Talk:Date of Easter/Archive 2

Sources

@User:John_Maynard_Friedman: you demanded additional/better sources for the Gregorian calendar. The one and only authoritative source: the Canons, are mentioned in that text. Point is that they are written in Latin, and published on paper centuries ago. I recall a re-issue was printed in France in the 19th century. Apart from maybe "Inter Gravissimas" they were never translated into English. The only on-line edition, with partial translations into English and French, was collected by Rodolphe Audette from Canada on his personal website in the begin of the 21st century. This was taken off-line, and a copy is now only available from the personal website of Henk Reints, as quoted. Clavius' "Opera Omnia" containing among others the Canons and his Explicatio have been scanned and put online by a few libraries, but pictures are not as accessible as HTML. So your demand can not be met. I like to add that the (ill-advised) Wikipedia rule to NOT use primary sources (meant to banish personal interpretations of texts like diaries) has been declared applicable to this lemma and to Epacts, with the result that the actual sources have to be ingnored, and only uninformed and wrong digests of translations of quotes in much later books are allowed here. Tom Peters (talk) 15:07, 30 April 2019 (UTC)

A good Dutch source on the Gregorian calendar — including a full translation of the Inter Gravissimas — is Walter Emile van Wijk's De Gregoriaansche kalender: Een technisch-tijdrekenkundige studie (Maastricht: A.A.M. Stols, 1932), online here. As far as I know no such work exists in the English language. AstroLynx (talk) 15:30, 30 April 2019 (UTC)

The paragraphs for which I sought citation should not need going back to 1582:

Easter Sunday is the Sunday following the paschal full moon date. The paschal full moon date is the ecclesiastical full moon date following 20 March. The Gregorian method derives paschal full moon dates by determining the epact for each year. The epact can have a value from * (0 or 30) to 29 days. The first day of a lunar month is considered the day of the first appearance of the crescent moon. The 14th day thereafter is considered the day of the full moon.

Historically the paschal full moon date for a year was found from its sequence number in the Metonic cycle, called the golden number, which cycle repeats the lunar phase on a certain date every 19 years. This method was abandoned in the Gregorian reform because the tabular dates go out of sync with reality after about two centuries, but from the epact method, a simplified table can be constructed that has a validity of one to three centuries.

Surely modern Western Christian churches have written rules that they applied just a few weeks ago. Where are these rules? You cannot believe that the various churches go back to the original Papal Bull? especially when half of them consider the Pope to be the Antichrist? What about the calculation from first principles (to avoid any mention of Rome) in the Calendar Act 1750? --John Maynard Friedman (talk) 18:19, 30 April 2019 (UTC)

John Maynard Friedman asked "Surely modern Western Christian churches have written rules that they applied just a few weeks ago. Where are these rules?" Just because Wikipedia decided to have a "Computus" and an "Easter" article does not mean churches will structure their binding rules about the date of Easter as free-standing rules. In the case of the Roman Catholic Church, the Church delegates to national conferences of bishops the authority to create a liturgical calendar which specified what is to be celebrated on practically every day of the year, including when Easter is to be celebrated. The liturgical calendar for the United States may be found here.

In the Catholic Church everything is quite hierarchical. The layperson or the parish priest does not have the duty, or authority, to calculate the date of Easter from first principles; the date is handed down each year by higher authority. No doubt those authorities are following a combination of tradition and hierarchical mandates that eventually lead to the Pope, but it would be laborious to trace out that path. Without a knowledge of Italian and Latin it could be quite difficult, and there is no guarantee that all the documents in the chain are publicly available (much less online). Jc3s5h (talk) 19:48, 30 April 2019 (UTC)

We're asking two different kinds of questions here. The first is what authorities the various Western churches used to adopt an equivalent to the Gregorian calendar reform. There is a literature out there on the phases by which the Gregorian reform was adopted -- it wasn't instant even in Catholic countries and the various Protestant countries took various steps to adopt national calendars that were roughly equivalent to the Gregorian reform, while avoiding any acceptance of the papal decree Inter gravissimus. Nothaft cites the major secondary sources in the brief discussion of the reception of the Gregorian reform that closes his Scandalous Error: Calendar Reform and Calendrical Astronomy in Medieval Europe, Oxford Univ. Pr., 2018, pp. 301-2.

The second question deals with whether or not local churchmen read official decrees: Inter gravissimus or its Protestant equivalents. The answer here is probably no, since most clerics don't do mathematical astronomy and they generally follow a calendar provided by local ecclesiastical or civil authorities—or even by commercial publishers of almanacs or calendars. I suspect there's a dissertation out there, or yet to be written, on this process. --SteveMcCluskey (talk) 21:46, 30 April 2019 (UTC)

We could be in danger of creating a wp:FORK of Gregorian calendar in this article, which is neither appropriate nor necessary. Indeed it is possibly not even relevant as the essential rules for computing the date of Easter were decided in 432, just better codified by Gregory. My fundamental challenge to this article as it stands is that it is a few thousand words long, goes into great detail on algorithms, yet fails to provide any evidence to support its most basic premise. It is a castle built on sand. Fortunately we all know it is true (or at least willingly suspend disbelief) but it really is a serious deficiency. --John Maynard Friedman (talk) 23:04, 30 April 2019 (UTC)

