Can a Mechanical Clock Compute Easter? Sort of.
May 6, 2017 5:39 PM Subscribe
"There are many indications that the sole important application of arithmetic in Europe in the Middle Ages was the calculation of the date of Easter," wrote Donald Knuth. The single most complicated computation in calendar math, Easter's cycle repeats only once every 5.7 million years. It's easy to figure out one year at a time with several tables and two calendars (lunar and solar), possible but hard to do with an algorithm -- but can it be done mechanically with a clock? What about a watch? (<--best link)
Spoiler: The watch needs a new program disc after 28 years. The great clock at Strasbourg cathedral will show an incorrect date in AD 11,999 (although its display will roll over after AD 10,000 and the builder suggests adding a "1" to the front of the year display at that point).
Spoiler: The watch needs a new program disc after 28 years. The great clock at Strasbourg cathedral will show an incorrect date in AD 11,999 (although its display will roll over after AD 10,000 and the builder suggests adding a "1" to the front of the year display at that point).
The TLDR for the figuring out is the first Sunday on or after the first full moon after the vernal equinox on March 21. See for instance this page at Astronomical Applications Department of the U.S. Naval Observatory.
posted by carter at 6:21 PM on May 6, 2017 [4 favorites]
posted by carter at 6:21 PM on May 6, 2017 [4 favorites]
"The TLDR for the figuring out is the first Sunday on or after the first full moon after the vernal equinox on March 21. "
Which is easy enough for a human, but fairly difficult for an algorithm ... and of course it's an ecclesiastical moon and a liturgical equinox and so on. :)
posted by Eyebrows McGee at 6:28 PM on May 6, 2017 [9 favorites]
Which is easy enough for a human, but fairly difficult for an algorithm ... and of course it's an ecclesiastical moon and a liturgical equinox and so on. :)
posted by Eyebrows McGee at 6:28 PM on May 6, 2017 [9 favorites]
"There are many indications that the sole important application of arithmetic in Europe in the Middle Ages was the calculation of the date of Easter," wrote Donald Knuth.
Generations of the far future may similarly marvel that the foundations of space travel were created almost entirely by the desire to lob nuclear weapons and spy on each other. Like, "wow, that's weird, I wonder if they even realized all of the useful applications this would have further down the road."
posted by indubitable at 6:34 PM on May 6, 2017 [6 favorites]
Generations of the far future may similarly marvel that the foundations of space travel were created almost entirely by the desire to lob nuclear weapons and spy on each other. Like, "wow, that's weird, I wonder if they even realized all of the useful applications this would have further down the road."
posted by indubitable at 6:34 PM on May 6, 2017 [6 favorites]
Fascinating, thank you.
posted by the man of twists and turns at 6:41 PM on May 6, 2017
posted by the man of twists and turns at 6:41 PM on May 6, 2017
Eyebrows - Indeed! It's an interesting example of something we find easy in terms of language but which is hard to program.
posted by carter at 6:42 PM on May 6, 2017
posted by carter at 6:42 PM on May 6, 2017
My first question was, "why don't we just determine the date of Passover and then work from there?"
And the answer is (for those of us who didn't know), Passover and Easter don't necessarily coincide (apologies for the blog post; I'm not finding an authoritative source, although all of the sites seem to agree on the subject). I quote:
"Why don’t Easter and Passover always fall together on the calendar?
Every two or three years the Jewish calendar requires the adjustment of a leap year. During a Jewish leap year an additional month of 29 days is inserted before the month of Nisan. The additional month is needed because the Jewish calendar year has less days than the solar year and begins to slip out of gear with the seasons. The extra month thus realigns the Jewish calendar year with the seasons of the solar year. This is important because the Jewish holidays are closely related to the seasons. For example, the Torah commands that Passover be celebrated in the spring.
Every so often the Jewish leap year will push Passover so far into April that a second full moon following the vernal equinox would appear before the Sunday following Passover. This happens anytime the Sunday following Passover falls later than April 25th on our calendar. On those rare occasions Easter is celebrated the month before Passover rather than the Sunday following Passover."
posted by steady-state strawberry at 7:08 PM on May 6, 2017 [3 favorites]
And the answer is (for those of us who didn't know), Passover and Easter don't necessarily coincide (apologies for the blog post; I'm not finding an authoritative source, although all of the sites seem to agree on the subject). I quote:
"Why don’t Easter and Passover always fall together on the calendar?
