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DMD #415287 03/11/16 08:10 AM
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Originally Posted by DMD
Have you considered contacting Father privately? I suspect you and he would have an interesting discussion...and not in a negative way.
I had not but have followed your suggestion, writing to him through his parish website:

Quote
Glory to Jesus Christ.

Father Andrew,

A link to your blog about the calendar was included in a recent post on the byzcath forum and I (ajk) responded:

https://www.byzcath.org/forums/ubbthreads.php/topics/415282/Re:_Calendar-Easter#Post415160

I very much appreciate what you wrote, and commented in encouragement more than critique. I have been writing on the forum for some time and in particular when misinformation is presented about the calendar issue, trying, thereby, to learn and better discern the role and functioning of the calendar in our liturgical life. I'm following the suggestion of a poster (DMD) who wrote in response to my comments:

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

Dcn. Anthony


Thank you, DMD, for the suggestion.



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Originally Posted by Mockingbird
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.
Yes, Jewish/Biblical "evening and morning," but is that how the Gregorian (and for that matter even the Julian) computus counts the days of the moon to construct its algorithm, and then how it presents the results in the use of the various tables. That is, one can construct a table based on an evening-to-evening day but present the result transposed to a midnight-to-midnight day for application since that is how the intended users commonly reckon the day, as an actual calendar day.

This also raises a question about the exact astronomical calculations and how and whether or not it considers a day of the moon, in particular the first or the fourteenth. It needn't but is this a further departure from the ancient -- patristic -- understanding that evolved for the Pascha formula? Did the early church understand the sense of the 14th day as an inclusion, in a solely Christian interpretation and implementation, of the Passover prescription, e.g., Leviticus 23:5-6 New King James Version (NKJV):

5 On the fourteenth day of the first month at twilight is the Lord’s Passover. 6 And on the fifteenth day of the same month is the Feast of Unleavened Bread to the Lord; seven days you must eat unleavened bread.

Two commonly invoked Patristic texts [as quoted in the interesting and informative study by James Campbell, “The Paschalion: An Icon of Time,” St. Vladimir’s Theological Quarterly, Vol. 28 No. 4 (1984) pp. 245-262. See also the same at https://www.academia.edu/8246608/The_Paschalion_An_Icon_of_Time)]:
Quote
Two fourth century documents testify to the presence and significance of this interaction between the old and new chronologies of Passover. First, in a homily attributed to St. John Chrysostom, dated by internal evidence to 387,6 we read:

Since we keep the first of times [spring], and the equinox, and after this the fourteenth of the moon, and together with these the three days Friday, Saturday, and Sunday; lacking any of these at one time it is impossible to fulfill the Pascha.7

A traditional Paschalion of three elements is here set forth. Its actual operation is clarified by the following passage from a letter attributed to St. Ambrose, probably dating from the year 386:

We must keep the law regarding Easter in such a way that we do not observe the fourteenth as the day of the Resurrection; that day or one very close to it is the day of the passion...[and] it is evident that the day of the Resurrection should be kept after the day of the Passion, [so] the former should not be on the fourteenth of the [lunar] month, but later.8

A Biblical 14th day, however, need not be invoked and is not explicitly for:

Sunday following the first full moon on or after the northern hemisphere vernal equinox.

[Here even a calendar is not necessary just the continuous counting of the seven days of the week.]

What is the time frame here of the day of the equinox and of a Sunday? The timing of the moon appears as an instant, not any kind of day. How did the WCC's Aleppo [Synodica V (Chambésy - Genève, Les Editions du Centre Orthodoxe, 1981) 133 - 149.] take into consideration the sense of the 14th day? The prescription above is a more modern expression that obscures -- ignores? -- the 14th day understood as only coincidentally the full of the moon but more so as the Biblical Passover, the Biblical day of the Passion to be followed by the 15th day, symbolically, on the 1st day of the week, Sunday, the day of the Resurrection.

Considering this difference for example:

Quote
A lunar conjunction is the event when the earth, moon and sun, in that order, are approximately in a straight line. (See conjunction (astronomy) for a precise definition.) It is sometimes referred to as the new moon, though in Judaism, the new moon refers to observance by earth bound individuals of the first visible crescent of the moon.
Lunar conjunction [en.wikipedia.org]

In being astronomically exact, and not just correct by some applicable standard -- e.g. observing a new moon ascribed to not an instant but the time frame of a day, or to a definition and table of Ecclesiastical, Paschal full moons -- is an intended Biblical rhythm and symbolism abandoned and lost?




