It must be noted, however, that while the timing, the linking of Passover and Unleavened Bread is explicit, the choice of the Sabbath and thus the "morrow after the sabbath" in the Leviticus passages is not explicit. This is true for Luke's account in Acts. Our liturgical year interprets that "morrow" as Pascha, and this was and is a common interpretation in Jewish practice also.
According to Josephus Antiquities 3.250/3.10.5 the sheaf was waved on the 16th of Nisan:
Originally Posted by Josephus
On the second day of Unleavened Bread, that is to say the sixteenth, our people partake of the crops which they have reaped and which have not been touched till then, and esteeming it right first to do homage to God, to whom they owe the abundance of these gifts, they offer to Him the first-fruits of the barley in the following wise. After parching and crushing the little sheaf of ears and purifying the barley for grinding, they bring to the altar an assaron for God, and, having flung a handful thereof on the altar, they leave the rest for the use of the priests. Thereafter all are permitted, publicly or individually, to begin harvest. Moreover, besides the first-fruits of the crops, they offer a young lamb as a burnt-offering to God.
In modern Rabbinic Judaism the counting of the Omer begins after sunset on the first day of Unleavened Bread, i.e. at the beginning of the 16th of Nisan. I am informed by a footnote in the Loeb Classical Library edition (from which the translation has been taken) that the Karaites begin counting the Omer on the Sunday of Unleavened Bread, but I have not confirmed this.
The 1997 Aleppo statement recommends that "the most likely way to succeed in achieving a common date for Easter in our own day would be," in II 11.(b), "to calculate the astronomical data ... by the most accurate possible scientific means."
It then explains
Quote
In regard to point b:In recommending calculation of the astronomical data by the most accurate possible scientific means (as distinct, for example, from reliance on conventional cyclical tables or personal observation), the consultation believes that it is being completely faithful to the spirit of the Council of Nicea itself, which also was willing to make use of the best available scientific knowledge. We are fortunate that experts in astronomy have already provided these necessary calculations; they are conveniently presented in Synodica V (Chambésy - Genève, Les Editions du Centre Orthodoxe, 1981) 133 - 149.
In that post I questioned how the Aleppo proposal would insure the churches "calculate the astronomical data ... by the most accurate possible scientific means." The calculations reported in Synodica V in 1981 were done by three groups in 1979. The three groups were led by top-notch, well respected ("Orthodox") astronomers, so the quality of their work is not an issue. There were some differences in the results of the three groups and they did not provide details about the methodology and scientific models used. Science is neutral (so similar results would have been obtained by even atheistic scientists) but it is not static and data and calculations are always being refined, reevaluated and improved.
Of the three groups reporting at Chambésy in 1979 the largest time period calculated was Prof. Lederle's, 1969-2500. His calculation was the only one using the meridian of Jerusalem, given as longitude -35° 11'. This is the specification recommended in the Aleppo proposal which has a partial table of results included at its end (Calendar-Easter); these numbers appear to be from Lederle.
How often are the churches going to evaluate the "astronomical data " to insure the calculated results are obtained "by the most accurate possible scientific means"? And what are, who has, those most accurate means? Having asked that last question, I'll give my answer in forthcoming posts.
Last edited by ajk; 02/22/2308:56 AM. Reason: link added
An astronomical Easter, according to The Oxford Companion to the Year
Quote
The calculus astronomicus remained in effect in Sweden till 1823 (though overridden on account of Passover in 1778 and 1798) and in Finland (which Sweden had ceded to Russia in 1809) till 1867.
After this the Swedish and Finnish Lutherans went on the Gregorian calendar.
An astronomical Easter, according to The Oxford Companion to the Year
Quote
The calculus astronomicus remained in effect in Sweden till 1823 (though overridden on account of Passover in 1778 and 1798) and in Finland (which Sweden had ceded to Russia in 1809) till 1867.
After this the Swedish and Finnish Lutherans went on the Gregorian calendar.