@John Maynard Friedman: Two points where we disagree:

• When you said "the essential rules for computing the date of Easter were decided in 432", you underestimate the magnitude of the computistical change involved in the Gregorian reform. That reform incorporated new astronomical values for the length of the solar year and the lunar month, provided one-time adjustments to both the solar and lunar calendars (visible most notably in the missing 10 days of the year 1582), and incorporated new computistical techniques to make this new calendar "essentially" perpetual. (The word "essentially" carries a heavy load here since the published Gregorian procedures do break down in the long term, but Pope Gregory and his technical advisors wrote an open-ended model, allowing for the possibility of future adjustments).
• Your suggestion that this article is a potential fork of Gregorian calendar ignores the fact that the Gregorian calendar article deals primarily with the solar part of the Gregorian reform. Note it's description: "The Gregorian calendar is a solar calendar…." This ignores the fact that a major part of computus involves the luni-solar calendar, since Easter is the first Sunday after the Paschal full moon. It was the complex problem of relating the Sun and the Moon that made computus such a fascinating challenge from the time of the Nicene Council to the present.

Setting aside those comments, I agree that this article tends to overemphasize the role of modern algorithms, reflecting the early development of this article as a discussion of algorithms, to which a historical section was eventually added and the fact that the topic is also of interest to modern mathematicians — just as it had been of interest to ancient and medieval mathematical astronomers.

Finally, I'm not quite sure what you mean when you say that this article "fails to provide any evidence to support its most basic premise." You may have a point there but could you clarify what premise you have in mind and what kind of evidence you'd like to see to support that premise. --SteveMcCluskey (talk) 01:13, 1 May 2019 (UTC)

The whole principle of Computus relies on this statement:

Easter Sunday is the Sunday following the paschal full moon date. The paschal full moon date is the ecclesiastical full moon date following 20 March. The Gregorian method derives paschal full moon dates by determining the epact for each year. The epact can have a value from * (0 or 30) to 29 days. The first day of a lunar month is considered the day of the first appearance of the crescent moon. The 14th day thereafter is considered the day of the full moon.

--John Maynard Friedman (talk) 09:39, 1 May 2019 (UTC)

Canon VI: "Quoniam ex decreto sacri concilii Nicæni Pascha, ex quo reliqua festa mobilia pendent, celebrari debet die dominico qui proxime succedit XIV lunæ primi mensis". Mind that all the sources mention day 14 of the lunar month, "Full Moon" is implied so the statement in the Computus article is not strictly correct.

Canon VI continues: "is vero apud Hebræos vocatur primus mensis cuius XIV luna vel cadit in diem verni æquinoctii, quod die XXI mensis Martii contingit, vel propius ipsum sequitur". Also here mind that 21 March is mentioned, inclusively, so "following 20 March" in the Computus article is an equivalent reformulation - does that count as "original research" forbidden in Wikipedia?

Canon VI continues: "efficitur ut si epacta cuiusvis anni inveniatur ex canone 2 et ab ea in calendario notata inter diem octavum Martii inclusive et quintum Aprilis inclusive (huius enim epactæ XIV luna cadit vel in diem æquinoctii verni, id est, in diem XXI Martii, vel eum propius sequitur)", referring to the 2nd Canon that deals with computing the epacts.

As for the first day of the lunar month being the day of first visible crescent rather than the day of astronomical conjunction (syzygy): Lilius' original tables were based on the conjunction, but while discussing the proposal, the committee was joined by the Syrian patriarch of Antioch ("Ignatius Necmet Alla"), see the signatures of the Ratio Corrigendi Fastos at http://henk-reints.nl/cal/gc-nl/index.htm?page=ratcorfast-nl.htm . He could demonstrate that with the Jews and early church the month started typically a day later, so the epact table was changed - I can't find the exact statement now, it may be hidden in Clavius later Explicatio. In any case it was worse to celebrate Easter too early than to late, as stated e.g. in the Ratio (and in similar wordings in the second Canon): "VII. Si igitur erratum committitur in cyclo, deterius est, si locus coniunctionis atque oppositionis luminarium antecedat, quam si consequatur novilunia ac plenilunia media.".