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ajk, I'm not sure I understand your questions. I'll make a few comments that might (or might not) be pertinent to them.

The traditional computi are based on the average synodic month (present-day value 29.530589 days). They don't try to account for any motions of the moon other than the average motion. At least one of the corrections to the lunar motion, called the "evection", was known to the ancients, but I can't find any of the early writers on the Easter cycle who bothers with it. The age of the moon is rounded off to whole days. The moon assumes its age at sunset. Bede writes (De Temporum Ratione 43, Faith Wallis's translation):

Quote
[T]his rule is to be observed: That we recognize that the age of the moon changes in the evening and not, as some do, that it does so at noon or mid-afternoon....

The age of a new moon is more appropriately calculated from the evening hour than from any other time, and it well retain the age which began in the evening until the following evening.
In the early writers, the terms "fourteenth moon", "full moon", and "Passover" (when it does not refer to the Easter festival itself) are interchangeable. Origen, writing about the first Passover in Egypt (Peri Pascha 20, Robert J. Daly's translation):

Quote
It [is] prescribed by law that the passover lamb is to be sacrificed in the first month, on the fourteenth of the month, between the two evenings (Lev 23.5) when the light of the moon has become full and perfect. For the lamb was sacrificed on the fourteenth day of the month, between the two evenings, when, beginning with the fifteenth day, the sphere of the moon reaches its fullest plentitude.
Theophilus, bishop of Alexandria, writing to Emperor Theodosius ca. A.D. 480 (Prologus Theodosii 1, Norman Russel's translation):

Quote
The holy and blessed Passover of God is explicitly acknowledged by the Law, which at the same time indicates the month in which it is to be celebrated and lays down that the day is to be observed with great scrupulousness. For what is conveyed by the Law is the voice of God: Observe the month of the new and keep the Passover to the Lord your God on the fourteenth day of the first month (Deut 16.1, Num 9.3. LXX). The new month is also called the first month, in which the fruits, having come to maturity, announce already the passing of the old. God commanded the Passover to be observed on the fourteenth day of the first month for no other reason than this, that by imitating the light of the moon when it is perfectly full, we might make the luminary of our understanding perfect, and not spend our time in the darkness of sin.
Jerome (Homilies on the Psalms 5, translator unknown since I got the quote from an anthology)
Quote
We read in Exodus that on the fourteenth day a lamb is sacrificed; on the fourteenth day when the moon is a full moon, when its light is at its brightest. You see Christ is not immolated except in perfect and full light.
Though I said that the age of the moon was rounded off to whole days and that "full moon" and "fourteenth day" were interchangeable terms, there is one qualification. The moment of opposition is considered to take place on the fourteenth day, nearer to the end of the day than to the beginning. So at the beginning of the fourteenth day, the moon is still not yet full, but everything that happens on the fifteenth day happens after the moment of opposition. Origen, in the passage quoted above, seems to count the opposition as taking place on the boundary between the 14th and 15th days. Theophilus also considers the moon not yet to be full at the beginning of the fourteenth day. Explaining why Easter Sunday cannot fall on the fourteenth of the moon, he writes:

Quote
Now because it happens that some people fall into error, on the grounds that when the fourteenth of the moon of the same first month falls on a Sunday, to end the fast on Saturday, which is then the thirteenth of the moon, is to act contrary to the Law, it is important to take careful note of the following. If it happens that the same fourteenth of the moon falls on a Sunday, it is better to postpone [Easter] to the following week, for two reasons: first, that we should not end the fast when the thirteenth of the moon falls on a Saturday (this is not fitting, since the law forbids it, and besides the moon is not yet full); and second that when Sunday and the fourteenth of the moon coincide, we should not be obliged to fast and thus do something unseemly (this is a practice characteristic of the Manichaeans.)
Theophilus takes it for granted that the celebration of Easter Sunday will begin on Saturday night. He states that it is wrong to set Easter to the 14th if the 14th is a Sunday because the moon is not yet full on Saturday night at the beginning of the 14th day, implying that it is full sometime later in the 14th day.