Every two or three years the Jewish calendar requires the adjustment of a leap year. During a Jewish leap year an additional month of 29 days is inserted before the month of Nisan. The additional month is needed because the Jewish calendar year has less days than the solar year and begins to slip out of gear with the seasons. The extra month thus realigns the Jewish calendar year with the seasons of the solar year. This is important because the Jewish holidays are closely related to the seasons. For example, the Torah commands that Passover be celebrated in the spring.
Every so often the Jewish leap year will push Passover so far into April that a second full moon following the vernal equinox would appear before the Sunday following Passover. This happens anytime the Sunday following Passover falls later than April 25th on our calendar. On those rare occasions Easter is celebrated the month before Passover rather than the Sunday following Passover."
posted by steady-state strawberry at 7:08 PM on May 6, 2017 [3 favorites]
Dammit, I was coming here to post this!
posted by Chrysostom at 7:12 PM on May 6, 2017 [1 favorite]
posted by Chrysostom at 7:12 PM on May 6, 2017 [1 favorite]
There's also the calculation of Easter in Orthdox churches, just to further complicate things.
posted by TedW at 7:17 PM on May 6, 2017
posted by TedW at 7:17 PM on May 6, 2017
"why don't we just determine the date of Passover and then work from there?"
The quartodecimans did this, but that hasn't been the practice since the fourth century. For one thing, the Hebrew calendar comes with a bunch of extra rules to make sure that, say, Yom Kippur doesn't fall on the day before or after the (Jewish) Sabbath - things that would be irrelevant if you're not Jewish. For another thing, the Hebrew calendar had gotten a bit disorganized and it looks like the Christians didn't want to depend on the Jews to tell them when their most important holiday was.
posted by madcaptenor at 7:41 PM on May 6, 2017 [1 favorite]
The quartodecimans did this, but that hasn't been the practice since the fourth century. For one thing, the Hebrew calendar comes with a bunch of extra rules to make sure that, say, Yom Kippur doesn't fall on the day before or after the (Jewish) Sabbath - things that would be irrelevant if you're not Jewish. For another thing, the Hebrew calendar had gotten a bit disorganized and it looks like the Christians didn't want to depend on the Jews to tell them when their most important holiday was.
posted by madcaptenor at 7:41 PM on May 6, 2017 [1 favorite]
"And the answer is (for those of us who didn't know), Passover and Easter don't necessarily coincide (apologies for the blog post; I'm not finding an authoritative source, although all of the sites seem to agree on the subject)."
That's quite correct. The Jewish calendar uses a leap month to correct itself, 7 times every 19 years. The Gregorian calendar is a solar calendar that uses a corrected luni-solar calculation to place Easter's migratory luni-solar date on a fully solar calendar. The Julian and Gregorian calendars were also concerned with freeing the Church from dependence on astronomical observation to determine the start of months (as with the Jewish lunar calendar), as the Church spread into a much more geographically diverse entity, which would have meant months could be starting at different times in different places depending on cloud cover and keenness of the eyes of the moon-spotters and so on. (Judaism now uses a standardized lunar calendar, but Islam still relies upon moon sighting.)
And, yeah, Easter has to be on a Sunday for theological reasons; Passover isn't tied to the day of the week. (Also a bunch of interesting stuff about the early split between the Jewish Jews and the Jewish Christians and how Official Timekeeping, which was done by religious authorities, entered into that.)
"There's also the calculation of Easter in Orthdox churches, just to further complicate things."
Using the Julian Calendar, which is much simpler, because it's not fully corrected to the actual astronomical calendar -- it miscalculates Leap Days fairly significantly, such that it's currently 13 days out of alignment with the Gregorian Calendar, which is far more accurate at correcting for Leap Days so the "official" calendar equinoxes remain near the actual equinoxes. Easter's cycle repeats every 19 years in the Julian calendar (like the Jewish calendar), rather than every 5.7 million years, so it's not so hard to sort.
