www.byzcath.org Forums Faith & Christian Life Faith & Theology TOWARDS A COMMON DATE OF EASTER: REMAINING FAITHFUL TO NICAEA

I have been reading "Thomas Strzempinski, Hermann Zoest, and the Initial Stages of the Calendar Reform Project Attempted at the Council of Basel (1434-1437)" by C. Philipp E. Nothaft, Cahiers de L'Instutut du Moyen-Âge Grec et Latin 84,166(2015), also available on Academia.edu. It discusses the two calendar-reform proposals made to the Council of Basle in 1435 and 1437. The first proposal, made in 1435, would have (a) omitted a bissextile day from the Julian calendar once every 136 years; (b) set the earliest date for Easter to March 16; (c) ommitted the day of the conjunction in counting the days of the lunations, so that the 14th day of the lunar month would not precede the full moon; (d) adjusted the dates associated with the Golden Numbers to correpond to the visible lunations; and (e) scheduled recalibrations of the Golden Numbers (and the earliest date for Easter) for future years in order to keep the Golden Numbers current with the visible lunations. The second proposal, made in 1437, would have (a) deleted a week from an upcoming year; and (b) shifted the Golden Numbers by 3 years, so that what was previously year 4 would become year 1. Either of these proposals would have improved the calculation of Easter, but neither was implemented in the end. The Council's general assembly voted in December 1440 to abandon the calendar reform project, "worried no doubt" Nothaft writes "by the newly arisen schism between the council's elected pope Felix V (1439-1449) and Eugene IV in Rome". Calendar reform would have to wait until 1582. Those of us who hope for calendar reform in the Eastern churches today can be encouraged by this example to take the long view.

In my notes on that paper by Nothaft, the two aspects that I highlight are the role of and interactions with the "representatives of the Eastern Church," and which of the various proposals would any have been an adequate solution.The first points to the need for a better and thorough history of the East-West interaction in order to understand the eventual rejection of the Gregorian reform under Patriarch Jeremias II. That rejection is still an issue today for some Orthodox.

The second pertains to my "Kalendar "approach as a possible tool to compare and evaluate the progression of the centuries of work and theories on the calendar issue. Since I claim it is the limiting case of the computus methodology, does it have utility as a standard for comparison? Nothaft documents the historical narrative and provides a good amount of data but to unravel and interpret that data in terms of its parameters (Alfonsine Tabels etc.), indices (Golden Numbers), range in years, computation of mean conjunctions etc., requires dedication and time.

A quick example, however, is the noted 136 leap year interval: p 187.

The comparison of leap year values can be done directly; Kalendar, however, allows them to be evaluated within a consistent and comprehensive framework. The Kalendar equation steps through each year and includes a leap day only when it is needed to avoid an accumulated residual -- an "error" -- of a day. The specified value of the mean vernal tropical year is a whole number of 365 days plus a fraction of a day. I used the value I calculated from the JPL's Developmental Ephemeris DE400: s (vernal equinox tropical year) = 365.24235 ± 0.0037 days (±1σ); see Post 423444. For the ratio = (leap years) / (total years), the goal of the leap year ratio is to match the fraction value. Here are the first values from Kalendar where a lower (fraction-ratio) absolute value indicates a better match :

fraction-ratio      ratio = (leap years) / (total years)
----------------------------------------------------------------------
-0.2423522186 : [ 0 / 1]
-0.2423522186 : [ 0 / 2]
0.0909811148 : [ 1 / 3]
0.0076477814 : [ 1 / 4]
-0.0423522186 : [ 1 / 5]
-0.0756855519 : [ 1 / 6]
0.0433620672 : [ 2 / 7]
0.0076477814 : [ 2 / 8]
-0.0201299963 : [ 2 / 9]
-0.0423522186 : [ 2 / 10]
0.0303750542 : [ 3 / 11]
0.0076477814 : [ 3 / 12]
-0.0115829878 : [ 3 / 13]
-0.0280665043 : [ 3 / 14]
0.0243144481 : [ 4 / 15]
0.0076477814 : [ 4 / 16]
-0.0070581009 : [ 4 / 17]
-0.0201299963 : [ 4 / 18]
0.0208056762 : [ 5 / 19]
0.0076477814 : [ 5 / 20]
-0.0042569805 : [ 5 / 21]
-0.0150794913 : [ 5 / 22]
0.0185173467 : [ 6 / 23]
0.0076477814 : [ 6 / 24]