The knowledge that the liturgical day begins at sunset is not necessarily transmitted in an Easter table. After all, the simplest Easter table is simply a list of 19 dates for the Passover or Paschal full moon (PFM), the 14th of Gregorian or Julian Nisan, for example:

Code
Year of cycle		Gregorian Passover (PFM)	Julian Passover (PFM)
	 1			April 14			April 18
	 2			April  3			April  7
	 3			March 23			April 26
	 4			April 11			April 15
	 5			March 31			April  4
	 6			April 18			April 23
	 7			April  8			April 12
	 8			March 28			May    1
	 9			April 16			April 20
	10			April  5			April  9
	11			March 25			April 28
	12			April 13			April 17
	13			April  2			April  6
	14			March 22			April 25
	15			April 10			April 14
	16			March 30			April  3	
	17			April 17			April 22
	18			April  7			April 11
	19			March 27			April 30

All dates are in the Gregorian calendar.

But by some of the writers it is considered common knowledge that the liturgical day starts at sunset. Theophilus refers to this practice in one of the quotes given above. Bede, stating on the basis of the Genesis account that the scriptural day runs from sunrise to sunrise, goes on to say (De Temporum Ratione 5):

Quote
It might well be be asked why the people of Israel who, following the tradition of Moses always preserved the order of the day from dawn to dawn, should have begun all their feast days, as we do today, at sundown, and finished them at sundown; as their Lawgiver says, from evening to evening you shall celebrate your Sabbath (Lev 23.32).
Since the 3rd- and 4th-century writers who developed the computus use only the average lunar motion, round off to whole days, and introduce an additional approximation by making the lunar age cyclic in the civil calendar, the Julian lunar, even in the days of its best accuracy, could not be exact. The Gregorian lunar calendar follows the same approach as the Julian more accurately, and because it uses the same approach--average lunation, whole days, cyclic in the civil calendar for 100-300 years at a time--it is necessarily approximate. The use of exact computations every year, whatever else might be said about it, would be a considerable break with tradition since it changes the whole approach to the lunar motion.

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Oops. Theophilus's date should be 380, not 480.

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Originally Posted by Mockingbird
ajk, I'm not sure I understand your questions. ..

The use of exact computations every year, whatever else might be said about it, would be a considerable break with tradition since it changes the whole approach to the lunar motion.

Thanks for all the details. I'll have more comments but focusing on your last statement: What's your appraisal then of the WCC's Towards a Common Date for Easter [oikoumene.org] proposal?

ajk #415312 03/12/16 04:01 PM
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Originally Posted by ajk
Originally Posted by Mockingbird
ajk, I'm not sure I understand your questions. ..

The use of exact computations every year, whatever else might be said about it, would be a considerable break with tradition since it changes the whole approach to the lunar motion.

Thanks for all the details. I'll have more comments but focusing on your last statement: What's your appraisal then of the WCC's Towards a Common Date for Easter [oikoumene.org] proposal?

The WCC proposal would work, and no one could say that we failed to observe the first full moon after the equinox, at least at the reference longitude.

On the other hand, the traditional approach almost always gets the same answer as exact calculations would. Years such as 2019, in which the Gregorian computus will overlook a full moon that occurs a few hours after the equinox, are the exception. One could argue that using exact computations is far beyond the point of diminishing returns in achieving the needed accuracy.

And as I noted, the WCC approach (which has much in common with Milankovic's proposal) would work for computing the Paschal full moon, but it would be a departure from the tradition of using a lunar almanac which assigns an age of the moon to every day of the year. Besides the Easter computation, the age of the moon was traditionally noted daily in the office of Prime, in which the next day's date and age of the moon were announced. In the Roman church, Prime has been abolished, but others elsewhere continue to use it. Maintaining a lunar almanac is not necessary for the computation of Easter, and those who sing Prime can always resort to the Old Farmer's Almanac; but it is a custom that does no harm. It might even be said to do good in reminding us of how "the heavens declare the glory of God" (Ps. 19.1 by the Hebrew count). So I don't see any need to scrap the custom.

