Tuesday, April 2, 2013

Jewish v. Catholic v. Orthodox Calendars

Sasha Volokh has a nice discussion of the differences between the Roman Catholic and Orthodox calendars and Easter calculations (which arose from the need to fit Easter to the Roman calendar, and the Roman Catholic embrace of calendar reforms to match the seasons which were not adopted by Orthodox Christians). 

Along the way, she also reminds us where the A.D. v. B.C. system of numbering years (which I customarily write C.E. for current era, or B.C.E. for before current era, to strip the meaning of the original abbreviations which in latin mean "year of our Lord" and "before Christ").

Part 1: Orthodox Easter, what's up with that?
Easter is this Sunday, March 31. But Orthodox Easter, celebrated by most branches of the Eastern Orthodox Church (including the Russian Orthodox Church) and some Oriental Orthodox churches, is May 5 this year, a full five weeks after Easter as celebrated by Western Christian churches. . . . The five-week difference has happened recently in 2002, 2005, and 2008. But in 2001, 2004, 2007, 2010, and 2011, Western and Orthodox Easter fell on the same day. And in 2000, 2003, 2006, 2009, and 2012, Orthodox Easter was one week after Western Easter. What’s up with that? . . .
The Julian calendar, introduced in 45 BC, is easy: the year is 365 days long, except that we have a leap year every four years. After some confusion caused by off-by-one errors, apparently the proper sequence of leap years was reestablished by AD 4 or AD 8. . . .  [The prior calendar has just 365 days which was worse.] Trouble is, the year isn’t quite 365.25 days long; the tropical year, which is the most relevant one for seasonal purposes, is more like 365.24219 days. . .  after 400 Julian years, you’ll be 3.124 days off.  . . . The Gregorian calendar fixes this problem by removing 3 days every 400 years. . . . remove the leap days in 2100, 2200, and 2300. So of the century years, the only ones that remain leap years are 1600, 2000, 2400, etc., the ones divisible by 400. Now the average year length is 365.2425, which is off from 365.24219 by 0.00031 days, so the years are still too long, but by a much smaller margin, so the date of the solstice will creep earlier and earlier much more slowly (by, on average, a day every 3226 years). . .

[B]ut how do you actually get it adopted? The Gregorian reform was proposed by Pope Gregory XIII, and Catholic countries mostly adopted it in or shortly after 1582. By then, the error was 10 days; to prevent the backward creep of the date of astronomical phenomena, it was necessary to move the calendar date forward in one swell foop. The first places to adopt were Spain, Portugal, the Polish-Lithuanian Commonwealth, and most of Italy; there, September 4, 1582 was immediately followed by September 15, 1582. France adopted the calendar later in 1582, and other places adopted in 1583. The Protestant countries mostly adopted the new calendar over the course of the 18th century; England did it in 1752, by which time the error was 11 days.

The Orthodox countries of Eastern Europe lagged behind, though, and by 1918, the error was 13 days. In 1918, the new Soviet government adopted the Gregorian calendar; January 31, 1918 was followed by February 14, 1918. But the Russian Orthodox church didn’t change calendars, and, as the other Orthodox countries adopted the new calendar in the 1910s and 1920s, neither did their churches. (Some churches have adopted the Revised Julian calendar or Milankovic calendar, which is different than the Gregorian calendar, but is temporarily aligned with it.) So most Orthodox churches continue to follow the old calendar. Since 2000 was a leap year for both the Julian and Gregorian calendars, the error continues to be 13 days, and will continue to be 13 days until 2100. Thus, the date that the Orthodox churches consider to be December 25 is what we call January 7. 
Part 2: Orthodox Easter, what's up with that?

