www.byzcath.org Forums General Discussions Town Hall Calendar-Easter

Thank you Fr. Deacon Peter for all your comments and interest.

I make this a separate post because it's more technical and may be more detail than many-most-all care to read. Milanković's (Serbian Cyrillic: Миланковић) calendar raises some further questions. A common purpose of a calendar is to keep the seasons fixed or equivalently predict when the change of seasons occur in a reasonably accurate way. The Gregorian calendar does this as a result of its purpose of getting the vernal equinox fixed to the calendar date of 21-MARCH. In brief, the Council of Nicaea_I though letters (not Canons) relayed its directive about the uniform dating of Pascha; this directive was correctly interpreted to give a working formula. The Church of Alexandria and astronomical schools associated with it as a center of learning in that field were influential in the development of the details. From what I've read the 21-MARCH date for the equinox comes from Alexandria and was emphasized and respected by Pope Gregory as from the Council itself as stated in the Bull Inter Gravissimas [myweb.ecu.edu]

In general, the purpose of a calendar is to span the the proper kind of year by a number of non-fractional days. No calendar can do this simply; this is because the average time of a year divided by the average time of a day is not an integer, a whole number. Rather, it's a number with a fractional part. There are different kinds of years; a proper one must be chosen and used for the intended purpose. A sidereal year brings the earth (as it's usually modeled) back to the same place it started in is revolution about the sun, i.e. as seen against the stellar background. This doesn't keep the seasons fixed on the calendar. The mean tropical year keeps the seasons fixed, all four seasons treated equally based on equinoxes and solstices. This is what the Milanković calendar does. If you're building a general purpose seasonal calendar it's the mean tropical year that is the number to match. If, however, the purpose is to stabilize one event, the vernal equinox, then that is a slightly different number for the year, the vernal equinox year. The Gregorian calendar, as a church calendar with the focus on the vernal equinox and Pascha, as should any calendar claiming to be following Nicaea_I, would want to give first consideration to the vernal equinox year although the tropical year would work, generally, in principle.

So what do the numbers give for the different calendars and years? The numbers change slightly but these are representative to illustrate the concept. All mentioned years have 365 days but the fractional component is different. The fractional components are:

Mean Tropical Year: 0.242181 mean solar day        Vernal Equinox Year: 0.24237 mean solar day

The goal is to match this fractional part by using a leap year method so that (number of leap days included)/(number of years involved) best matches one of the two numbers above depending on a choice of mean tropical calendar or a vernal equinox calendar.

As example, the Julian calendar is the familiar (1 leap day)/(4 years) = 0.250 day/year. The difference with the true numbers above, just using a common 0.242 day value is a difference of just 0.250-0.242= 0.008 day/year. This may seem small and insignificant; how long, however, before the error amounts to 1 day? The answer using simple arithmetic is (1 day)/(125 years). At the time of Nicaea_I, AD 325, relative to Caesar's 46 BC 25-March equinox date (assuming that's when it actually occurred) the error is (46+325)(0.008)= 2.968 days = ~3 days. The actual correction that has come down to us and used in the Gregorian reform was 4 days relative to Caesar's 25-March equinox, thus giving the 21-March date for the equinox (apparently as established by the Alexandrian Church at the time it made the determination) used in the Gregorian reform. At the time of the Gregorian reform the error was 13 days from the 25-March date, thus the Pope's mandated 10 day correction to get to the desired 21-March equinox date.

So, here are some numbers to compare and make a choice. Which one is best for the desired kind of calendar? The best may not be the most practical for various reasons.

Julian                1/4 = 0.2500
Gregorian      97/400 = 0.2425
Milanković   109/450 = 0.242222...

So the Gregorian does better for the Vernal Equinox Year, the Milanković for the Mean Tropical Year.