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Originally Posted by Mockingbird
The WCC proposal would work, and no one could say that we failed to observe the first full moon after the equinox, at least at the reference longitude.
That should read, "no one could say that we failed to observe the first Sunday after the first full moon after the equinox."

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Originally Posted by Mockingbird
Originally Posted by Mockingbird
The WCC proposal would work, and no one could say that we failed to observe the first full moon after the equinox, at least at the reference longitude.
That should read, "no one could say that we failed to observe the first Sunday after the first full moon after the equinox."
Yes, but is that compatible with the formulation using the 14th day of the moon? I'm not necessarily saying that the newer wording is wrong and that an evolution in the directive isn't possible only that it be done with an appreciation of the difference and the consequences. For instance:

Originally Posted by Mockingbird
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.
Right, Feb. 22 2016 in this example comprises the 14th and 15th day of the lunar month. I presume the assignment to a calendar day as in the table below then would be:

Feb. 22 the 14th day
Feb. 23 the 15th day

Considering:

Originally Posted by Mockingbird
The age of the moon is rounded off to whole days. The moon assumes its age at sunset...

The knowledge that the liturgical day begins at sunset is not necessarily transmitted in an Easter table. After all, the simplest Easter table is simply a list of 19 dates for the Passover or Paschal full moon (PFM), the 14th of Gregorian or Julian Nisan, for example:

Code
Year of cycle		Gregorian Passover (PFM)	Julian Passover (PFM)
...
	 3			March 23			April 26
...

All dates are in the Gregorian calendar.

But by some of the writers it is considered common knowledge that the liturgical day starts at sunset...
So for 2016 as an example, #3, the Gregorian PFM means that the 14th day of the moon, as determined by the Gregorian computus, is understood as from the evening of March 22 to the evening of March 23? If March 23 were a Sunday, Easter is the following Sunday, March 30.

Comments are common about the inaccuracy of the Gregorian computus. The criticisms are often biased themselves or incomplete in either the choice of meridian or not taking it as a consideration at all in making the comparison. The Gregorian computus, and I presume the Julian also, are internally consistent and in that sense correct based on the (idealized) model they employ. The Gregorian differs from the Julian in that it also corresponds, to within an accepted degree of accuracy, with what the earth, moon and sun are actually doing. The specification for that model is based of the fourteenth day of the moon (as in Inter Gravissimas [myweb.ecu.edu] ), not the full moon per se, and a lunar day as noted above. It seems the modern formulation does not properly reflect this. Besides having to specify a meridian for its determination -- not wrong but a necessary added feature -- in also prescinding from an explicit accounting for a lunar day, does it introduce a departure from the primitive understanding of the directive and desire of Nicaea_I as it had evolved up until the Gregorian reform? For instance, using the example of G.N.#3 above, using the WCC's approach, what is the result if the astronomical equinox has occurred and astronomical full moon is on the evening of March 22 and March 23 (as above) is a Sunday? Easter is March 23 (rather than March 30 as above for the computus)?



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Originally Posted by Mockingbird
Besides the Easter computation, the age of the moon was traditionally noted daily in the office of Prime, in which the next day's date and age of the moon were announced. In the Roman church, Prime has been abolished, but others elsewhere continue to use it. Maintaining a lunar almanac is not necessary for the computation of Easter, and those who sing Prime can always resort to the Old Farmer's Almanac; but it is a custom that does no harm. It might even be said to do good in reminding us of how "the heavens declare the glory of God" (Ps. 19.1 by the Hebrew count). So I don't see any need to scrap the custom.
Does the Old Farmer's Almanac use the computus? Prime is still observed in some Latin (i.e western vs. eastern) Catholic monasteries.

Something I did not appreciate at first is that the Gregorian reform provides a complete calendar understood in the sense of of a solar and lunar accounting. We moderns take the moon for granted by comparison. As Inter Gravissimas [myweb.ecu.edu] notes, however:
Quote
10. Moreover, so that the fourteenth day of the Paschal moon is given with precision and that the age of the moon is presented with precision to the faithful in accordance with the antique use of the Church, to take note of it each day with the reading of martyrology , we order that once the Golden Number is withdrawn from the calendar, one substitutes the cycle of the epacts for it which, thanks to its very precise rules mentioned above for the Golden Number, makes so that the new moon and the fourteenth day of the Paschal moon always hold their place. And this is seen clearly in the explanation of our calendar, where are also presented Paschal tables in conformity with the ancient habits of the Church and which make it possible to find more surely and more easily the sacred date of the Easter.