The low value at [ 1 / 4] is the well known Julian Calendar leap year. It continues for several of its multiples: [ 2 /8], [ 3 / 12], [ 6 / 24] etc. The value -0.0070581009 : [ 4 / 17], is lower so a better match; however, it is for a 17 year interval (total years) that does not lend itself as an adaptation to the, at-the-time-existing, Julian calendar. Thus the trade off is accuracy, compatibility, ease of use and with a workable range of years.

Here is a list including the proposal of Zoest at the Council of Basel and several other historical values. It goes to 470k lunations, 380004 years, 138793700 days. Going to such ridiculously large numbers is to search for patterns and test the numerical stability of the method. The CF's are values that Kalendar finds; these match the independently calculated continued fraction values base on the JPL value of the tropical year.

fraction-ratio     ratio = (leap years) / (total years)
-----------------------------------------------------------------------
0.0000000000 : [18150 / 74891] :                          = CF(11)
-0.0000000002 : [14989 / 61848] :                          = CF(10)
0.0000000010 : [ 3161 / 13043] :                          = CF( 9)
-0.0000000069 : [ 2345 / 9676] :                            = CF( 8)
0.0000000238 : [ 816 / 3367] :                            = CF( 7)
-0.0000000772 : [ 713 / 2942] :                            = CF( 6)
0.0000007226 : [ 103 / 425] :                             = CF( 5)
-0.0000052798 : [ 95 / 392] :                               = CF( 4)
0.0000720239 : [ 8 / 33] :                                     = CF( 3) & OMAR KHAYYAM
-0.0001022186 : [ 969 / 4000] :                             Herschel modified Gregorian
-0.0001299963 : [ 218 / 900] :                              MILANKOVIC
-0.0001299963 : [ 872 / 3600] :                            Kotlar modified Gregorian
0.0001477814 : [ 97 / 400] :                              GREGORIAN
-0.0001647186 : [ 31 / 128] :                              MADLER, STANOJEVIC
0.0002948403 : [ 33 / 136] :                              COUNCIL OF BASEL 1435
-0.0009729082 : [ 7 / 29] :                                = CF( 2)
0.0076477814 : [ 1 / 4] :                                   = CF( 1) & JULIUS CAESAR

I should also have calculated the "omission of a day every 134 years." To do this, since 134 is not a multiple of 4, I calculated the equivalent ratio for 2x134=268 years less 2 years: (67-2)/268 = 65/268.

This subset of the results for each year (as in the previous post) is sorted by fraction-ratio, so the 134 year case spanning twice the number of years would have been a 37% improvement but requiring a longer time span.


fraction-ratio     ratio = (leap years) / (total years)
-----------------------------------------------------------------------
0.0000000000 : [18150 / 74891] :                          = CF(11)
-0.0000000002 : [14989 / 61848] :                          = CF(10)
0.0000000010 : [ 3161 / 13043] :                          = CF( 9)
-0.0000000069 : [ 2345 / 9676] :                            = CF( 8)
0.0000000238 : [ 816 / 3367] :                            = CF( 7)
-0.0000000772 : [ 713 / 2942] :                            = CF( 6)
0.0000007226 : [ 103 / 425] :                             = CF( 5)
-0.0000052798 : [ 95 / 392] :                               = CF( 4)
0.0000720239 : [ 8 / 33] :                                     = CF( 3) & OMAR KHAYYAM
-0.0001022186 : [ 969 / 4000] :                             Herschel modified Gregorian
-0.0001299963 : [ 218 / 900] :                              MILANKOVIC
-0.0001299963 : [ 872 / 3600] :                            Kotlar modified Gregorian
0.0001477814 : [ 97 / 400] :                              GREGORIAN
-0.0001647186 : [ 31 / 128] :                              MADLER, STANOJEVIC
0.0001850949 : [ 65 / 268] :                             COUNCIL OF BASEL AD 1435: 134
0.0002948403 : [ 33 / 136] :                              COUNCIL OF BASEL AD 1435: 136
-0.0009729082 : [ 7 / 29] :                                = CF( 2)
0.0076477814 : [ 1 / 4] :                                   = CF( 1) & JULIUS CAESAR

