5750000 Easter Sundays

 

Today is Easter Sunday, which is of course the primary “movable feast” in the church fullcyclecalendar, which is of course relevant to the other movable feasts.  Easter Sunday is supposed to fall on the first Sunday after the first full moon after the Vernal Equinox because it’s connected to the Jewish passover.  That’s complicated enough as it is, and it’s further complicated by the fact that it varies in the Eastern Orthodox Church and Western Churches, and complicated again by the fact that both the Vernal Equinox and the full moon are defined by the Church rather than by looking at the actual sky.  The equinox is fixed on 21st March and the ecclesiastical full moon, which is what the full moon as defined by the Church, is the fourteenth day of the ecclesiastical lunar month.  This differs from the real full moon, intervals between which can vary between 29.27 and 29.83 days.  There is a calculation referred to as computus which was instituted in 1583 by the Roman Catholic Church when it fixed the Vernal Equinox.  In 2015, Pope Francis proposed harmonising the date with the Orthodox Church, whose calendar is still Julian rather than Gregorian like ours, as a show of support.  The Julian calendar is around a fortnight behind ours because it treats all years ending in two zeroes as leap years whereas ours skips the ones which are not divisible by four.

It’s all a bit complicated and peculiar.  The “movable feasts”, whose dates depend on the dates of Easter, include, in the Western churches the days of rogation, the Global Day Of Prayer For Peace, Pentecost, Whitsun and the other Whit Days, the Feasts of Christ the Priest and the Crown of Thorns, Trinity Sunday, Corpus Christi, Petertide, Sea Sunday, the Day Of Prayer For The Peace Of Jerusalem, World Communion and Mission Sundays, All Saints’ Day (which is surprising as Hallowe’en is  not movable), Septuagesima, Sexagesima, Shrove Tuesday, Ash Wednesday, Quadragesima, Palm Sunday, Maundy Thursday, Good Friday and Quinquagesima, and no, I don’t know what all of those are.

As time goes by this planet rotates more slowly.  This is because it’s slowed by the Moon (I’m resisting calling it Cynthia although it does feel wrong to call it the Moon still), and as that happens the Moon moves outward from us and the month consequently gets longer.  This is because the energy of Earth’s spin is gradually being transferred to the Moon, which causes it to orbit faster and therefore move out and take longer to orbit.  Meanwhile, the date of the Vernal Equinox varies because the ellipse that is our orbit round the sun gradually moves like a spirograph pen would.  Various other things happen as well.  Consequently, the question arises of how many Easters there can possibly be according to computus.

How can we know how long the day was in prehistoric times?  The answer is that there are certain living things, and other processes, which occur in daily cycles, and rings can be counted in shells and corals which also have seasonal variations according to hot and cold.  Also, layers of silt can be laid down and baked seasonally, forming a primitive calendar.  The further back you go, the more days there are per year.  This would mean either that the days are getting longer or that the years are.  However, if the years were getting longer it would mean our orbit used to be smaller and the planet would have been much hotter unless the sun was warming at precisely the same rate as the orbit was widening.  For some reason the day, though it lengthens constantly, doesn’t do so particularly steadily.  At around the time of the extinction of the non-avian dinosaurs, the day was around twenty minutes shorter than it is now, so there were around 370 days a year.  That was 65 million years ago.  Go back to the beginning of the age of dinosaurs, which was 120 million years earlier, though, and the day was only half an hour shorter than it is now, so it’s not slowing in linear terms.

The year currently lasts about 365.25 days.  Incidentally, there is no definitive day length because it depends on whether it’s measured by when the sun, stars or Moon rises, all of which are different.  Leaving that aside, the question arises of when there were last 366 days in a year and when there will be exactly 365 days.  The answer to the first question is that it was true around 20 million years ago, when there were definitely apes but none of them were particularly human-like.  With reference to Easter and Passover, that point isn’t particularly important because this is about religious festivals.  However, since we do now have Abrahamic religion, the question arises of how long it would make sense to adhere to such a calendar.  This calendar, with its leap years generally every four years skipping one every few centuries, will cease to make sense once there are exactly 365 days a year.  By that time the month will also be longer and the date of the Vernal Equinox will have changed – it will in fact have cycled completely round the calendar a couple of hundred times.

The answer is that it will be roughly 5 700 000 years from now when Easter, along with various other aspects of this calendar, ceases to make sense according to that reckoning.  By an interesting coincidence, it so happens that if the days, years, position of the Vernal Equinox and length of the month are all assumed to be constant, the cycle of possible dates on which Easter Sunday falls repeats exactly over the same period of time – 5 700 millenia.  Hence the cycle coincides quite closely to the number of possible dates on which Easter can fall before which the calendar as it currently stands stops working completely.

The bar graph at the top of this post represents the number of possible Easter Sundays in this cycle.  It so happens that this is also the actual number of possible Easter Sundays in all time, from the first Passover right up until the sun becomes a red giant and wipes out the Earth.  Easter as we know it will by some quirk happen roughly 220 875 times on 19th April, standing out as more frequent than the other possible dates.  The rarest date, 22nd March, will only take place 28 500 times or so.  The first year it occurred on 19th April after the Council of Nicaea, which determined the date in 325, was 330.

As a Christian, I just slightly wonder if that 19th April date was the actual date of the first Easter Sunday, but I haven’t done the maths on that and I should probably just leave it.

Another consequence of movable feasts is that they mean that the years on which the same dates occur on the same days of the week, for instance 1978 and 2017, are nevertheless different in other ways.  Easter Sunday 1978 fell on 26th March.  Therefore any “perpetual” calendar (which isn’t, because of what I just said) would need to take the date of Easter into consideration to be genuinely reliable from the perspective of a Christian-influenced culture.

The other thing this makes me think, though, is how Easter could possibly have any meaning at all in getting on for six million years from now.  I mentioned in the last post that there are different “theories of atonement”.  Similarly there are different theories of eschatology, the study of the end of the world, and where these are Christian they don’t all require the Day of Judgement will come to pass at all.  It still seems to me that for Christianity as most Christians currently understand it to be true, surely it would’ve blown it if the Second Coming still hadn’t happened by the year 5 700 000 AD.  I don’t know what I think, but I do think there is no way there will be 5 700 000 celebrations of Easter Sunday.

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