Returning to the sense of a computus vs. "exact astronomical" determination, we should consider the compromises that we take for granted and readily accept. Any calendar of whole days must allow an error to accumulate that is then periodically corrected; our 12/24 hour clocks don't conform exactly with the Equation of time [en.wikipedia.org] , the lunar cycle is usefully and conveniently presented with a Tide clock [en.wikipedia.org] or Astronomical clock [en.wikipedia.org] (an even more) or the Moon Dial On Grandfather Clocks [theclockdepot.com] the last using an average based on the 15th day as the full moon:
Quote
The Full Moon always occurs on the 15th day of the Lunar Calendar. If it were a full moon today, the image of the moon on the dial would be centered below the 15 on the dial. There are two moons on the dial and it makes no difference which one is under the 15. Grandfather clock moon dials consist of a round disk displaying two pictures of the moon. A one half rotation of the disk occures [sic] every 29.5 days which is one lunar cycle.



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If the first day of a lunar month of 29.5 days is taken to begin 24 hours after conjunction and the moon moves through its phases with a constant angular velocity, then opposition will occur 14.75 days after conjunction--on the 14th day about 6 hours before the beginning of the 15th day.

If the first day of the mean lunar month is taken as beginning with the mean conjunction, then of course the mean opposition will occur on the 15th day.

In the case of the Gregorian lunar calendar, Clavius made sure to start the lunar months a day or so after the mean conjunction in order to give the full moon a strong association with the 14th day of the lunar month. That he succeeded is shown by the following data:

Code
Date of true 	       14th of Gregorian lunar month	Day of Gregorian lunar month 
opposition (UT)						on which opposition occurs
Jan 27 2013		Jan 27				14
Feb 25			Feb 25				14
Mar 27			Mar 27				14
Apr 25			Apr 25				14
May 25			May 25				14
Jun 23			Jun 23				14
Jul 22			Jul 23				13
Aug 21			Aug 21				14
Sep 19			Sep 20				13
Oct 18			Oct 19				13
Nov 17			Nov 18				13
Dec 17			Dec 17				14
Jan 16 2014		Jan 15				15
Feb 14			Feb 14				14
Mar 16			Mar 15				15
Apr 15			Apr 14				15
May 14			May 13				15
Jun 13			Jun 12				15
Jul 12			Jul 11				15
Aug 10			Aug 10				14
Sep  9			Sep  8				15
Oct  8			Oct  8				14
Nov  6			Nov  6				14
Dec  6			Dec  6				14
Jan  5 2015		Jan  4				15
Feb  3			Feb  3				14
Mar  5			Mar  4				15
Apr  4			Apr  3				15
Jun  2			Jun  1				15
Jul  2			Jun 30				16
Jul 31			Jul 30				15
Aug 29			Aug 28				15
Sep 28			Sep 28				14
Oct 27			Oct 26				15
Nov 25			Nov 25				14
Dec 25			Dec 25				14
Jan 24 2016		Jan 23				15
Feb 22 			Feb 21				15
Mar 23			Mar 23				14
Apr 22			Apr 21				15
May 21			May 21				14
Jun 20			Jun 19				15
Jul 19			Jul 19				14
Aug 18			Aug 17				15
Sep 16			Sep 16				14
Oct 16			Oct 15				15
Nov 14			Nov 14				14
Dec 14			Dec 13				14
Jan 12 2017		Jan 12				14
Feb 11			Feb 11				14
Mar 12			Mar 12				14
Apr 11			Apr 11				14
May 10			May 10				14
Jun  9			Jun  9				14
Jul  9			Jul  8				15
Aug  7			Aug  7				14
Sep  6			Sep  5				15
Oct  5			Oct  5				14
Nov  4			Nov  3				15
Dec  3			Dec  3				14
So as ajk has been saying, the Gregorian computus implements the outlook of the 3rd-4th century Christian computistical writers very well.