For either year the Gregorian calendar will not reach a 1 day error until after the year 4750. If one leap-year day is removed from the Gregorian method in 3600 years its fraction after 9 of its 400 year cycle (9x97-1=872) becomes, 872/3600 or (dividing top & bottom by 8) the 109/450 of Milanković. If the mean tropical year is the standard both calendars have the same potential accuracy but the Milanković does it automatically and more elegantly but by a more involved leap year algorithm (i.e. prescription) every 450 years rather than the 3600 years of the Gregorian with a 1-day ad hoc correction. But would a switch really be worth it considering the small gain relative to the possible complications of everyone adopting a new calendar?

For the Vernal Equinox Year there is even a better value than the Gregorian. It seems it was know by Clavius, Pope Gregory's calendar expert, from (allegedly) the Persians (recall the Magi) through the Syrian Patriarch mentioned by me in a previous post. That values is

Persian 8/33 = 0.242424...

Why not use it? It seems to me Pope Gregory favored a simple leap-year formula correction that worked in conjunction with the already well-know and used 1-day-in-4-years method.

A side note: Apparently this 8/33 value was known also by Protestant England where some, in particular one John Dee, wanted to create a calendar based on it and thus better the Pope, as it seems some Orthodox would insist also be done; see the stuff here [orthodoxinfo.com] noted in a prior post. Not only that but they found the place on earth whereby the drift in the 21-March date of the equinox would be the least. Whether true or lore it is fascinating historical intrigue and gave rise to the concept (though called so such much later) of God's Meridian or God's Longitude. Where would that meridian be? Depending on how it's taken, it can cover parts of the Eastern and Central time zones of the US. At the time of the Gregorian calendar promulgation the English calendar proponents determined it to be on the average 77°W. As related (based on an at times flamboyant so I don't know how reliable source):

Just lore and legend? And with hindsight one can finesse the data to produce a coincidence. As it turns out, though, is there anything of particular note at 77° W?

[Linked Image]

When?

The pictures are from the U.S. Navy's "What the moon looks like now" online application:

What the moon looks like now [aa.usno.navy.mil]

They were taken at the end of the 14th and beginning of the 15th day of their respective lunar calendars, when, according to the approximation presupposed by both computi, the moon is just slightly past full and so should have a full, round appearance. The Gregorian picture was captured at 19:36 Central Time on August 28, 2015. The Julian picture was taken at 18:23 Central Time on September 1, 2015.

The link given produces an image of what the moon looks like now. I like the USNO cite but could not find a link there that gives an image of the moon for past dates. Please give that link if it's available.[OK, found it.]

What is the interpretation of this data in terms of calendar and paschalion and computus accuracy, and their correspondence to the observed occurrences?

The interpretation is obvious: The Gregorian approximation to the lunar phases is a good approximation. The Julian approximation is a bad approximation because it has accumulated an error of around 4 days.

Thanks, your point is noted, but the interpretation was not obvious for me. For one thing, what's the significance of the dates chosen for the images from the USNO site? Why August-September and not a March-April-May time fame that would include the ecclesiastical Paschal full moon dates?

The comparison can be done at any time. The Gregorian and Julian lunar calendars assign an age of the moon to every day of the year. Sunset tonight, February 19, 2016, began the 12th day of the Gregorian moon and the 8th day of the Julian moon. The two systems' lunar ages typically differ by 4 days, though sometimes by 5 days. So the Gregorian calendar predicts that the moon tonight has the appearance of a waxing gibbous moon and the Julian calendar predicts that she will appear as a first-quarter moon. A single glance at the sky shows that the Gregorian calendar is closer to the facts.

The schematic moon used by both calendars associates the full moon with the 14th day of the lunar month. The full moon is considered to occur on the 14th day, so that at the sunset beginning the 14th day the moon is considered to be a little short of full, and at the following sunset, ending the 14th day and beginning the 15th, the moon is considered to be just past full. I picked the day that was the 14th day of the lunar month for each calendar and captured the picture from the navy website at an hour that was near sunset ending the 14th day and beginning the 15th in the respective calendars. Because of both calendars' association of the full moon with the 14th day of the lunar month, both calendars predict a full, round moon rising at the sunset that begins the 15th day. The Navy website allows one to compare the visible moon to each calendar's prediction.