Tom Peters (talk) 11:22, 1 May 2019 (UTC)

and it is unsourced. --John Maynard Friedman (talk) 09:39, 1 May 2019 (UTC)

qoud non, sources are the Canons which are most readily available on-line as Audette's transcription on Reints's site. Tom Peters (talk) 11:22, 1 May 2019 (UTC)

Thinking about it again overnight, it certainly strikes me that it would be entirely legitimate to cite the Calendar Act 1750 because (a) it is in English! (b) readily accessible and (c) valid. Of course it would not be a valid citation for the reform as defined by Gregory but it doesn't matter for this article. But it does mean perhaps that the section might have to be recast so that it is less obviously religious – a contradiction in terms, I admit! so maybe less Roman Catholic.--John Maynard Friedman (talk) 09:39, 1 May 2019 (UTC)

Fine, then please do so. Tom Peters (talk) 11:22, 1 May 2019 (UTC)

Useful and reliable English sources on the Gregorian calendar (and a few other calendars) can be found in the Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac (London: Her Majesty's Stationery Office, 1961), pp. 407–442 [online here] and in the Explanatory Supplement to the Astronomical Almanac: A Revision to the Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac (Sausalito [CA]: University Science Books, 1992), pp. 575–608 [online here]. Expanded from a shorter discussion originally written by John Knight Fotheringham in The Nautical Almanac and Astronomical Ephemeris for the Year 1931 (London: His Majesty's Stationery Office, 1929), pp. 734–747 [online here] and revised in The Nautical Almanac and Astronomical Ephemeris for the Year 1935 (London: His Majesty's Stationery Office, 1934), pp. 754–770 [online here]. AstroLynx (talk) 09:58, 1 May 2019 (UTC)

A good but derived source. Mind that it is not as trustworthy as it should be, the list of errata of the latest editions are huge. Fotheringhams analysis is noteworthy, being the first to derive the 5.7 Myr period of recurrence of the Gregorian paschal cycle. Overall, modern analyses focus too much on accurate astronomy, which was not the main concern of the reformers. The original contemporary sources stress: counting the days of a lunar month (rather than an exact moment of syzygy in whatever timezone); 14th day of the lunar month (rather than full moon); try keep the aequinox on 21 March but always use that date as the canonical aequinox date; never ever celebrate Easter on or before 21 March or on or before the 14th day of the first lunar month of spring. Tom Peters (talk) 11:43, 1 May 2019 (UTC)

The list of errata [online here] for the latest edition, Explanatory Supplement to the Astronomical Almanac: Third Edition (Mill Valley [CA]: University Science Books, 2013), indeed currently spans seven pages but only four corrections are actually listed for the section on calendars (pp. 585–624). AstroLynx (talk) 12:53, 1 May 2019 (UTC)

@Tom Peters: I'm a bit concerned with your proposal to cite primary sources such as the Canons (of unclear source?) and John Maynard Friedman proposal to cite the Calendar Act. Both of them are primary sources which are only to be used with care on Wikipedia and "Any interpretation of primary source material requires a reliable secondary source for that interpretation." Since there is an extensive body of secondary historical literature on the development of the calendar I would strongly recommend using that instead of primary sources.

@SteveMcCluskey: I never understood this Wikipedia ban on primary sources. In the description of the policy they are concerned about interpretations of ego documents like diaries - which is totally not applicable here. In this case this policy leaves us with a choice of sloppy rehashes of misinformed simplifications. Much of the secondary literature in English gives a recipe for the computation, with no understanding of the why. You will find that only in the Canons and Explicatio - which happen to be in Latin. Until very recently anyone who cared about this was able to understand Latin. Occasionally I've tried providing my own English translations, but that is considered "original research" and also forbidden. Wikipedia only accepts books printed on paper written in English as source, and accepts only statements taken verbatim from such books, and requires that it must be possible for any visitor of the site to verify the text irrespective of their competence. Wikipedia forgets that an encyclopedia is a digest of knowledge made by those who know for those who do not know. Excuse the rant but these policies get in the way of making things right. Tom Peters (talk) 17:20, 1 May 2019 (UTC)

I sympathize with your preference for primary sources, but as a historian working on Wikipedia, I've come to recognize the wisdom of Wikipedia's deprecation of primary sources. Primary historical sources are not transparent statements of fact; they reflect the concerns and perspectives of the people of a particular time and context and can best be understood by those who have studied that time and context (normally published historians). I've seen enough cases where this self interpretation has gone astray to realize that Wikipedia's deprecation of primary sources is wise.

When presenting historical issues, Wikipedia, as an encyclopedia, is concerned to present the consensus of the scholarly community based on published historical accounts. You said "Wikipedia is a digest of knowledge made by those who know." Those of us who edit Wikipedia cannot claim to be "those who know"; here we are all amateurs and "those who know" are those who write the secondary sources we are citing. Hence we must cite published scholarship and cannot do original historical research by presenting our own interpretations of primary historical sources. The only way I can put my interpretations into Wikipedia is by citing an article or book I wrote, which has gone through the normal process of peer review.--SteveMcCluskey (talk) 20:46, 1 May 2019 (UTC)

Much of this secondary literature can be used to support the passage with the frequent citation needed flags from the section on Tabular Methods. I'm busy at the moment but will provide appropriate citations in a few days. --SteveMcCluskey (talk) 14:43, 1 May 2019 (UTC)

Please do. Tom Peters (talk) 17:20, 1 May 2019 (UTC)