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Mockingbird presents a useful comparison. The results of a similar comparison for just the Paschal full moons is given in Gregorian Reform of the Calendar [casinapioiv.va] [Proceedings of the Vatican Conference to commemorate its 400th Anniversary, 1582-1982, Extra Series 3, Specola Vaticana, Vatican City, 1982, pp. xxv-323. Contents and Preface by Fr Coyne].

The following excerpts, (p 220-221) from the paper by A. Ziggelaar, S.J., in that Proceeding, augment some of the considerations in this thread. In the excerpts: Clavius, S.J., is the chief scientist of the reform committee; Ignatius is the Syrian (abdicated, called a former Nestorian in the paper and who I referred to in previous posts) Patriarch of Antioch; Professor T. Lederle is the same whose calculations were used by the WCC's Aleppo gathering; the Compendium is the initial detailed proposal by one Luigi Giglio that was chosen as the basis for the reform; the Explicatlo is the published detailed explanation of the calendar and computus by Clavius.

Contrary to what I had written in a prior post, exact astronomical calculations were considered, initially favored by Clavius but rejected in favor of keeping the traditional approach of using a computus. It is clear that the Gregorian reform's goal was to disturb the prior, traditional approach as little as possible and function in the same overall manner. It strove for continuity with the prior Metonic cycle formalism requiring, however, that an acceptable fidelity of the calendar and paschalion to the actual celestial events obtain.

So, science and tradition are harmonized; better to be late than too early, in line with patristic thought:

Quote
The cyclic dates of new and full moons were adjusted to the Prutenic tables so Clavius could say that the reform followed the Prutenic or Copernican tables. However, all epacts have been made one unit less. This may perhaps be seen as a response to the criticism of Ignatius that the Compendium took the conjunctions of the sun and moon for visible new moons. However, nowhere in the calendar nor in the Explicatlo of Clavius is this distinction made. Perhaps the commission did not wish to take sides in a controversy. Clavius gives as a reason the need to avoid that Easter should be celebrated too early. Indeed, errors cannot be completely avoided because artificial cycles cannot represent exactly the real motions of sun and moon with their anomalies. The reform preferred, therefore, to place the new and full moons too late rather than too early because it would be a lesser error to celebrate Easter in the second month after the equinox than in the last month before the equinox or even to celebrate Easter on the same date as the Jews, that is on the fourteenth day of the moon instead of the day thereafter.

The new model strives to minimize "error":

Quote
But perhaps the commission had made its choice by a somewhat experimental method. It may have calculated full moons according to the available astronomical tables and chosen its epacts such that a minimum of errors results. In fact, Clavius defends the epacts of the calendar by showing that any other choice would make the errors more frequent. We can check it also by comparing the Easter date for the years 2000 to 2500 with the dates for full moon, calculated by Professor T. Lederle. It can be seen that a shift of the epacts by one day, whether forwards or backwards, increases the errors. In the following table P-Q means the number of weeks that (the Gregorian) Easter precedes the Easter date according to modem calculations of the dates for the real equinox and the real full moon. The top row lists the number of Easter dates between 2000 and 2500 where the different cases apply when the epacts of Giglio and the Compendium are used; next the numbers for the actual Gregorian calendar; finally the numbers for the case when the epacts are decreased by even one more unit.

The issue of how the lunar day should be reckoned and the question of how that impacts exact calculations such as the WCC's is noted along with a concern. Referring to the table (p 221):

Quote
In parentheses are the numbers which result when we keep to the principle that new moon after six in the evening is attributed to the following day. This principle, announced by the commission in its report of 14 September, 1580, I have not seen respected neither by the Gregorian calendar nor by Professor Lederle, but we see that it reduces the errors. It is obvious that the least errors occur when new moon is assumed to take place exactly when it becomes visible, one or two days after conjunction; so perhaps the criticism of Ignatius was accepted in practice, though never overtly. Nowadays we ate able to compare the Gregorian calendar with accurate predictions of the true motions of the moon. Clavius made a comparison but had to be guided by the mean motions of the moon, the only ones which he could predict sufficiently. The saying that Gregorian cycles follow the mean motion of sun and moon is however misleading, as Clavius points out in his explanation of the calendar. ..

ajk #415366 03/20/16 05:39 PM
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Originally Posted by ajk
I presume the assignment to a calendar day as in the table below then would be:

Feb. 22 the 14th day
Feb. 23 the 15th day
That's right. The lunar day formally corresponds to the civil day whose hours of daylight will coincide with the lunar day's hours of daylight. Put another way, the lunar day begins 6 hours before the civil day.