I'm surprised that the Kalendar predicts, in a sense, the continued fractions. I wonder if there is some inherent mathematical relationship between the Kalendar equation and the continued fraction for the mean solar year.

The lunar cycle analysis is more involved. Something of a test case is the anomaly for the year 16399. Here again we're looking at the application of the Gregorian rule-based methodology for the solar and lunar cycles and the equation based, rather than rule based, Kalendar.

In “The missing new moon of A.D. 16399 and other anomalies of the Gregorian calendar,” Denis Roegel [Interim Report [researchgate.net]] A04-R-436 ( 2004) p7 :
“Hence, the Compendium rule forgets to add a new moon between December 2, 16399 and January 30, 16400. This is actually only the first problem of this kind.” Kalendar correctly has the “missing” new moon since it has new moons for 16399-DEC-29 WED and 16400-JAN-27 THU .

N=NEW          F=FULL
[Lunation Year Day]

____________KALENDAR___________ ___GREGORIAN____ __JDK__ _____KAL_____
      [ 209651   16950   6191114]  N:  30      16399-NOV-29  MON    7711004    7711004.36363
      [ 209651   16950   6191129]  F:  30      16399-DEC-14  TUE     7711019    7711019.12863
      [ 209652   16950   6191143]  N:  29     16399-DEC-29  WED     7711034   7711033.89420
      [ 209652   16950   6191158]  F:  29      16400-JAN-13  THU     7711049   7711048.65920
      [ 209653   16950   6191173]  N:  30      16400-JAN-27  THU      7711063   7711063.42477


For this comparison, Kalendar had to be aligned with a Julian Date, see Julian day [en.wikipedia.org], from which Gregorian calendar dates can readily be calculated using standard algorithms; see Converting Between Julian Dates and Gregorian Calendar Dates [aa.usno.navy.mil] and referenced therein, Richards, E.G. 2012, "Calendars," from the Explanatory Supplement to the Astronomical Almanac, 3rd edition, S.E Urban and P.K. Seidelmann eds., (Mill Valley, CA: University Science Books), Chapter 15, pp. 585-624.

I have been reading some old threads in this forum from the past 20 years or so in which the calendar question comes up. I note how often partisans of the Julian calendar raise the canard about how Pascha/Easter can never coincide with the 15th of Nisan in the Rabbinic Jewish calendar, the first day of Unleavened Bread, almost universally but inaccurately called "Passover." Indeed some partisans of the Julian calendar hold that Pascha/Easter can never fall within the 7 or 8 days of Unleavened Bread in the Rabbinic Jewish calendar, even though this form of the canard is falsified by numerous counterexamples, such as Pascha/Easter of 2011. Some of those who promote these theories appeal to the Canons of Nicea, even though none of the Canons of Nicea deals with Pascha/Easter. More sophisticated partisans appeal to Apostolic Canon 7 and Antioch Canon 1 even though these canons are inapposite since they refer to a form of the Jewish calendar that no longer exists. Another mistake that partisans of the Julian calendar sometimes make is to confuse the Julian Day system of the astronomers (named after Julius Caesar Scaliger, who lived in the 16th century) with the Julian calendar (named after Julius Caesar, dictator of Rome who lived in the 1st century B.C.) It is true that a Julian century of 36525 days is used in certain long-distance astrometric calculations. But when I did astrophysical calculations at NASA in the early 1990s, the only calendar I used was the Gregorian, to make sure I got to meetings on time.

ajk, have you read Hieromonk Cassian's defense of the Julian calendar?