Easter Sunday is the day when Jesus Christ rose from the dead, and the Gospels say that happened when he came to Jerusalem to celebrate Passover. So in principle, you could think that Easter happens at Passover — more precisely, on 14 Nisan, the day before Passover starts on 15 Nisan. . . . Now the Jewish calendar is a complicated thing, but the bottom line is that 15 Nisan is always on a full moon after the spring equinox. How do they guarantee that this happens? Intercalation, that’s how. Because Jewish months are lunar, the folks in charge of the calendar stick in a whole nother month, called Adar II, before Nisan just to ensure that Passover is on a full moon after the equinox.
So why not tie Easter to Passover and celebrate it whenever 14 Nisan would fall in the Jewish calendar? The Christians who believed you should do this were called Quartodecimans, or “fourteeners” if you will. Various Christian communities followed the “14 Nisan” rule and just asked their local Jews when Passover started, but after controversies in the second and third centuries, Christians ended up settling the matter at the Council of Nicaea in 325.
The Nicene rule separated the Christian computation method from the Jewish one. In the first place, there was a concern over being in spring: though these days, 15 Nisan is always a full moon after the spring equinox, sometimes Easter ended up being celebrated before the equinox, apparently, said the bishop of Alexandria, “through negligence and error” on the part of the Jewish calendrical authorities. (It’s not necessarily negligence and error, because you could also choose to date the start of spring, as some Jews did, as the time the barley ripens. If you did that, Passover could sometimes fall before the equinox.)
In the second place . . . apparently, not all Jewish communities at the time calculated their months in exactly the same way. This might actually be the same concern, if some communities used the equinox and others used the barley, or if barley ripened at different times in different places.
In the third place, reported Emperor Constantine: “It was . . . declared improper to follow the custom of the Jews in the celebration of this holy festival, because, their hands having been stained with crime, the minds of these wretched men are necessarily blinded.” . . .
Christian churches . . . figure out the full moon after the spring equinox — but also add on an extra rule, which is that Easter should fall on a Sunday. So that’s where we get the rule that Easter is the Sunday after the full moon after the spring equinox. (In principle, that still means that Western Easter should fall within Passover, but since Hillel II’s reforms in the 4th century, the Jewish calculations for Nisan are based on a formula and not on astronomy — see Gauss’s formula for the date of Pesach. Thus, in 2008, Western Easter fell on March 23, while Passover didn’t start until April 20.) . . .
For purposes of calculating Easter, [Roman Catholics and Orthodox Christians] use March 21 instead of the true date of the equinox, which could be March 19 or March 20. (The complexities behind “full moon” will be in a later post.) . . .March 21 is considered to fall on a different day depending on your calendar, and March 21 in the Julian calendar is what we in the West would call April 3.
Part 3: Orthdox Easter, what's up with that?

[A]n “ecclesiastical full moon,” . . . is defined as being 14 days after the “ecclesiastical new moon,” which is different than the actual new moon. Why do this? Well, you want to be able to figure out when Easter falls ahead of time rather than when you actually observe a new moon, so you want to be able to have tables to predict the new moon. Hopefully the tables correspond with astronomical reality, but the Council of Nicaea also thought it was important that all Christians celebrate Easter on the same date, and people in different places in the world might observe a new moon on slightly different days. So, in practice, we determine the ecclesiastical new moon by means of tables, and different tables (with different accuracies) are responsible for disagreements in calculating the date of Easter. . . .  there’s a big section on how to do the actual calculations in the Wikipedia article on the Computus. Consider a lunar month of 29.5 days. We could define a lunar year as consisting of 12 lunar months, with lengths alternating between 29 and 30 days. That gives us a year of 29.5 x 12 = 354 days. That’s 11 days shorter than a solar (non-leap) year. . . . [the] lunar month . . . [is] actually 29.53059 days. All this gets us a table predicting when ecclesiastical full moons (i.e., 14 days after ecclesiastical new moons) fall.  This works for most years. But comparing this Easter table with an actual table of full moons, we see that, for the period 2005-2013, it’s off in 2008 (Mar. 22 vs. Mar. 21), 2009 (Apr. 10 vs. Apr. 9), 2010 (Mar. 30 vs. Mar. 29), and 2012 (Apr. 7 vs. Apr. 6).
This particular Easter table is based on the Metonic cycle, named after Meton of Athens, who figured it out in the 5th century BC. This method is still how they figure out when to intercalate months in the Jewish (lunar) calendar. The monk Dionysius Exiguus published an adaptation of Metonic cycles into the Julian calendar in 525 (along the way he invented the practice of counting years [incorrectly] from the birth of Christ). His tables replaced earlier (less accurate) tables, for instance by Victorius of Aquitaine. It took a while for the Dionysian tables to replace the Victorian tables everywhere, and this difference is responsible for the differences in Easter calculation between the Irish church and the Roman church that were resolved at the Synod of Whitby in Northumbria in 664.
How do the Orthodox do it? They just use the Metonic cycle without any corrections, which departs from the full moon by more than three days every millennium. . . . You can see the results in Table 1 on this website, showing the differences between Western and Orthodox Easter. From 1583 to the 2000s, the differences are 0, 1, 4, or 5 weeks. After 2100, the four-week difference drops out, and we only have differences of 0, 1, or 5 weeks. By the 2400s, the differences will be 0, 1, 5, or 6 weeks. By the 2700s, the two Easters will never overlap, and we’ll have differences of 1, 2, 5, or 6 weeks.
There was also an April Fool's Day fake post.