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Thanks to these postings I've come to have a greater appreciation for the first chapter of the Prophecy of Isaiah!

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Originally Posted by Ot'ets Nastoiatel'
Thanks to these postings I've come to have a greater appreciation for the first chapter of the Prophecy of Isaiah!
Have you? And what is that?

ajk #415384 03/22/16 11:37 AM
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Originally Posted by ajk
Originally Posted by Ot'ets Nastoiatel'
Thanks to these postings I've come to have a greater appreciation for the first chapter of the Prophecy of Isaiah!
Have you? And what is that?
While awaiting an exegesis of Isaiah 1, what may seem an abstract discussion about this Calendar-Easter thread can be put in concrete, observable terms. According to the Astronomical Applications Department of the U.S. Naval Observatory [aa.usno.navy.mil] we on planet earth recently experienced the vernal, i.e. spring northern hemisphere equinox:
Quote
2016 Mar 20 04 30
The calendar date is no doubt that of the commonly used de facto international calendar. It's the one most of us have hanging on our walls. So spring began Sunday March 20, 2016 at 4:30AM UTC (roughly Greenwich, England). Across the globe that translates to as early and late as

Baker Island Sat, Mar 19, 2016 4:30 PM local time
Kiritimati Sun, Mar 20, 2016 6:30 PM local time

and for a well-know location

Washington DC Sun, Mar 20, 2016 12:30 AM local daylight saving time

The point is that if we trust this date the March equinox has taken place everywhere. These times are based on a modern definition:
Quote
The astronomical definition of the vernal equinox is the instant when the Sun, as seen from the Earth, has a zero apparent ecliptic longitude. (Yes, the Sun's ecliptic longitude, not its declination, is used for the astronomical definition.) This instant shifts slightly from year to year within the civil calendar. In the ecclesiastical system the vernal equinox does not shift. It is fixed on March 21 regardless of the actual position of the Sun.
The Date of Easter [aa.usno.navy.mil]

Following the prescriptions of our predecessors in the church, early Canons, Nicaea_I and Patristic writings, this is the first requirement for determining the observance of the annual Pascha feast, what we will sing as the "feast of feasts" at Matins.

Next, according to the Patristic wording, we are to wait until the fourteenth day of the moon. The first day of the moon can mean the new (dark) moon or the first observable crescent, or making some observation and adjustment of a day; the lunar day in this context is from sunset to sunset or 6 pm to 6 pm. The fourteenth day is the fourteenth day, not the full moon, but it can be and has been so associated. Patristic writers are insistent that Pascha be after the (biblical) fourteenth day of the moon. (It is easier, I presume, to determine an on-off phenomenon like the first light of the moon than degrees of fullness, plus it allows 14 days for preparation.)

Using the USNO site, the astronomical New moon [en.wikipedia.org] --

Quote
In astronomy, new moon is the first phase of the Moon, when it orbits as seen from the Earth, the moment when the Moon and the Sun have the same ecliptical longitude.
--

was March 9, 2016 at 01:54 UTC. The full moon is 14.4215 days later on March 23, 2016 at 12:01 UTC. (The full range of local occurrences is +/- 12 hours of UTC and for adjustments for local time and time zone convention this could be as much as +/- 14 hours.)

The bottom line is that we are expecting to see a very full moon the evenings of Wednesday & Thursday, March 23 & 24 (go outside and take a look). Then according to the traditional prescription understood in any combination of the Patristic or modern wordings (today being March 22 11:37 AM EDT as I write) Pascha is to be this Sunday, March 27, 2016.

The date here is on that common civil calendar I mentioned above and is used for convenience. Using any calendar that preserves the 7-day biblical week, taking today as a reference, mark the above relative times for the -- actual, as given above -- equinox and full moon; the next Sunday, that is this coming Sunday on the chosen calendar by the above criteria, is Pascha according to the biblical/patristic/counciliar directive.



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