Digressions in the introduction

I note that the already the second paragraph of the introduction of this article bogs down in digressions on unspecified (who? when? where?) and unsourced alternative practices even before the current common practice is outlined. Please move that elsewehere or remove altogether, for lack of specific sources. Also I like to mention again that "Full Moon" has nothing to do with Easter. All the original sources from Dionysius through Bede to Clavius always mention day 14 of the lunar month, which is not quite the same. I corrected this error several times but people keep putting the popular phrase back in. Tom Peters (talk) 11:59, 1 May 2019 (UTC)

I've recently provided a citation for that paragraph that troubles you. I have two points regarding your problem with the term "full moon":

• The source I cited (Mosshammer, 2008) uses the term "full moon" and defines its meaning:

"The general rule is that Easter is the first Sunday on or after the first full moon that occurs on or after the vernal equinox. Even in the twenty-first century, the date is determined not through astronomical calculations of the equinox and the phases of the moon, but on the basis of a calencrical convention for the date of the equinox and mathematical formulae for the phases of the moon, both of which derive from the third century AD."

• In computistical contexts, the term full moon means the ecclesiastical full moon, which is equivalent to Luna 14.

"Luna 14" seems an excessively pedantic use of jargon and I see no reason to employ it here. --SteveMcCluskey (talk) 16:16, 1 May 2019 (UTC)

@SteveMcCluskey this is exactly why I insist on using the canonical sources in this and other cases, and not rely on some uninformed repetition of someone elses erroneous interpretation. Using the 14th day of the lunar month is not pedantic but is what is actually and consistently mentioned in the sources and used in the computation, whereas a new or full moon is mentioned only occasionally. Day 14 of the lunar month is not the same as the day of "full moon" for 2 reasons:

1) The traditional first day of the lunar month is not the day of astronomical New Moon, which is the moment of apparent conjunction: but the evening of the first visibility of the crescent, and generally falls a day later (and this is reflected in the computation: Lilius original epact table may have been based on the astronomical New Moon, but this was later changed after patriarch Ignatius had demonstrated that the day of first crescent had traditionally been used) - in any case this means that the 14th day after the 1st day of lunar appearance, may or may not be day on which the Full Moon opposition occurs: in case of difference, the 14th day is correct, not the date of opposition.

2) All this is about *dates*, i.e. ordinal numbers, and not some precise moment in time: so the syzygy may fall on either of 2 dates, depending on the timezone you are in, and also for this reason is useless for establishing the date of the calendrical lunar month.

The emphasis on "Full Moon" and astronomical calculations lead to misguided claims that some Easter date is "wrong" because people use the wrong definition.

Tom Peters (talk) 17:00, 1 May 2019 (UTC)

Readers should be able to compare the article to other reliable sources, and not just the ones we cite, which might not be available to the reader, or might seem less reliable than one a particular reader finds. If most sources use "luna 14" or "when the age of the moon is 14", or whatever, we should use the terminology, perhaps with a discussion of how that compares to the astronomical full moon, and whether there is such a thing as an ecclesiastical full moon. Jc3s5h (talk) 17:06, 1 May 2019 (UTC)

Using canonical sources can be selective, to the extent that it ignores other sources. For example,

Bede, in his letter to Nechtan, (Hist. Eccl. 5.21): "Whoever argues, therefore, that the full Paschal moon can fall before the equinox disagrees with the teachings of the holy Scriptures in the celebration of the greatest mysteries, and agrees with those who… presume to teach that they could have attained perfect righteousness even though the true Light had never conquered the darkness of the world by dying and rising again. And so after sunrise at the equinox and after the full moon of the first month has followed in due order, that is after the close of the fourteenth day of the month…, we will wait for the Lord's day in the third week as the Gospel directs."

Pseudo-Augustine, sermo 164, in Pascha, vi: "The whole of nature, which till this moment had the semblance of death, celebrates the Resurrection together with her Lord.… Sol, the kindling of all the stars, lifts up his face and lets it shine, and, like a king in his glory, sets on his head the diadem of the stars.... Luna, who sets herself farther away from her rising each day, decks herself for Easter with her full raiment of shining light."

The point I'm making here is that if you look at other early texts, we find people expressly talking about the full moon as expressing the religious symbolism of Easter. Both Luna 14 and the Paschal Full Moon are in authentic historical sources. Faced with this duality we can't just pick the sources that fit our particular point of view. It is both wise, and in accordance with Wikipedia policy, to follow what the secondary writers, who have extensively studied a wide range of historical sources, have to say. --SteveMcCluskey (talk) 21:32, 1 May 2019 (UTC)

The bottom line is that all computations, which this article is about, mention and actually use 14th day: from Exodus 12:18, by Dionysius and the Gregorian reformers. Specifying "full moon" in the rule is confusing because it leads to astronomical computations which yield a specific moment which is at odds with setting a date as I argued above. To quote another author who did study the matter, Johannes Kepler: "Ostern ist ein Fest und kein Stern" http://www.nabkal.de/gauss.html. Tom Peters (talk) 06:37, 2 May 2019 (UTC)

You're quite right that ecclesiastical computists were usually concerned with the day on which the full moon appeared and not the exact moment of syzygy; I recall reading Grosseteste making a comment about this distinction in the thirteenth century but I don't have the quote at hand.