Calendars, Religion and Agriculture.

These calendars and their history are particularly interesting because they represent a convergence of astronomy (which the Roman Catholic church has long invested resources to study because of its relevance of the calendar), mathematics (which has generally been less secular than empirical science), and religion.

Most have had religious affiliations, with some rare exceptions like the short lived French Republican Calendar which was intentionally a secular departure from the Roman Catholic Georgian calendar on the theory that the Roman Catholic Church was deeply intertwined with the French monarchy that the French Revolution deposed.  As Wikipedia explains, it was "used by the French government for about 12 years from late 1793 to 1805, and for 18 days by the Paris Commune in 1871. The new system was designed in part to remove all religious and royalist influences from the calendar, and was part of a larger attempt at decimalisation in France."  The effort to shed the quasi-base twelve/base sixty Sumerian time keeping system failed more quickly:
Each day in the Republican Calendar was divided into ten hours, each hour into 100 decimal minutes, and each decimal minute into 100 decimal seconds. Thus an hour was 144 conventional minutes (more than twice as long as a conventional hour), a minute was 86.4 conventional seconds (44% longer than a conventional minute), and a second was 0.864 conventional seconds (13.6% shorter than a conventional second). Clocks were manufactured to display this decimal time, but it did not catch on. Mandatory use of decimal time was officially suspended 7 April 1795, although some cities continued to use decimal time as late as 1801.
Also, for all of its archacism, the Papal Observatory was actually instrumental in the Roman Catholic doctrinal acceptance of the Big Bang, which, while not literally the account(s) given in the Torah's Book of Genesis, does at least provide a scientific basis for stating that the world has a beginning and was in a sense "created" at a particular moment in time, contrary to pre-Big Bang scientific cosmology which had assumed an eternal and unchanging universe for the most part. This is a big part of the reason that there are so few Young Earth Creationists in Europe. Galileo, who was famous punished by the Roman Catholic church for spreading his astronomy discoveries was a target only because the Roman Catholic church had cared about the calendar and astronomy and developed offical views on it in the first place.

Calendars and Ancient Cultures

Many independent Neolithic cultures have apparently developed its own rather sophisticated calendar as this is necessary for optimum agricultural production. The Roman solar calendar is adapted from 365 day solar calendar developed by the Egyptians, probably based on an earlier or at least influenced by a parallel lunisolar Sumerian calendar with twelve months of thirty days and some extra-calendary days.

There is a lunisolar Chinese calendar that is still in use for ceremonial and holiday purposes in areas formerly in the Chinese sphere of influence (i.e. China, Japan, Korea, Tibet, all of much of Southeast Asia, Mongolia and the homeland of the Turkish peoples).

There was a Mayan calendar that has been reconstructed that died when the Conquistadors crushed the Aztec Empire in the 1500s.

There are a related mix of lunisolar Hindu calendars.

There have been a number of African calendars.  There was a pre-Islamic, Julian calendar derived Berber calendar.  Timbuktu in its heyday also made use of the Julian calendar.  There is evidence of African megalithic era calendars in addition to the Egyptian one and there are other traditional African calendars.
[The] Namoratunga a group of megaliths, dated 300 BCE, was used by Cushitic speaking people as an alignment with star systems tuned to a lunar calendar of 354 days. . . . Great Zimbabwe could have been an astronomical observatory . . . In southern Zimbabwe the shadow of the Moon appears between 0610 and 0620 near the site. Megaliths east of the Great Enclosure align with the Moon, the Sun, and stars during important astronomical events of the year. One Megalith could be an eclipse predictor. The conical structure aligns with a supernova in the Vela, 700–800 years ago.
Three types of calendars can be found in Africa: 1. Lunar 2. Solar 3. Stellar. Most African calendar are a combination of the three. African Calendars: Akan Calendar, Egyptian calendar, Berber calendar, Ethiopian Calendar, Igbo calendar, Yoruba Calendar, Shona calendar, Swahili calendar, Xhosa calendar, Borana calendar, Luba calendar
I'm haven't researched traditional African calendars to know the era of their origins and influences.