I've encountered it several times in my searches, and have only read what's available online, but do not recall finding (except in print) the complete work "A SCIENTIFIC EXAMINATION OF THE ORTHODOX CHURCH CALENDAR." "... the Church Calendar actually has greater scientific merit than the Gregorian Calendar." Where, how, does one begin to respond? Orthodox calendar reforms with a mixed calendar compromise have only made clarification more difficult. Real, practicing scientists who are Orthodox, have admitted -- even recommended -- the Gregorian Calendar as a solution to the severe misrepresentation of nature -- nature = God's creation, and not 3rd century man's creation -- that is now enshrined in Orthodoxy (and equally benighted Catholics) via the Julian Paschalion.

Chapter 4 of Hieromonk Cassian's pamphlet is here. [orthodoxinfo.com] He makes exaggerated claims for the fathers of Nicea.

Indeed. From Chapter 4: He lives, then, in fantasy land. His poor grasp of science is complemented by his poor grasp of theology:

With one year to go, I refer back to the original post of this thread. There's a lot going on in the Church and the world, so a common Pascha/Easter and the calendar would not be an obvious or a top concern. Nevertheless, in a year, Nicaea, its anniversary, will be upon us. The WCC has Nicaea 2025 [oikoumene.org] and there is Nicaea and the Church of the Third Millennium: Towards Catholic-Orthodox Unity [iota-web.org], Rome, 4-8 June 2025, which does list:
I'm recapping here, and completing at least in a penultimate sense, what I have gotten from this discussion and study. Looking at scripture there's Passover, timed to be at the 14th day of the sighting of the new moon of spring, around the time of the green barley, Aviv. In both Christian and Hebrew observance, this came to be approximated as being close to the full moon immediately after spring, taken as the time of the equinox. For Christians, especially after Nicaea, the observance was always on the Lord's Day, Sunday, the day of the Resurrection.

For over 100 years now the Ecumenical Patriarchate, recently joined by the WCC (culminating in Aleppo, 1997), have been putting forth a proposal that looks to science, astronomy, for a rigorous dating strategy. This is a valid and intelligent proposal that, however, is far, far beyond the demands of scripture.

In between Nicaea and this 20th century initiative is the period of historical development that is dominated by an approach called computus. It looks to arithmetic relationships between the year, the cycle of the sun, and the cycles of the moon, to identify rules and produce tables to match as faithfully as possible, in spirit and in fact, the scriptural directive. The examples, in use today, are the Julian and Gregorian Calendars and their Paschalia. Despite their differences and the associated controversy, the two Calendars and their Paschalia share a common heritage and ethos. They are traditional and Patristic and historical, and as such, are witnesses that the computus framework provided a common ground accommodating the scripture's direct experience of nature and our God-given talent to understand and engage God's design. The computus framework culminated in the Gregorian reform of 1582 but since then there has not been a continuing development of the computus, an investigation into the underlying relationship of the basic cyclic elements of the year and the lunar cycle. The Gregorian reform seems to have been good enough (in fact it was very good!) as a general luni-solar accounting, that further improvement has not been deemed necessary. After all, for order and ease of use and general timekeeping we do not need, nor should we want to account for and accommodate the precise variations in earth-sun-moon movements.

So I would argue that the computus approach is "just right" (And yes, there is even a Goldilocks principle [en.wikipedia.org] .)

What if the computus methodology, however, had continued its development after 1582? Or did it? What insight might it provide for the churches and the Church to achieve a common understanding and perhaps even the much-discussed-and-argued, for at least 1700 years, common observance for the annual Pasch, Easter? I mentioned in a previous post my answer to the (my) question. I believe it's as far as one can go with the computus methodology; going just farther is choosing the significantly different detailed scientific-calculation approach. I started out just looking at the dating of Easter and realized that the basic component for cultural and religious timing -- Hindu, Chinese, Moslem, Christian, Hebrew etc.-- is a lunisolar calendar. The Julian and Gregorian calendars are solar calendars but each have a complete lunar component -- the main thrust of the computus -- for all cycles of the moon throughout the year, not just for the dating of Easter.