However, beginning around the 11th century, a series of writers began to discuss natural computus and began to compute the time of syzygys to increasingly precise fractions of a day. This tradition gave rise in the thirteenth century to a compotus philosophicus, whose writers (including Grosseteste) compared their computistical calculations to the astronomical parameters guiding the Arabic lunar calendar and to the computations of the molad (New Moon) guiding the Hebrew luni-solar calendar. These computistical calculations provided the theoretical background for the Gregorian calendar reform. For details see the detailed study of Medieval and Renaissance computistical texts by Philipp Nothaft, Scandalous Error: Calendar Reform and Calendrical Astronomy in Medieval Europe, Oxford University Press, 2018; the texts are discussed in pages 64-163. --SteveMcCluskey (talk) 14:15, 2 May 2019 (UTC)

Reducing article size

There seems to be some renewed interest in improving the article, and I think a good place to start would be to reduce the article size. The size range suggested in Wikipedia:Article size is 30 to 50 kB, and this article is around 100 kB.

As I start, I suggest deleting these sections:

• Week table: Julian and Gregorian calendars. Too confusing and complex to be useful to readers, and many more convenient ways to find the day of the week are available online or as algorithms.
• Revised Julian calendar. This does not seem to be about how to find Easter when using the Revised Julian Calendar, it seems to be how to use the above-mentioned week table with the Revised Julian Calendar.
• Dominical letter. This is already explained, in different form, in other parts of the article. No reason to have a separate section about it. Jc3s5h (talk) 00:04, 8 May 2019 (UTC)

Agree – there is much too much on various algorithms for determining Easter Sunday. Only mention the most notable. AstroLynx (talk) 08:23, 8 May 2019 (UTC)

Support Jc3s5h's plan. On the algorithms, my preference would be to move then out completely to a separate article too, with not much more that a section saying that they exist. If each has a one-liner giving its unique features, that could be repeated. --John Maynard Friedman (talk) 10:00, 8 May 2019 (UTC)

Perhaps we could make a judgement about which algorithm for Julian and which for Gregorian is the best, for a reader who plans to implement one with modern computing tools, and leave those two. If desired a separate article could be forked off to describe the more notable algorithms. The criteria for inclusion could be whether some other encyclopedia, like Britannica or a suitable encyclopedia of mathematics or religion, has an article or other coverage for a particular algorithm. Jc3s5h (talk) 15:01, 8 May 2019 (UTC)

Who are we to judge which two are 'best'? Most accurate over 10,000 years? Easiest to implement? Fastest but accurate enough for dates to say 2119? --John Maynard Friedman (talk) 15:35, 8 May 2019 (UTC)

I would suggest the algorithm come from a well-recognized source such as Edward Reingold and Nachum Dershowitz's Calendrical Calculations, which is aimed at current computer practitioners rather than historians of religion, math, or computing. I would also suggest the Julian algorithm be accurate since the First Council of Nicaea or earlier and the Gregorian algorithm be valid for 1583 or earlier. The valid date furthest in the future is more arbitrary; given research about when the Gregorian calendar will break down, I would like to see the algorithms be valid until at least 9999. Jc3s5h (talk) 17:04, 8 May 2019 (UTC)

Sounds good to me. That satisfies my wp:NOR concern. --John Maynard Friedman (talk) 14:58, 9 May 2019 (UTC)

What should be focus of this article

I inserted this subsection header after first two replies below, because it takes a slightly different take. --John Maynard Friedman (talk) 15:27, 9 May 2019 (UTC)

Comment This article has certainly grown wildly and it seems that this can be traced to its lack of focus. Originally the article was titled "Calculating the Date of Easter", but around 2003 it was renamed "Computus". Under the earlier name the focus on various modern algorithms may have been appropriate, but the new name of computus shifted the focus to the development of that practical science which, as Faith Wallis wrote in her introduction to Bede's The Reckoning of Time, (p. xxvi) has "elastic boundaries [that] include astronomy and cosmology, but also moral theology and biblical exegesis, as applied to time.… Computus, then hovers somewhere between technique and a kind of science-in-progress, tentatively combing the flotsam and jetsam of ancient tradition in search of some yet undefined identity." Other scholars have written extensively on the historical transformations of the computistical art, which seems to be an essential part of an article on a historically rooted subject like computus. If this article is to be improved, we need some sort of consensus of what its subject is and what aspects of that subject it is intended to cover. --SteveMcCluskey (talk) 16:17, 8 May 2019 (UTC)

I like to comment that I changed the title to "Computus" because I could never memorize the proper capitalization of the phrase of the original article, and Wikipedia is case-sensitive. I think a lemma should be short and not a whole phrase anyhow, and "computus" has historically been precisely the name for "calculating The date Of easter". It has not been my intention to shift focus, but as we have noticed the subject matter is vast. ceterum censeo giving any special significance to the moment or date (in which timezone??) of the Full Moon is misguided, whatever secondary sources parroting each other may say. Tom Peters (talk) 11:57, 12 May 2019 (UTC)

I envy your access to Faith Wallis's book. It's worth noting that Wallis wrote a whole book about some of the work of one important computus-related author. Obviously an encyclopedia article should be much more concise. Jc3s5h (talk) 17:08, 8 May 2019 (UTC)

IMO, an encyclopaedic article should most definitely focus on the whys and wherefores that brought about this moveable feast, as the primary article. The practical issues of doing the calculation are important but subsidiary. --John Maynard Friedman (talk) 15:27, 9 May 2019 (UTC)

@Jc3s5h: Quite right, the historical literature can be overwhelming. Nothaft cites 40 pages of modern writers; Mosshammer cites 15. How should we limit the historical section?

