Our solar,/lunar/hebdomadalian holiday
I thought I'd figured out the schedule for Easter a while back: the first Sunday after the first full moon after the vernal equinox. This complicated formula draws together the solar cycle (equiox), the lunar cycle (full moon), and the weekly cycle (Sunday). But imagine my surprise when this month's full moon turned out to be today (April 12). Why isn't Easter tomorrow? Instead, tomorrow is Palm Sunday, and Easter is not until April 20.
The mystery turns on the Western Christian Church's ancient practice of calculating the vernal equinox according to a formula that doesn't quite line up with the astronomically observed full moon or equinox. This year the archaic formula, which requires us to divide the year by 19 and look up the remainder in a chart, yields a liturgical Paschal Full Moon on April 13, which is Sunday (tomorrow). When the post-equinox full moon lands on a Sunday, Easter is celebrated on the following Sunday.
The accepted view seems to be that the seven-day week, which depends on neither the solar nor the lunar cycle, has its roots in Genesis: the seven days of creation. Romans used an 8-day week for many centuries B.C. and A.D., but switched to the Jewish 7-day week with Constantine's converstion to Christianity. Later Europeans continued the Roman custom of naming the days of the week after the five classically visible planets plus the sun and the moon (though the Romans had added an eighth day with a name that had something to do with markets). In English, the modern names of the seven days of the week are rooted in the Norse gods for Tuesday through Friday, to the Roman god Saturn for Saturday, and to the Teutonic words for sun and moon for Sunday and Monday. In Romance languages, the days of the week are rooted in the Latin names for "Lord" for Sunday, moon for Monday, Mars for Tuesday, Mercury for Wednesday, Jupiter for Thursday, Venus for Friday, and sabbath for Saturday.
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The US Navy has a good page on this:
https://aa.usno.navy.mil/faq/easter
Where for the Western churches we get the following integer calculation:
(NB: y = year, m = month, d = day)
c = y / 100
n = y - 19 * ( y / 19 )
k = ( c - 17 ) / 25
i = c - c / 4 - ( c - k ) / 3 + 19
* n + 15
i = i - 30 * ( i / 30 )
i = i - ( i / 28 ) * ( 1 - ( i / 28 )
* ( 29 / ( i + 1 ) )
* ( ( 21 - n ) / 11 ) )
j = y + y / 4 + i + 2 - c + c / 4
j = j - 7 * ( j / 7 )
l = i - j
m = 3 + ( l + 40 ) / 44
d = l + 28 - 31 * ( m / 4 )
Meanwhile, Wikipedia offers this formula for the Eastern side of things:
a = Ymod4
b = Ymod7
c = Ymod19
d = (19c+15)mod30
e = (2a+4b−d+34)mod7
month = ⌊ (d+e+114)/31⌋
day = ((d+e+114)mod31)+1
Or, for lazy people like me, there's a table that covers the next 20 years:
https://en.wikipedia.org/wiki/List_of_dates_for_Easter
Next year I'm giving up math for Lent.
The dividing by 19 occurs because of the Metonic Lunar Cycle.
https://mythicalireland.com/blogs/astronomy/metonic-cycle-the-19-year-cycle-of-the-moon
Stone circles sometimes have 19 stones, or nine stones and a smaller one. It is assumed this is why, mostly because no other explanation makes any sense (yet). Think of how many years of observation and measurement that would take before a tribe figured it out without pencil and paper.
Nineteen years! Gracious. You're right, that's a tremendous amount of observation and memory at work.
It really is. The ancients who did this kind of stuff were amazing.
This is exactly why you see so many ancient constructions that are astronomically aligned. They're *tools* as much as anything else. Allowing you to track and mark the cycles. Eventually, you get enough of the cycles marked and it goes from being a tool to a recorded but of knowledge. Every ancient society did this. The pity is that we've removed ourselves from it so much.
And thanks for making me look up Hebdomadarian- it's etymology is pretty interesting in it's own right. https://en.wikipedia.org/wiki/Hebdomadarian
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