My approach -- I refer to it as Kalendar as noted in a previous post-- is an equation based, rather than the classic computus rule-based, lunisolar calendar. It is rather simple and uses just the two average values of the year and the lunar cycle but it becomes a bookkeeping challenge that generates automatically, once identified, the basic patterns that have been discover and historically documented: leap year rules; lunar cycles such as the Metonic and Callippic; epact adjustments of the Gregorian reform; etc.. I have not gone into the dating of Easter (yet???) in that paper but here is an updated summary comparing my results and the Gregorian and the modern calculations. This is a general calendar approach rather than focusing on the determination of Pascha.

K = Kalendar, my stuff
J = JPL, the latest high tech astronomical, almost exactly what the Orthodox reported in 1980
G = Gregorian
(The Juilian Paschalion was not included here since it is so different.)

The total number of years considered is 1100, the range of the JPL database, AD 1550-2650.

Out of 1100, all three agree:
K&J&G:     986        89.64 %

             Additional                   Giving
             agreement            Agreement Totals
             --------------            ---------------------
K&J:            50                    1036   94.18 %
J&G:            11                      997   90.64 %
G&K:           53                    1039   94.45 %

All three agree a large % of the time, almost 90%. My method, using modern insights and virtually unlimited computation ability, at just over 94% is only somewhat in better agreement than the Gregorian at around 91% agreement, both relative to the JPL. The Gregorian reform had limited 15th c. data; I had the full 64-bit precision of the complete range of JPL data that I could use to evaluate and calibrate my results.

What this tells me is that the 16th century Gregorian reform did a darn good job. Remarkably, my method, using the JPL average values, and the Gregorian are in slightly better agreement, 94.45 %, than my method and the JPL, 94.18 %. I think this confirms my approach as being a true extension of the computus methodology using the best available, current, astronomical data.

Details are at An Equation Based Lunisolar Calendar [academia.edu].

ajk, I have o'erglanced your new article. As I may have said before, your use of the mean conjunction provides continuity with the computus tradition.

I acquired Hieromonk Cassian's book A Scientific Examination of the Orthodox Church Calendar from a print-on-demand shop. It contains little that you would not find in on-line debates, except perhaps for an argument that because science has demonstrated time to be a dynamic phenomenon, therefore it was futile for the framers of the Gregorian calendar to try to reduce the length of the average calendar year:

The Gregorian reform does not depend on the difference between the Spring equinox tropical year and the average calendar year to be constant. It merely depends on it having a slowly-varying average value.

Hieromonk Cassian believes that Easter must never coincide with the 15th of Nisan on the Rabbinic Jewish calendar:

He is wrong about the date of Easter in 1921. Easter that year was on March 27 (March 14 Julian) not March 11 Julian. But April 10 Julian that year--April 23 Gregorian--was indeed the first day of Unleavened Bread, 15 Nisan, according to the Rabbinic Jewish calendar. The problem is that if Rule 4 is to be considered a genuinely ancient rule at all, it refers to Passover (14 Nisan) and not the Feast of Unleavened Bread (15-21 Nisan), and that by the Christian calculation, not by the Jewish calculation. This is the way the Alexandrian computus works: Easter is always in the 15-21 day of the moon, never on the 14th of the moon. The Gregorian computus follows this rule exactly.

Ironically, the question of the distinction between the Passover (14 Nisan) and the Feast of Unleavened Bread (15-21 Nisan) comes up in an essay by Archimandrite Sergius, "The Late Celebration of Pascha in 1983" which is included in Hieromonk Cassian's book as Addendum 1:But the date Hieromonk Cassian cites as the Jewish Passover in 1921 is Nisan 15--April 23 1921-- not Nisan 14. But if Archimandrite Sergius is right, he need not worry. In the Rabbinic Jewish calendar, Nisan 14 never falls on Sunday. But as already noted, it is Nisan 14 by the Christian computation that the Paschalion avoids celebrating Easter on.