I often say, "Do the experiment," and the Swedish and Finnish Lutherans have done this for us. Eventually choosing the Gregorian calendar makes sense. What doesn't make sense to me is that the scientific "calculus astronomicus" succumbs to a less scientific Passover determination -- applying the spurious Zonaras Proviso [orthodoxwiki.org])? If it's required to check the Jewish determined date of Passover, why bother doing it yourself at all. Get the Jewish date for their Nisan 14 and then the next Sunday is Pascha-- simple, except that it's the Protopaschite approach discredited at/after Nicaea I.
We only need one thread dealing with this topic. Currently it runs in this section--Faith and Theology--and in Town Hall. Should these two be combined?
We only need one thread dealing with this topic. Currently it runs in this section--Faith and Theology--and in Town Hall. Should these two be combined?
Bob Moderator
The other thread, Calendar-Easter, is a sporadic, ongoing general discussion dating back to 2016. The present thread deals with an immediate and specific proposal of the Ecumenical Patriarchate focusing on 2025 and the anniversary of Nicaea I. I think combining the threads would blur that focus. Also, this thread is meant to draw attention to a common theological framework that should ultimately supersede the stumbling blocks of history, sociology, ecumenism, ethnicity, political considerations etc., as I stated in the initial post:
Originally Posted by ajk
We've had several spirited discussions related to this topic on this forum. What will it take for this new initiative to be viable?
I invite all to give their views on what it will take for there to be real progress, not the stagnation and stalemate of the past. I say progress and not (complete) success because I suspect there will be some who will never accept anything but THEIR status quo. Will truth prevail -- and should it -- at the risk of schism?
This calendar question, more precisely a unified observance of the annual feast of Pascha, acknowledged as the Feast of Feasts, is not dogma but it is theology, specifically (I'd say) Liturgical Theology. That is why this thread is here in Faith and Theology and not a News forum.
How often are the churches going to evaluate the "astronomical data " to insure the calculated results are obtained "by the most accurate possible scientific means"? And what are, who has, those most accurate means? Having asked that last question, I'll give my answer in forthcoming posts.
This is the first of those "forthcoming posts."
Before addressing those two essential questions and the technological, scientific, astronomical details and calculations, an overview that gives the historical and chronological context and the theological and liturgical foundations should be briefly reviewed.
This discussion arises from repeated initiatives of the Ecumenical Patriarchate (EP) over the past 100+ years aimed at liturgical-calendar reform. That initiative and its lengthy endurance is a clear indication that the Julian Paschalion needs to be replaced: It no longer adheres to the prescriptions of Scripture and the norms attributed to the Council of Nicaea. The EP’s initiative has been affirmed to various degrees by other churches and was put in a sound theological framework by the WCC's Aleppo proposal. The EP’s initiative has also produced (in 1923, published in 1924) a “New Calendar of the Eastern Churches” (aka Milankovitch or Revised Julian Calendar, same as the Gregorian until 2800).
In accord with the EP’s initiative, the Aleppo proposal modifies the traditional approach of both the Julian and Gregorian calendars in several significant ways: - It is based directly on the full moon rather than the 14th day of the moon of Scripture. - Its granularity (the smallest chunk of time considered) is the instant (second or fraction of second) rather than the day. - It is not “perpetual” in the sense of a “perpetual calendar,” i.e. it does not have an inherent repeating cycle, a complete repetition of Pascha dates. - It is not dependent on a calendar -- but as a practical matter must be referenced to a calendar.
The ideal of a Perpetual Calendar was an important feature of the computus of the Julian Paschalion and it was maintained, by design, in the Gregorian Paschalion, though the latter has a much longer cycle period. Based on calendar arithmetic, the full sequence of the Julian Paschalion repeats every 532 years; the full sequence of the Gregorian Paschalion repeats every 5,700,000 years. A consequence of this feature needs to be addressed: How often should revisions to the Paschalion be made and how contingent should the Paschalion be on minute and subtle shifts in timekeeping and predictive calculations?
Last edited by ajk; 03/07/2308:47 AM. Reason: added the word "complete"
The 100+ year effort led by the Ecumenical Patriarchate (EP) is a testimony to the inadequacy of the Julian Paschalion.