A Julian Year is 365.25 days; a Gregorian Year is 365.2425 days (10 minutes 48 seconds less per year); there are 365.2422 sidereal days per year astronomically, so the Gregorian is considerably closer! The Julian Calendar moved a day off astronomical 1 day every 128 years; the Gregorian Calendar shifts 1 day every 3,000 years or so.
"Dammit, I was coming here to post this!"
Yesssssssss, liturgical nerds unite!
posted by Eyebrows McGee at 7:52 PM on May 6, 2017 [8 favorites]
That's quite correct. The Jewish calendar uses a leap month to correct itself, 7 times every 19 years. The Gregorian calendar is a solar calendar that uses a corrected luni-solar calculation to place Easter's migratory luni-solar date on a fully solar calendar. The Julian and Gregorian calendars were also concerned with freeing the Church from dependence on astronomical observation to determine the start of months (as with the Jewish lunar calendar), as the Church spread into a much more geographically diverse entity, which would have meant months could be starting at different times in different places depending on cloud cover and keenness of the eyes of the moon-spotters and so on. (Judaism now uses a standardized lunar calendar, but Islam still relies upon moon sighting.)
And, yeah, Easter has to be on a Sunday for theological reasons; Passover isn't tied to the day of the week. (Also a bunch of interesting stuff about the early split between the Jewish Jews and the Jewish Christians and how Official Timekeeping, which was done by religious authorities, entered into that.)
"There's also the calculation of Easter in Orthdox churches, just to further complicate things."
Using the Julian Calendar, which is much simpler, because it's not fully corrected to the actual astronomical calendar -- it miscalculates Leap Days fairly significantly, such that it's currently 13 days out of alignment with the Gregorian Calendar, which is far more accurate at correcting for Leap Days so the "official" calendar equinoxes remain near the actual equinoxes. Easter's cycle repeats every 19 years in the Julian calendar (like the Jewish calendar), rather than every 5.7 million years, so it's not so hard to sort.
A Julian Year is 365.25 days; a Gregorian Year is 365.2425 days (10 minutes 48 seconds less per year); there are 365.2422 sidereal days per year astronomically, so the Gregorian is considerably closer! The Julian Calendar moved a day off astronomical 1 day every 128 years; the Gregorian Calendar shifts 1 day every 3,000 years or so.
"Dammit, I was coming here to post this!"
Yesssssssss, liturgical nerds unite!
posted by Eyebrows McGee at 7:52 PM on May 6, 2017 [8 favorites]
"The additional month is needed because the Jewish calendar year has less days than the solar year and begins to slip out of gear with the seasons. The extra month thus realigns the Jewish calendar year with the seasons of the solar year. "
For anyone who's particularly curious, Christianity uses a solar calendar (with a luni-solar calendar overlay for the Easter-related movable feasts); Judaism uses a luni-solar calendar that periodically corrects itself to sync the lunar months back up with the seasons; and Islam uses a fully lunar calendar, which is only 354.37 solar days long, which is why Ramadan scoots backwards 10 or 11 days every year. All three are closely related and arise from the same geographical area and the same calendaring traditions, but all three have chosen different solutions to the yearly timekeeping problem.
posted by Eyebrows McGee at 7:57 PM on May 6, 2017 [6 favorites]
For anyone who's particularly curious, Christianity uses a solar calendar (with a luni-solar calendar overlay for the Easter-related movable feasts); Judaism uses a luni-solar calendar that periodically corrects itself to sync the lunar months back up with the seasons; and Islam uses a fully lunar calendar, which is only 354.37 solar days long, which is why Ramadan scoots backwards 10 or 11 days every year. All three are closely related and arise from the same geographical area and the same calendaring traditions, but all three have chosen different solutions to the yearly timekeeping problem.
posted by Eyebrows McGee at 7:57 PM on May 6, 2017 [6 favorites]
Really fascinating stuff here! But has anyone else noticed the bizarre product placement in the last link in the FPP:
Even though aligning human teeth is quite different from aligning machinery teeth, any Invisalign dental professional can appreciate the workmanship of this mechanical calculator. Teeth straightening treatment with Invisalign replaces the metal wires of traditional braces with soft plastic for a more comfortable fit.