My suggestion is that we should briefly discuss the general principles and historical development of the principle cycles that relate the solar, lunar, and Sunday/weekly periods, these include the 84-year "Irish" cycle, the Dionysian 19-year cycle, and the Gregorian cycle. For the technically inclined, it might be worthwhile to evaluate these methods using the measures of slippage against the vernal equinox J and the true syzygies M that John North proposed in his "The Western Calendar - 'Intolerabilis, Horribilis, et Derisibilis': Four Centuries of Discontent." --SteveMcCluskey (talk) 15:31, 9 May 2019 (UTC)

I just came across a few medieval definitions of computus that help us understand the historical scope of the discipline and might even have a place in this article (my rough translations). The definitions are fragmentary, as I found them in a catalogue of opening phrases (Incipits) of medieval manuscripts.

• John of Sacrobosco, Computus: Computus est scientia considerans tempora ex solis et lune motibus… (Computus is the science that considers times from the motions of the Sun and the Moon…).
• Robert Grosseteste, Tract. de computo: Computus est scientia numerationis et divisionis temporum… (Computus is the science of the numeration and division of times…). Some manuscripts have variationis for numerationis.
• Anonymous, 12 c.: Computus est scientia rationis temporum… (Computus is the science of the reckoning of times…).
• Anonymous, 12 c., Ysagoge in computum lune: Computus est computatio temporum secundum cursum solis et lune… (Computus is the computation of times according to the motions of the Sun and the Moon…).
• Anonymous, 14 c., De computo ecclesiastico: Computus est ordinata distinctio temporum ad ecclesiasticorum… (Computus is ordained for the division of times for ecclesiastical…).

--SteveMcCluskey (talk) 20:21, 9 May 2019 (UTC)

We already have History of astronomy, Celestial mechanics#History, Julian calendar, and Gregorian calendar. The two calendar articles have extensive history sections. However, "Gregorian calendar" refers the reader to this article for the lunar aspects of that calendar, and since the Julian calendar was created well before the birth of Jesus, that article treats it as a solar calendar and seems to consider lunar months and Easter as an entirely separate matter.

Thus, I think this article should be limited to the ecclesiastical lunar calendars and the computation of the date of Easter. Astronomy and solar aspects of the Gregorian and Julian calendar should be left to the other articles, except for the drift in the date of the vernal equinox leading to Easter being celebrated in a different season if enough time passes.

I would also say that time is mostly a matter for civil authorities and astronomers, and should mostly be left to the time-related articles. The only time issues I see that might be addressed in this article are

1. When judging the drift of an ecclesiastical lunar calendar compared to the astronomical position of the moon, what time zone is most appropriate to use?
2. How does the difference between the count of real days (one solar noon to the next) and atomic days (86,400 SI seconds) affect the drift of the ecclesiastical lunar calendars?

Jc3s5h (talk) 20:53, 9 May 2019 (UTC)

@1: Neither Dionysius nor Lillius and Clavius seemed to have considered time zone complications when setting the rules, so the question is irrelevant. Of course any moment of syzygy will fall on 2 calendar dates, depending on the timezone of where you are on the globe. But the Easter computus is about establishing a date, not an astronomical event (remember Kepler's aforism?). Which is one of the reasons why I oppose the current focus on "Full Moon" instead of 14th day. All that said, I recall that the Gregorian solar calendar is effectively valid for the meridian of Königsberg in German Bavaria, because the calculations were done with the tables of Regiomontanus. I do not have time to find the source, I think it is in the proceedings of the Vatican conference of 1983. The construction (and source) of the epact tables for the Moon are ill-defined, probably a mismash of ancient and then-current sources, so not valid for any particular meridian.

@2: Of course in the 16th cy. the distinction between mean solar time and atomic time was unknown so not considered in the definition of the rules. Since we are looking for a civil calendar date, any astronomical computations (in ET so practically in TAI) should be reduced to UT (UT1 or UTC), as long as we keep inserting leap seconds. If and when the leap second is discontinued, a frozen UTC based on atomic time is our civil time and your question evaporates. I like to add that for the solar calendar it so happens that the mean length of the tropical year specifically from vernal aequinox to vernal aequinox has been fairly constant (365.2424 days) and close to the Gregorian value (365.2425) IF measured in UT. See https://www.hermetic.ch/cal_stud/cassidy/err_trop.htm , http://individual.utoronto.ca/kalendis/seasons.htm#years . The mean length of the synodic month is somewhat variable in any timescale (see New moon, Lunar month).