The EP’s initiative has produced and reported (1979-1981) Pascha dates based on then current scientific models rather than a traditional computus. This initiative embarks upon a high-tech approach to the solar and lunar cycle applied to a determination of Pascha. Aleppo has considered this and correctly observes:
Quote
In recommending calculation of the astronomical data by the most accurate possible scientific means (as distinct, for example, from reliance on conventional cyclical tables or personal observation), the consultation believes that it is being completely faithful to the spirit of the Council of Nicea itself, which also was willing to make use of the best available scientific knowledge. We are fortunate that experts in astronomy have already provided these necessary calculations; they are conveniently presented in Synodica V (Chambésy - Genève, Les Editions du Centre Orthodoxe, 1981) 133 - 149.
Although not an unwarranted approach, is it advisable?
Here is an excerpt from the 1979 Chambésy meeting as published in Synodika V (1981) [original in French] 113-117:
Quote
ANNEX: RECENT SECRETARIAT EFFORTS TO REVIEW THE QUESTION OF THE COMMON CELEBRATION OF EASTER. by H.E. Metropolitan Damaskinos of Tranoupolis
... the Secretariat for the Preparation of the Holy and Great Council made contact with several astronomers who sent it notices and Tables concerning the exact determination of the Sunday after the first full moon following the vernal equinox (Astronomical Council of the Academy of Sciences of the U.S.S.R. – Prof. L.R. Mustel – , Astronomisches Rechen-Institut – Prof. T. Lederle – , U.S. Naval Observatory, Athens University Observatory – Prof. G. Contopoulos – , Geneva University Observatory – Prof. Marcel Golay –).
The astronomical data collected by the Secretariat have been made the object of study of a commission of astronomers who met at the Orthodox Center on February 3, 1979....
During this meeting two proposals were studied as to the determination of Easter Sunday. The first was developed by Dr. T. Lederle of the Astronomisches Rechen - Heidelberg Institute based on the meridian of Jerusalem – 35° 11' east of Greenwich – and for the years 1969-2500. The second by Prof. Georges Contopoulos of the observatory of the University of Athens based on the meridian of Greenwich and for the years 1970-2200.
The comparative study of the tables of Pascha made both by the congress and by the private studies of astronomers following the congress, led to the following conclusions:
1. that the extent of the tables of the Paschalion (constitution des tables de la pascalie) must be limited, i.e. until the year 2200. 2. that the proposal of Dr. T. Lederle as to the astronomical date of Pascha/Easter for the years 1969-2200 is accurate.
Dr. T. Lederle gives the astronomical dates of Easter for the years 1969 to 2500 ... The calculations are based on the Newcomb Table for the sun and those of Brown for the moon.
Lederle’s approach relied on generally accepted and, it appears, tabulated values and not new calculations per se. This is an acceptable and reasonable procedure. At that time what was considered high-powered electronic computing was not generally available and calculations were routinely done "by hand" (by people know as computers!). Even today (as I'll note in a future post) true state-of-the-art computations are the domain of super-computers and those who can afford them. Results are then stored in computer files of ephemerides [en.wikipedia.org] (diary or journal), raw data such as coordinates (positions) and velocities that can be used as needed such as predicting astronomical events, e.g. vernal equinox, full moon etc. Also note that although Lererle's dates are determined for 1969-2500, only those to 2200 are, in a sense, being certified, i.e. recommended.
Lederle’s source for the moon data, as stated, is Brown:
Brown's Tables were adopted by nearly all of the national ephemerides in 1923 for their calculations of the Moon's position, and continued to be used with some modification until 1983....Eventually, in 1984, Brown's work was replaced by results gained from more modern observational data (including data from lunar laser ranging) and altogether new computational methods for calculating the Moon's ephemeris.[15]
Lederle’s source for the sun data, as stated, is Newcomb:
Newcomb's Tables were the basis for practically all ephemerides of the Sun published from 1900 through 1983, including the annual almanacs of the U.S. Naval Observatory and the Royal Greenwich Observatory. The physical tables themselves were used by the ephemerides from 1900 to 1959, computerized versions were used from 1960 to 1980, and evaluations of the Newcomb's theories were used from 1981 to 1983.[2] The tables are seldom used now; since the Astronomical Almanac for 1984 they have been superseded by more accurate numerically-integrated ephemerides developed at Jet Propulsion Laboratory, based on much more accurate observations than were available to Newcomb. … By 1970 the astronomical community recognized the need for improved ephemerides, which are used to prepare national almanacs..., and the new system would go into effect for the 1984 edition of the ephemerides. "The majority of the resolutions were prepared and adopted by the General Assembly of the IAU at the 1976 and 1979 meetings."...The new fundamental ephemeris was prepared by the Jet Propulsion Laboratory and named DE200/LE200. It uses numerical integration.