Neither offering respectable science, history or theology, both Hieromonk Cassian and Archimandrite Sergius are a menace to the truth. Yet they are revered by Julian Calendar devotees and that counts for more than objective facts.

I thought a hands-on tool might be a better demonstration of the concept than just words, tables, equations and graphs: Kalendar.exe. Run Kalendar.exe KALENDAR [patronage-church.squarespace.com], for Windows; download and double-click to run). An important test and illustration of how crucial timing (location) can be is Y=2025 and the agreement of the astronomical (Aleppo), the Julian and the Gregorian. For Israel Standard Time (UTC+2) it is hours shy of giving the expected April 20 date. Run it for the the exact Jerusalem longitude used in the Aleppo proposal, UTC+2.34556 hr, and get the expected

E: equinox
N: new moon (conjunction)
m: molad [en.wikipedia.org] (nominal first sighting of crescent; Day 1); a Jewish term for the "birth" of the moon here, nominally, "the first visibility of the new lunar crescent after a lunar conjunction."
F: Fourteenth day (nominal full moon); Leviticus 23:5
P: Pascha - Easter

__Gregorian__    _<==>_    ____Julian____     _____J2000______
   2025  4  13         SUN F        2025   3   31        2460778.50753827
   2025  4  20        SUN *P*       2025   4    7

Another interesting case tests the numerical stability at very large values for the year. From “The missing new moon of A.D. 16399 and other anomalies of the Gregorian calendar,” Denis Roegel [Intern report] A04-R-436 ( 2004) p7.[link] [hal.science]
Kalendar correctly predicts the “missing” new moon of December 31, 16399.

Also of interest are:

Y=30 and 33: 7 Clues Tell Us *Precisely* When Jesus Died (the Year, Month, Day and Hour Revealed) [ncregister.com]
Y:373, 377, 387 Re: Calendar-Easter
Y: 1981, 1984,The Paschalion: An Icon of Time [academia.edu] and 2019, so-called "problem years"
Y=1582 equinox dates show the 10 day offset that the Gregorian calendar reform corrected. Issued Julian 24 February 1582, proleptic-Gregorian March 6,1582 (a day of molad according to Kalendar.

Continuing to see this through to the end, that is, to Nicaea 2025 ... first, a meditation.

RSV Mark 14:38 & Matthew 26:41 : "Watch and pray that you may not enter into temptation; the spirit indeed is willing, but the flesh is weak."

The Future of Easter [newoxfordreview.org]
March 31, 2024 Orthodox Patriarch Bartholomew hopes for ‘unified date’ for Easter in East and West [catholicnewsagency.com]

and

Ecumenical Patriarch Calls for Joint Easter Celebration for Eastern- and Western-Rite Christians [kyivpost.com] Expressing his hopes for unity, the Patriarch suggested that an agreement on a common date for Easter, which is calculated differently, could be reached as early as next year.
03 May 2024 Joint Celebration of Easter: Is There a Desire to do so? [risu.ua]
May 1, 2024 Preparing the Orthodox for the Date of Pascha [publicorthodoxy.org]

One more.
May 3, 2024 Orthodox Easter: Calendar Question Continues To Split The Church [religionunplugged.com]

In 2025, for the first time in 11 years there will be a "universal Pascha" when all calendars align, inaugurating a cycle of ever-third-year together" through mid 2030's.

This will not be due to any efforts by Patriarchs and Popes.

Christ is Risen!1

ajk,


The only fly in the ointment is Fiducia Supplicans. There has been some powerful pushback among the Apostolic Churches over this document and the practice that has developed from it. I don't see any of the Apostolic Churches signing on to full communion while this monstrosity is in place. I think it will take a lot more than a common date of Pascha for that to happen.