 I don't know if the Papuans had indigeneous calendars, which may have been less important for tropical agriculture. However, my ignorance of the ancient traditional calendar practices of non-Western civilizations that have since adopted the Western calendar doesn't mean that they didn't exist.

To my knowledge, there is no evidence that any pre-agricultural society developed sophisticated and precise calendars of these kind. The literary trope is that they kept track of the passing of lunar months without naming them, knew the seasons (probably with more internal definition than the modern four seasons) and counted years but didn't necessarily have a system for numbering them over long periods of time (perhaps using reginal systems based on the reign of chiefs whose names were recalled in oral histories). I don't know how accurate that is, but the lack of a system of writing would cetainly be detrimental to maintaining a formal calendar or keeping track of dates in the modern fashion, and some of this trope may be derived from actual interactions with Native Americans who were hunters and gathers or pastoralists, so I won't discount it out of hand either.

Other Calendars

The Islamic Calendar
The Islamic calendar, Muslim calendar or Hijri calendar (AH) is a lunar calendar consisting of 12 months in a year of 354 or 355 days. Being a purely lunar calendar, it is not synchronized with the seasons. With an annual drift of 10 or 11 days, the seasonal relation repeats about every 33 Islamic years (every 32 solar years). It is used to date events in many Muslim countries (concurrently with the Gregorian calendar), and used by Muslims everywhere to determine the proper days on which to observe the annual fast (see Ramadan), to attend Hajj, and to celebrate other Islamic holidays and festivals. The first year was the Islamic year beginning in AD 622 during which the emigration of Muhammad from Mecca to Medina, known as the Hijra, occurred. Each numbered year is designated either H for Hijra or AH for the Latin anno Hegirae (in the year of the Hijra), hence, Muslims typically call their calendar the Hijri calendar.  The current Islamic year is 1434 AH. In the Gregorian calendar 1434 AH runs from approximately 14 November 2012 (evening) to 4 November 2013 (evening).

Thus, the Islamic calendar is closer to the lunar Hebrew calendar than to the Gregorian calendar that is the dominant one worldwide.

The Hebrew Calendar

[U]ntil the Tannaitic period (approximately 10–220 CE) the months were set by observation of a new crescent moon, with an additional month added every two or three years to correct for the difference between twelve lunar months and the solar year and, therefore, to keep Passover in the spring. The addition of the extra month was also based on observation of natural events: specifically, the ripening of the barley crop; the age of the kids, lambs, and doves; the ripeness of the fruit trees; and the relation of the date to the tekufah (seasons). Through the Amoraic period (200–500 CE) and into the Geonic period, this system was displaced by mathematical rules. The principles and rules appear to have been settled by the time Maimonides compiled the Mishneh Torah in the 12th century. . . . The Hebrew calendar era used at present is the Anno Mundi epoch (Latin for "in the year of the world"; Hebrew: לבריאת העולם, "from the creation of the world") . . . the words or abbreviation (A.M. or AM) for the era should properly precede the date rather than follow it, although this is no longer always followed. . . . AM 5772 began at sunset on 28 September 2011 and ended on 16 September 2012. AM 5773 began at sunset on 16 September 2012 and will end on 4 September 2013.    
Despite the fact that the Hebrew calendar is implicitly based on a Young Earth Creationist theology, few Jews in Israel and the United States (which is where the majority of Jews live), are Young Earth Creationists.


Maju said...

Oh, the ten days that did never exist, hehe. That's why the February Revolution happened on March 8th (International Women's Day and not by accident, because the women began it in fact) and the October Revolution was actually in November.

"... the Sunday after the full moon after the spring equinox".

What kind of astrology had these in mind? The alleged resurrection should be in waxing, not waning Moon, right?

"This is a big part of the reason that there are so few Young Earth Creationists in Europe".

Indeed. Anyhow it also has to do with Christians (specially Catholics but also most mainstream Protestant churches) totally ignoring nowadays the OT except for a few common places and treating it with less faith on what is written there than the Iliad, for example. And it also has to do with 200+ years of strong struggles against religion and its continuous mingling in politics, science and other earthly affairs. Most Western Europeans are de facto atheist, even if many may still make use of religious services for special occasions (otherwise churches are nearly empty) and have a vague claim to some sort of religious affiliation, which is merely nominal.

"... there is no evidence that any pre-agricultural society developed sophisticated and precise calendars of these kind".