That "new fundamental ephemeris" calculation, DE200/LE200, is already rather old and has been continuously improved. The most recent (2020) updates are DE440 and DE441:
Quote
DE440[18]... The 114 Megabyte ephemeris files include the orientation of the Moon. It spans the dates 1550 to 2650. JPL started transitioning to DE440 in early April 2021. DE441[18] was created in June 2020. This ephemeris is longer than DE440, -13,200 to 17,191, but less accurate. It is useful for analyzing historical observations that are outside the span of DE440.
Here is a brief description of these Development Ephemeris (DE) files, how they are calculated, the model employed and how they are used:
Quote
Jet Propulsion Laboratory Development Ephemeris (abbreved JPL DE(number), or simply DE(number)) designates one of a series of mathematical models of the Solar System produced at the Jet Propulsion Laboratory in Pasadena, California, for use in spacecraft navigation and astronomy. The models consist of numeric representations of positions, velocities and accelerations of major Solar System bodies, tabulated at equally spaced intervals of time, covering a specified span of years....The JPL ephemerides have been the basis of the Astronomical Almanac since 1981's DE200. The 2018 Almanac was derived from DE430... Each ephemeris was produced by numerical integration of the equations of motion, starting from a set of initial conditions. Due to the precision of modern observational data, the analytical method of general perturbations could no longer be applied to a high enough accuracy to adequately reproduce the observations. The method of special perturbations was applied, using numerical integration to solve the n-body problem, in effect putting the entire Solar System into motion in the computer's memory, accounting for all relevant physical laws.
These data and software tools are made available to the public and researchers:
Quote
NASA's Navigation and Ancillary Information Facility (NAIF) was established at the Jet Propulsion Laboratory to lead the design and implementation of the "SPICE" ancillary information system. SPICE is used throughout the life cycle of NASA planetary science missions to help scientists and engineers design missions, plan scientific observations, analyze science data and conduct various engineering functions associated with flight projects.
SPICE is subtitled “An Observation Geometry System for Space Science Missions” and is provided to the public :
Quote
The SPICE system is freely available to space agencies, scientists and engineers around the globe ... It is also available to the general public with the caveat that support from NAIF is VERY LIMITED.
SPICE deployment begins with production of a set of ancillary data. The SPICE system includes a software suite known as the SPICE Toolkit consisting of application program interfaces (APIs) that customers incorporate in their own application programs to read the SPICE ancillary data files and, using those data, compute derived observation geometry such as altitude, latitude/longitude, and lighting angles, and to also determine various kinds of solar system events....
It is the “various kinds of solar system events” that are of interest for determining Pascha. The current version of the SPICE Toolkit [naif.jpl.nasa.gov], Version N67, was released January 3, 2022. The toolkit is available for “several computing environments (platform/operating system/compiler).” It comprises a 1416 subroutine/function library SPICELIB [naif.jpl.nasa.gov], for manipulating data and performing calculations.
There are some other possible approaches (e.g. SOFA [iausofa.org]; VSOP [en.wikipedia.org]) that can be considered but I would say that these DE calculations by JPL are the best candidate to satisfy Aleppo's proposal "recommending calculation of the astronomical data by the most accurate possible scientific means."
The point is that there is more to this aspect of Aleppo's Proposal than may have been appreciated.
Last edited by ajk; 03/11/2303:01 PM. Reason: typos
DE441 would probably be of sufficient accuracy for computistical purposes.
I like the Aleppo proposal's use of the meridian of Jerusalem. But I continue to maintain that, instead of calculations of the full moon, we should establish a Babylonian-style lunar calendar based on the first visibility of the lunar crescent. In practice, some convenient substitute for the first visibility would be used, such as the moment when the moon achieves a 10% illuminated fraction (or some other convenient value.)