Tom Peters (talk) 12:29, 12 May 2019 (UTC)

I like your idea of focusing on the lunar aspects of computus, it not only avoids repetition but reflects the emphasis of most of the medieval treatments I've read. They're concerned with finding mathematical cycles to relate lunations (which govern Easter and Passover) to the commonly used solar calendar. Bede (for example) accepts the Julian calendar as a given, with his main concern with the solar year being justifying the need for the leap day, discussing its different place in the year in the Egyptian (Alexandrian) and Roman (Julian) calendars, and showing its effects on computing luni-solar cycles. We don't need to present all those details but for internal completeness we still need to briefly mention the role of the solar year / vernal equinox and the constant seven day cycle of Sundays, with links to more complete discussions elsewhere. --SteveMcCluskey (talk) 21:52, 9 May 2019 (UTC)

Orthodox computus

is it different? Or just continues with an astronomically 'incorrect' 21 March (Julian)? --John Maynard Friedman (talk) 20:42, 14 May 2019 (UTC)

From what I've read, some Orthodox churches used astronomical calculations for a while in the first half of the 20th century. Some have adopted the Gregorian calendar (or possibly the Revised Julian calendar, which agrees with Gregorian, except for the Easter calculation, until 2800). But most, today, use both the Julian calendar and the calculation written about by Dionysius Exiguus. Jc3s5h (talk) 22:33, 14 May 2019 (UTC)

A section on that, suitable cited, would be a good addition. --John Maynard Friedman (talk) 21:02, 15 May 2019 (UTC)

Meeus's Julian algorithm is the Easter used by almost all Orthodox churches. This is the same Easter used by the Church of Alexandria, Dionysius Exiguus, Bede, and all Churches from 931 to 1582 (except Oriental Churches east of the Orthodox Churches). I do not know whether they state their Julian Easter as a date in the Julian calendar, the Gregorian calendar, or both. All Orthodox countries now use the Gregorian calendar as their civil calendar, so I suspect the Orthodox churches also publish the date of their Julian Easter at least in the Gregorian calendar. No Orthodox church has ever used astronomical calculations. Such a method was proposed by a 1923 synod (see Revised Julian calendar), but was never used. An Aleppo meeting in 1997 by the World Council of Churches did propose a similar astronomical calculation for use by all churches, East and West, but it was never used. The table it published is at Easter#Table of the dates of Easter. Our article does note that German Protestant churches did use an astronomical method of calculating Easter from 1700 to 1774, also used by Sweden from 1739 to 1844, using Kepler's Rudolphine Tables and the meridian of the island of Ven where Tycho Brahe's observatory was located. — Joe Kress (talk) 06:29, 16 May 2019 (UTC)

This comment will probably betray the fact that I don't know what I'm talking about, but in that case I wonder whether the section (in the article) called "Meeus's Julian algorithm" should be renamed to 'Orthodox computus' since, to the uninformed reader, that title gives a better idea what to expect? --John Maynard Friedman (talk) 17:16, 16 May 2019 (UTC)

Meeus's Julian algorithm

I'm afraid that I find this section of the article incomprehensible. Is it trying to give the date in the Gregorian calendar of the Orthodox Easter that was computed against the Julian? If yes, then why? Surely we already have a simple calculation that renders any arbitrary date in the Julian calendar to it Gregorian equivalent? If not, then I definitely have no idea what it is about. Either way, a copyedit seems advisable, if someone has the source text? --John Maynard Friedman (talk) 21:02, 15 May 2019 (UTC)

I have the source, but this article's table is substantially different. Meeus does not solve for any intermediate results, a, b, c, d, e, etc. He does not provide the Julian calendar date of the Julian Easter in the Gregorian calendar by adding 13 days, which our article correctly states is only valid for 1900–2099. In contrast, Meeus states that the Julian Easter is April 12 in the years 179, 711, and 1243, which are 532 years apart, its periodicity. The biggest difference is the table's construction. He uses four columns, headed Divide, by, Quotient, and Remainder. He does not use mod or div. Most expressions under Divide only list the Remainder as a to e. The expression d + e + 114 divided by 31 lists both the Quotient f and Remainder g. He then states f is the "number of the month", and that g + 1 is the "day of that month upon which Easter Sunday falls". — Joe Kress (talk) 05:10, 16 May 2019 (UTC)

Sounds like you ought to correct it. But it is still impenetrable to anyone coming on it cold – it needs more text to explain what is being calculated, then why, and only then how. --John Maynard Friedman (talk) 17:16, 16 May 2019 (UTC)

Computistical Equinoxes

Lplessard (talk · contribs · count) has repeatedly deleted a section with the justification "Removed bogus sentence. All equinoxes are astronomical". This misunderstands the nature of the study of Computus, which concerns methods used to compute the date of Easter. In this discipline the most commonly used value of the equinox is the date of 21 March (in either the Julian or Gregorian calendar). In the early history of Computus the conventional Roman date of 25 March was sometimes used. Neither of these values is tied to the true astronomical value of the equinox. I will shortly restore the section, once again. --SteveMcCluskey (talk) 02:36, 4 July 2019 (UTC)