Magdalenians were probably quite aware of the solar cycle or year. There are consistent claims that they only chose to decorate caves with the correct orientation and that the animals they depicted were in fact constellations. Australian Aborigines also keep their own very complex calendars: link 1, link 2:

Aboriginal calendars tend to be more complex than European calendars. Many groups in northern Australia use a calendar with six seasons, and some groups mark the seasons by the stars which are visible during them.[5] For the Pitjantjatjara, for example, the rising of the Pleiades at dawn (in May) marks the start of winter.[5][11]

Many stories exist where the heliacal rising or setting of stars or constellations are used to tell Aboriginal Australians when it's time to move to a new place and/or look for a new food source.[5]

The Boorong people in Victoria know that when the Malleefowl constellation (Lyra) disappears in October, to "sit with the Sun", it's time to start gathering her eggs on Earth. Other groups know that when Orion first appears in the sky, the Dingo puppies are about to be born.[5] When Scorpius appears, the Yolngu know that the Macassan fisherman would soon arrive to fish for trepang.[5]

terryt said...

"What kind of astrology had these in mind?"

Not actually 'astrological'. More to do with time to plant, harvest etc. The 'full moon' aspect is what I find strange. But that looks like a new development:

"[U]ntil the Tannaitic period (approximately 10–220 CE) the months were set by observation of a new crescent moon"

It is very easy to see accurately when the new moon first appears but the moon appears full over a period of two or three days. Consequently most agricultural societies use the new moon to mark the passing of months. Usually they simply ignore the last few extra days (as much as a month) extra before the start of a new year. The adjustment usually seems to rely on the first appearance of particular stars. And even non-agricultural people use that system to mark the passing time periods. The use of equinoxes and solstices seems to be a more sophisticated development as they are difficult to see unless a population has remained in exactly the same place for many years.

"The alleged resurrection should be in waxing, not waning Moon, right?"

To me 'passover' has always seemed to be a spring festival, perhaps disguised as an origin myth. The 'resurrection' should be associated with the dying and reborn year at the Winter Solstice I would have thought.

andrew said...

@ Maju Thanks for the input on the pre-agricultural calendars and in particular the role of astronomy observations in the Aboriginal one. (The more finely grained season point is actually in my original post text on the stereotypical hunter-gatherer calendar, so in that respect it is confirming, but the star based reckoning was a surprise to me.)

* terryt

Greek pagan resurrection celebrations were in the spring which is a good fit since everything dies in the late fall, and then comes back to life in the spring, lying fallow in between (sort of, Mediterranean seasons are a bit more muddled than those experienced by those of us living in deciduous forests as most people in the Northern U.S. do) and the intellectual history of the Christian resurrection idea is a synthesis (mostly by St. Paul) of Greek thought and a particular branch of Hebrew thought that was part of the Jewish Jesus movement and some other messianic Jewish movements in the same era, but was not part of the branch of Hebrew thought ancestral to modern Rabbinic Judaism.

Passover may very well have connections to the sacrifice rituals described in the Torah of Temple and pre-Temple Judiasm, possibly incorporating with a new religious gloss some pre-Hebrew pagan spring festival (and a first born male animal is going to be the oldest and closest to slaughter age in the spring in addition to having already provided stud duty for the current round of spring born animals).

But, so far as I know, while parts of the Moses story have Mesopotamian antecedents, the Passover story in particular is a Hebrew innovation. To the extent that it does have a kernel of legend embellished history in it, a plain old contagious disease outbreak that Jews escaped due to Kosher laws (e.g. a pig born infectious agent that lept to humans) that happened to coincide with a spring sacrificial slaughter of lambs seems reasonably plausible to me. Correlation is not causation but is a great way to generate legendary history.

Maju said...

"but the star based reckoning was a surprise to me"...

It should not be: hunter-gatherers often sleep in the open and spend a lot of time outdoors: the sky is there for their imagination and logic to fill it. Being forager does not mean to be dumb or blind, not at all, and anyhow seasons were as important to them as they are for agriculturalists.

What I am a bit surprised of is that we do have a calendar at all with our decadent indoors way of life. Alright, not really but we are nowadays relying on science not personal observation in most cases: we trust what authorities and high-tech clocks tell us. Foragers relied on repeated personal observation within their cultural context (legends and teachings) and so did farmers after them.

terryt said...

"Greek pagan resurrection celebrations were in the spring which is a good fit since everything dies in the late fall, and then comes back to life in the spring, lying fallow in between"

Ah. That explains it.