DE441 would probably be of sufficient accuracy for computistical purposes.
I like the Aleppo proposal's use of the meridian of Jerusalem. But I continue to maintain that, instead of calculations of the full moon, we should establish a Babylonian-style lunar calendar based on the first visibility of the lunar crescent. In practice, some convenient substitute for the first visibility would be used, such as the moment when the moon achieves a 10% illuminated fraction (or some other convenient value.)
I agree. I have used DE441 for some preliminary 6 BC to AD 325 calculations (especially for around AD 30-33) and the full range (1550-2649) of DE440 for addressing the Aleppo proposal. Results to follow.
Less innovative than Aleppo's full moon would be Scripture's 14h of the observable-new moon simulated by a related calculated parameter and an "observation" time window. It seems 6 PM gets mentioned as the locus for the time. Since the equinox and new and full moon are (astronomically) defined by geometry, I've been looking at the Lunar phase [en.wikipedia.org] "expressed quantitatively using ... angles," for a luna 1 separation angle of 3-10%.
The comparative study of the tables of Pascha made both by the congress and by the private studies of astronomers following the congress, led to the following conclusions:
1. that the extent of the tables of the Paschalion (constitution des tables de la pascalie) must be limited, i.e. until the year 2200. 2. that the proposal of Dr. T. Lederle as to the astronomical date of Pascha/Easter for the years 1969-2200 is accurate.
Dr. T. Lederle gives the astronomical dates of Easter for the years 1969 to 2500 ...
Why the limitation up to year 2200? The report notes three years where the Easter date differs because of the different locations, UTC (Greenwich, 0 offset) and Jerusalem, UTC- (35° 11'). These are differences in the day of the full moon: When it is late Saturday at Greenwich England it can be early Sunday in Jerusalem. These are expected differences since, when they occur, the new and full moon (and the equinox) occur at the same instant for everyone over all the earth, the difference being what time is on your clock when they happen. Although not specified in the Chambésy report or in the Aleppo Proposal, the results are for a “midnight-to-midnight day” (see this as noted in Revised Julian calendar [en.wikipedia.org]).
Lederle does question one of his own results, for the year 2468. In his detailed table, he gives the full moon, TABLE V, p 148 as Sunday APR-8 0h 1m which bumps Easter to the following Sunday, APR-15. Gregorian and even Julian Easter are in agreement (Passover noted as APR-8). In his summary table however, TABLE I p 121, he gives the same date but notes “DATE INCERTAlNE, PROBABLEMENT 8.4 (2468)”. The 1 minute past midnight is a really close call but why propose that Easter is probably 8.4, APR-8?
I did the calculations using DE440 and SPICE and get (giving computer not actual precision) for Jerusalem, UTC-(35° 11'):
2468 APR 08 00:32:20.050749 SUN FULL MOON JD2000 = 2622576.52325505111367 Phase=97.82%
So he really had a buffer of over 32 minutes and was correct to go with the APR-15 date for Easter.
The proper way to check Lederle (his reported1979-1981 values) against DE440 is to compare times of the full moon and vernal equinox. Lederle gives these full moon and vernal equinox values; they are a lot of data that is not available in digital form. I have checked his Pascha/Easter results, however, for the total years he reported, 1969-2500, and did find two years of disagreement:
Lederle also gives the Gregorian and Julian dates:
2214 MAR-27(G) MAY-1(J) 2319 APR-06(G) APR-13(J)
These are beyond the imposed limit of year 2200.
Given virtually instantaneous communication, how soon do we need to know Pascha and the feasts tied to it in advance? Why not follow a variation of the primitive practice: The Church announces the next Pascha soon after (immediately ?, Ascension ?, Pentecost?) the conclusion of the last? Knowing no more than 100 years should satisfy anyone's functional curiosity.
I have characterized this calendar/paschalion issue as comprising theology and technology. A substantial amount of scientific/astronomical advancement took place from the time of Nicaea, AD 325 to the Gregorian revision, AD 1582. I recommend the writings of C. Philipp E. Nothaft and Alden A. Mosshammer to anyone interested in this development (primarily) in the West.
