the day and night are of equal length, but he can get a general feel for it, and you can have a few people set aside whose job in the springtime is to watch the length of each day.

For the common man, an easier thing to watch is the moon. The phases of the moon are not only regular, but they're highly visible and uncomplicated. This means that if your calendar has something to do with the moon, then it's not only easy for your astronomers to track, but it's easy to explain to the unwashed masses: just tell them the festival is on the next new or full moon, and they'll know exactly what you mean. You can also track days for a very small number of days; 7, for instance. You can tell people "go out and work really hard for 6 days, and on the seventh, take a break," and most people can do that (and those that can't can just notice that those who can aren't working on some days). In the Jewish tradition, as you're probably aware, the seventh day is called the Sabbath, and is considered sacred.

A mix of the two was popular -- the accessibility of the lunar calendar was nice, but the agricultural significance of a sidereal calendar was needed as well. For the Liturgical year, the calendar starts with the first new moon after the spring equinox. This means that there's not even any pretense that the calendar is equivalent to a sidereal year; the orbital period of the moon just isn't any fraction of the orbital period of the earth.

Easter tries to mix the 3 logical units of measurement: the rules are complicated, but it essentially boils down to finding a date which 1) falls on a Sabbath, 2) comes quickly after an equinox and 3) ties into lunar phase. The way they chose was to set it at the first Sabbath following the first full moon following the spring equinox. But, approximations are applied to make it easier to plan: ancient astronomy was amazing for what they had at their disposal, but really very far from perfect. So, since the need to plan out a major annual festival was superior to the need for people to be able to look in the sky and see it get close, approximations were accepted over time. The "full moon" was assumed to occur 14 days after the new moon, which was in turn predicted from tables generated using an agreed-upon system of reckoning. The equinox was eventually taken to occur on March 21. The end result is that it no longer actually directly corresponds to an equinox or a lunar phase, and is instead based off of approximations that were chosen to make the date easier to work with. Nowadays, the approximation that most proponents of Easter date reform put forth is just to pick something like the first Sunday of April and use that. Others want to go back to a pure lunisolar basis and throw out the approximations. At this point, however, there's not much motivation to do either: we can compute Easter out arbitrarily far now, and it's printed on every c

Re:It was a mistranslation.

[scottblascocomposer]

Yes and no. In the Hebrew Bible, the word used by Isaiah is rightly translated as "young woman." In the Septuagint (the Greek translation of the Hebrew Bible produced nearly 200 years before Christ, and much older than the oldest extant Hebrew language Bible), however, the word is in fact "virgin."

Many Christians themselves, not to mention those who don't know much about the religion (no offense, but the majority of /.), are unaware of the fact that the Apostles themselves would most likely have used the Greek scriptures--indeed, it is apparent throughout the New Testament that the Hebrew scriptures being quoted nearly all are of Septuagintal origin.

Re:And the first scientists were monks because . .

[psychodelicacy]

Copernicus: 1473-1543 Mendel: 1822-1884 Kelvin: 1824-1907 Planck: 1858-1947 Eddington: 1882-1944 Lemaitre: 1894-1966 Knuth: 1938-

So, Copernicus may have been a Christian for the sake of convenience, but I think the others had/have other choices!

Re:It was a mistranslation.

[scottblascocomposer]

Whether it is the majority I don't know, but it is certainly many.

You have been substantially misled if that is your understanding. The history of the KJV [wikipedia.org] is somewhat interesting, although I admit to having tired long ago of the debates over its continued and/or exclusive use.

Long story almost criminally shortened, there were problems with the available English translations at the time. In response to complaints to that effect from the clergy, King James proposed, authorized, and funded a project to produce a new interpretation for use in the Church of England. There is no "God told me to fix the Bible" about it, and King James himself took no hand in the translation work. There certainly are controversies and problems around the project, but it was not as you have been lead to believe.

Virgin Birth

[Khomar]

The virgin birth was/is an essential part of the Messianic prophecies of the Jewish people. It derives from Isaiah 7:14:

"Therefore the Lord Himself will give you a sign: Behold, a virgin will be with child and bear a son, and she will call His name Immanuel.

This passage has been dated to a date prior to the death of Christ in the Dead Sea Scrolls [wikipedia.org] -- somewhere between 335 and 107 BC. So the idea of a virgin birth was well established long before Jesus' actual birth as are many of the miracles that Jesus performed. In fact, if you study the history of the time you will find that there were many others who claimed to be the Messiah and fulfill various prophecies including King Herod himself (the king who killed all of the male babies in Bethlehem in an attempt to end Jesus' life). According to the gospels in the New Testament, Jesus has fulfilled nearly every Messianic prophecy -- far more than any other figure in history.

The only prophecy Jesus has yet to fulfill is the establishment of an eternal government of peace and holiness which Christians believe will occur at his second coming. The fact that he did not fulfill this prophecy is one of the primary reasons that Jews of that day and even today rejected Jesus as their Messiah.

There is a lot more information here to cover than I can possibly relate in a Slashdot post, but there is far, far more to Biblical and Messianic prophecies that you realize. Each miraculous act and many of the statements attributed to Jesus in the New Testament are loaded with meaning and significance to people who understand the Old Testament -- most clearly in the book of Isaiah.

Re:Metric School Terms

[psychodelicacy]

Well, I can only really speak about the Anglo-Saxons on this, but you need to remember that books were scarce, and literacy was by no means universal. There's no guarantee someone would have had access to the whole Bible at any one time, or could read it even if they did. Add to this the fact that there was a great distrust of Jews - I doubt most Anglo-Saxon thinkers would have accepted that Christianity "included" Jewish scriptures and proscriptions; they would say that Christianity fulfilled the Hebrew scriptures and re-interpreted them in light of the teachings of Christ. Add to this an almost total ignorance of actual Jewish practice (i.e. anything outside the Hebrew scriptures themselves, which I think don't allow us to calculate Passover accurately on their own), and it's not surprising that a Christian king would have absolutely no idea how to date Passover or Easter.

Re:Huh.

[jonadab]

> I always thought it was based on when the Hebrew calendar said the week of Passover was.

It was, originally, and _sort of_ still is.

But over the centuries, as the Jews and Christians codified the rules for their calendars differently, some differences have arisen.

At the time when the Western formula for Easter was set, the Jews tried pretty hard to keep the spring equinox in the first half of the first month (Nisan), so the Easter formula that was established assumes that to be the case -- but the modern Jewish calendar doesn't do that. Arguably, this is a deviation on the Jewish side that takes their calendar out of sync with where it should be.

Additionally, the Western formula for Easter assumes that the Gregorian calendar is always perfectly in sync with the astronomical solar year, and that isn't always necessarily true. (Over long numbers of years it tracks very closely, but in any given year it can be off by a little.) Arguably this is a deviation on the Christian side that takes our calendar out of sync with where it should be -- but in a different way from what the Jewish deviation does.

If we got rid of both deviations and reckoned both calendars in a way that kept them strictly in alignment with the astronomical solar year, then Easter Sunday would always be, if I understand correctly, the Sunday after the Passover Seder.

But the important thing, to my way of thinking, is not the exact date on which the events are celebrated, but the fact that they *are* celebrated. Though the date calculations are interesting. (Then again, I majored in math, so I may define "interesting" differently from some people.)