Indeed, a "single glance at the sky shows that the Gregorian calendar is closer to the facts."

Does the computus reckon and count the full moon day of the lunar month by its occurrence from sunset to sunset?

That's right. The lunar day begins at sunset. Today, Monday February 22 2016, for example, was the 14th of the lunar month in the Gregorian lunar calendar during the hours of daylight. But once the sun set at your location it became the 15th, and it will remain the 15th until sunset on Tuesday. If you like, it is the 15th of Christian Adar, though obviously not of Rabbinic Jewish II Adar, which is next month.

I think we posted this and talked about it last year, but this AFB by Father Andrew Damick provides some insight into the issue. He took a lot of heat from Orthodox traditionalists who thought he was pressing an 'agenda'. Sadly when it comes to religion, like politics these days, ill founded opinion usually trumps (no pun intended) facts. Anyway, Father Andrew addresses the critiques of his musings in italics in this revised version. It is worth a read. https://blogs.ancientfaith.com/road...ssover-and-other-orthodox-urban-legends/

Fr. Andrew speaks the truth. Then what happens? While he doesn't retract -- and needn't, he spoke correctly -- he clarifies.
Believing what he wrote, he should be advocating for change in practice. He should have a strong opinion even while following his bishop. On the basis of what he describes he should advocate for a change to the (Julian pashalion) "Orthodox practice." One counteracts the "800+ year old urban legend" that is correctly "chalk[ed] ... up to bad catechism" by forceful, good catechism not by just saying there it is folks, these are the real facts but I'm not advocating anything.

If ever there's a case of the tail wagging the dog it's this calendar issue where those who know better are stymied by the threats of reactionaries who practice ecclesiastical McCarthyism ( = "the practice of making accusations of subversion or treason without proper regard for evidence") to get their way.

In light of some truly disturbing and uninformed recent comments by the Archbishop of Canterbury and the Pope on a fixed date for Pascha, advocates for the mandate of Nicaea_I need to be united. There's a lot of dismissing this calendar issue as simply man-made -- "not set by the Apostles" -- but I believe there is a lot more at stake here that especially the fixed-date advocates don't realize. As Fr. Andrew writes, the Church's practice

I do not so read the history. The bishops of Rome and Alexandria had been corresponding for years before Nicea in order to agree on the date of Easter, and they probably already had tables. Contemporary documents indicate that only in Syria did the practice continue of setting Easter according to the Jewish month of Nisan, rather than according to an independently-computed, Christian, Nisan. Independent computations were already in use almost everywhere else. The use of tables did not begin with bishop Theophilus.

The council, for its part, gave no special privileges to Alexandria. Most of the bishops were probably unaware that the Roman and Alexandrine tables sometimes disagreed with each other. Any that were aware of it appear to have expected any discrepancies to be worked out in practice, and this is what the history shows happening. From Athanasius's festal letters and the Aramaic index to them, and from a Latin document known as the Chronograph of 354, we find that, when there was a difference, sometimes Alexandria accepted Rome's date (346 and 349), sometimes Rome accepted Alexandria's date (330), on one occasion (333) they split the difference with a date that accorded with neither table as best we can reconstruct them, and sometimes, indeed (343), they had separate Easters. But we know that both cities already had tables. For the Latin West, some early 8-year Easter tables survive from the 3rd century. For Egypt, Eusebius tells us, or at least implies, that Alexandria was using a 19-year "cycle", which for practical purposes is no different from having tables.

Have you considered contacting Father privately? I suspect you and he would have an interesting discussion...and not in a negative way.

LOL! I was speaking with a friend last night who is Orthodox and is not overly thrilled at Julian Pascha falling in May. He jokingly said his Lenten schedule will be as follows:

March 13: Forgiveness Sunday
March 14-18: First Week of the Fast
March 18: Join New Calendar Parish
March 19: Begin Holy Week
March 20: Palm Sunday
March 25: Annunciation
March 27: Pascha
April 30: Re-join Old Calendar Parish for more ham and kielbasi