There are three quantities in particular that are important in that history and they are still relevant today: (1) the vernal/spring equinox tropical year; (2) the mean tropical year; (3) the synodic month. Concerning (1) and (2) for instance, see Calendar-Easter [byzcath.org], leap year specification; (3) determines the lunar cycle, the lunar month as prescribed in the Old Testament verses for Passover; see posts in this thread.
A problem I have found is that numbers given for those quantities are poorly documented as to their source, and if that is given, then the method and database used for the determination of the events considered. Here I document as a summary typical events evaluated for the full range of the JPL DE440 data, AD 1550-2649, using the SPICE Toolkit:
The present year 2023 is provided as an example (2023 JPL DE440.pdf) of the data for each of the years included in the average values for the designated "EVENT."
Did anyone feel different or notice something out of the ordinary about yesterday? Probably not, and that is the point.
Specifically yesterday 2023 MAR 20 at 21:13 UTC,* UTC-4 = EDT 5:13 PM, Eastern Daylight Time (adjust for your time zone). It was that instantaneous, global event, the astronomical vernal equinox:
Quote
The vernal equinox has a precise astronomical definition determined by the actual apparent motion of the Sun as seen from the Earth. It is the precise time at which the apparent ecliptic longitude of the Sun is zero … This precise time shifts within the civil calendar very slightly from year to year. -- United States Naval Observatory
This is the definition also noted in Synodica V (1981) for the 1977 Chambésy meeting (see attached Equinox and New Moon, 1) , and then incorporated into the 1997 Aleppo proposal -- very precise but doesn't exactly warm the heart or engage the senses. Most of the times we are satisfied to be aware that "yesterday" (though not the same calendar day for everyone) was the first day of Spring.
That sense of the day and not the instant is the granularity of the first two "phases," the Biblical and the Computus, relative to the Modern, which looks at the instant. The Biblical approach was based on direct observations of the environment, specifically the aviv, the new barley as specified in Scripture. For me, eastern US just north of Baltimore MD, my forsythias are a reliable and striking indicator that Spring is near or here.
Unlike the equinox, the moon is a very prominent observable. The moon has been waning since being full on MAR-07 and has now gone dark, so it's time to start looking for that first crescent of the new moon at the beginning of the biblical day, in the early evening in the west where the sun has just set. This, according to Scripture, will mark the beginning of the lunar month (Aviv - Nisan) and the beginning of the liturgical year: the moon of Pesach/Passover; the moon of Pascha/Easter. For Jerusalem at the longitude used by Lederle at Chambésy (using JPL SPICE toolkit and DE440) :
2023 MAR 07 15:33:29 TUE FULL MOON before equinox so too early to be the Paschal moon 2023 MAR 20 23:34:26 MON VERNAL EQUINOX 2023 MAR 21 20:09:03 TUE NEW MOON JD2000†=2460025.34; Astronomical Luna 1 ??? Observed new moon crescent giving Biblical Luna I ??? Biblical Luna XIV (14th of the moon, inclusive) 2023 APR 06 07:14:30 THU FULL MOON JD2000=2460040.80; Astronomical Luna Δ = 15.46 days
Going by Aleppo using the full moon gives:
2023-APR-09 SUN PASCHA
This is also Gregorian Pascha; Julian Pascha is a week late, APR-16 (APR-03 on Julian Calendar).
Both Jew and Gentile eventually adopted the "rule of the equinox" as a discriminator for determining the the Passove/Paschal Moon. Over time they both switched to a computus for solar and lunar timings.
While using the astronomical full moon is acceptable, the 14th of the moon was retained by the computus as conforming to the directive of scripture. The question is how to reasonably model that timing using the sophisticate computations available: % of phase/elongation observed for some time window, e.g. ≥ 5-10% at 4-8 pm (see attached Equinox and New Moon, 2, regarding 6 pm )?
So this is a practical opportunity for us to get close to nature and experience the biblical rhythm for Pascha: Keep an eye for that first sighting of the lunar crescent and let us know when and where it was observed.
--------------------------------------------------------------------------------------------------- * based on DE440; see previous post 2023 JPL DE440.pdf † JD2000: days since Julian Date of 2000 JAN 1.5
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