What's up with that?
posted by TedW at 7:59 PM on May 6, 2017 [4 favorites]
Even though aligning human teeth is quite different from aligning machinery teeth, any Invisalign dental professional can appreciate the workmanship of this mechanical calculator. Teeth straightening treatment with Invisalign replaces the metal wires of traditional braces with soft plastic for a more comfortable fit.
What's up with that?
posted by TedW at 7:59 PM on May 6, 2017 [4 favorites]
Beautiful post. Knowing when Easter falls is unfailingly aligned to the time when certain of our trees and plants will flower so I track this year by year. The calculation is valuable for e.g. spraying peaches for peach leaf curl, pruning pome fruit trees and expecting the day when the rains end. There is a narrow window between Easter and hot weather when brush clearing is at its least hazardous point, here.
posted by jet_silver at 8:14 PM on May 6, 2017 [1 favorite]
posted by jet_silver at 8:14 PM on May 6, 2017 [1 favorite]
Rosetta Code versions of the Easter algorithm in most languages
posted by benzenedream at 9:23 PM on May 6, 2017
posted by benzenedream at 9:23 PM on May 6, 2017
One of the oldest continuous examples of writing in the Welsh language (so old that some of the words are not understood) is the Computus Fragment, which is documentation of an algorithm whose inputs are the position of the moon and the contents of a lookup table, and whose output is the date of Easter.
posted by Harvey Kilobit at 9:27 PM on May 6, 2017 [1 favorite]
posted by Harvey Kilobit at 9:27 PM on May 6, 2017 [1 favorite]
Do you know why, in 1582, when they implemented the Gregorian Calendar, they dropped 10 days out of the calendar? Why not just start using the new leap year rules from that point forward? The answer is because the Catholic Church decided they had been calculating Easter wrong for over a thousand years. The rules for the date of Easter was decided at the First Council of Nicaea in 325 CE. When the Gregorian Calendar was implemented, it was decided to rewind the calculations for Easter back to 325 CE. This meant that there had been 10 extra leap years that needed to be removed from the calendar. There is all sorts of weird stuff like this in our calendar. This is a link to a really good public domain book (because it was written in 1921) on all the lunacy in our calendar.
posted by Xoc at 9:50 PM on May 6, 2017 [4 favorites]
posted by Xoc at 9:50 PM on May 6, 2017 [4 favorites]
This is a link to a really good public domain book (because it was written in 1921) on all the lunacy in our calendar.
Something something clever.
posted by Insert Clever Name Here at 11:25 PM on May 6, 2017 [2 favorites]
Something something clever.
posted by Insert Clever Name Here at 11:25 PM on May 6, 2017 [2 favorites]
Has anyone located the original watch mechanism patent? (The links in the article points to the writer's home directory, which is of only limited usefulness) #lazyweb
posted by effbot at 3:43 AM on May 7, 2017
posted by effbot at 3:43 AM on May 7, 2017
Has anyone located the original watch mechanism patent?
Here's the patent application on the European Patent Office's Espacenet (this is a link to text generated via OCR, but a PDF of the application is also available), but it being a Swiss application with no patent family documents, only the abstract is available in English. (Incidentally, as someone who translates patents, I wish they all could be as concise as this one appears to be.)
posted by Strutter Cane - United Planets Stilt Patrol at 6:02 AM on May 7, 2017
Here's the patent application on the European Patent Office's Espacenet (this is a link to text generated via OCR, but a PDF of the application is also available), but it being a Swiss application with no patent family documents, only the abstract is available in English. (Incidentally, as someone who translates patents, I wish they all could be as concise as this one appears to be.)
posted by Strutter Cane - United Planets Stilt Patrol at 6:02 AM on May 7, 2017
I first read about Epacts and Golden Numbers as a teenager in my father's Encyclopædia Britannica (11th ed).
Seems like a lot of work to give a lasting proof that the Jewish Passover was not ... an ordinance of Christianity.
posted by MtDewd at 3:40 PM on May 7, 2017
Seems like a lot of work to give a lasting proof that the Jewish Passover was not ... an ordinance of Christianity.
posted by MtDewd at 3:40 PM on May 7, 2017
I bet we've celebrated it on the wrong day at least once, if it's that tricky
posted by thelonius at 4:48 PM on May 7, 2017
posted by thelonius at 4:48 PM on May 7, 2017
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