I wonder whether qualifying it as "canonical equinox" might save future confusion. But does mean creating a neologism? --John Maynard Friedman (talk) 11:56, 4 July 2019 (UTC)

The new moons and full moons that are computed by religious calendar rules are often called ecclesiastical moons. Perhaps we should call it an ecclesiastical equinox. This term is used, on at least one web page, by the US Naval Observatory.— Preceding unsigned comment added by Jc3s5h (talk • contribs) 13:04, 4 July 2019 (UTC)

Other possibilities such as calendrical equinox or paschal equinox appear to be used more often. AstroLynx (talk) 13:27, 4 July 2019 (UTC)

Nice alternatives to avoid confusion. I had only favored the phrase "calendar-dependent equinox" because it comes close to Mosshammer's description:

"Even in the twenty-first century, the date is determined not through astronomical calculations of the equinox and the phases of the moon, but on the basis of a calendrical convention for the date of the equinox and mathematical formulae for the phases of the moon, both of which derive from the third century AD."

I may just add that quotation to a citation of Mosshammer in the article. --SteveMcCluskey (talk) 21:16, 4 July 2019 (UTC)

I suggest we go with 'ecclesiastical or paschal "equinox"' in the problematic passage, complete with scare quotes to make the point. --SteveMcCluskey (talk) 21:24, 4 July 2019 (UTC)

Sounds good to me. Maybe with a footnote to explain what is meant, should anyone need it. --John Maynard Friedman (talk) 00:04, 5 July 2019 (UTC)

The earliest Julian/Alexandrian computus that is extant was used by the Church of Alexandria during the first decade of the 4th century, certainly before 311, which is the earliest of 59 consecutive tabular Easters listed along with many dates leading to them (including Passover) in a fully-developed computus. It was based on the Alexandrian calendar (began 25 BC) which had 12 × 30-day months + 5/6 epagomenal days. Its seasons were not equal due to the epagomenal days, being 90, 90, 90 (spring), and 95/96 days long (four seasons, not the three of the ancient Egyptian calendar). However, the equinoxes/solstices occurred on the 25th of months I (Thoth), IV, VII, and X, the last day of each season, not their first day on the 26th of those months. The computus explicitly states that the equinox is Phamenoth (VII) 25 (March 21). So it is a schematic equinox, not an astronomical equinox. — Joe Kress (talk) 00:57, 5 July 2019 (UTC)

That is really useful and probably merits a subsection rather than just a footnote. The only question I have is what ajective to use: I discard my 'canonical' suggestion and support the 'pascal' adjective. I could not support 'schematic'. --John Maynard Friedman (talk) 13:01, 5 July 2019 (UTC)

Thanks for the vote for Paschal equinox, but standing by itself it looks strange — particularly in the context of the first two paragraphs of the article. I'm going to do some copyediting that I think will clarify things. Feel free to revise. As to further detail, since this sentence is in the lead, such detail isn't appropriate here, although it would definitely fit into the history section.

References

When is an equinox not an equinox

Even if an equinox is found at a particular date, it does not mean that this date hss not been computed astronomically. Just read the definition of equinox to know that all equinox are astronomical. Lplessard (talk) 11:12, 5 July 2019 (UTC)

True but irrelevant. The Computus does not use the real equinox but a declared approximation of it: 21 March, irrespective of astronomical reality. The discussion above is about finding a way to express this fact. --John Maynard Friedman (talk) 13:01, 5 July 2019 (UTC)

Indeed the technical basis for the Gregorian reform was the realization that the Paschal "equinox" had become days adrift of the astronomical equinox, not the few hours either way that seems to concern you. --John Maynard Friedman (talk) 13:18, 5 July 2019 (UTC)

And to underline the point, the Orthodox Easter is calculated in the same way with respect to 21 March – but on the Julian Calendar, which means that is 12 days (13?) adrift of the astronomical equinox. What matters in the determination of religious events is not observed reality but Holy Writ. --John Maynard Friedman (talk) 18:44, 5 July 2019 (UTC)

"Conventional"

Ok, maybe this is angels on the head of a pin time, but am I alone in finding the word "conventional" is being used at the beginning of the lead in an unconventional (sic) way? It seems to me that the sense being used here ("according to a convention") is archaic. Even to use "convention" in the sense of a formal rule (rather than the informal "appropriate in polite society" sense), is itself archaic.

I accept that my (short-lived) "declared" wasn't a great improvement, which is why I reverted.

If no-one else is bothered, I'll get my coat... --John Maynard Friedman (talk) 23:03, 5 July 2019 (UTC)

I agree. "Hague Convention" is fine, and in context "convention" may clearly refer to some meeting or it's concluding agreement, but "conventional" is stretching it. Unless it actually means something like "customary", of course--Nø (talk) 09:54, 7 July 2019 (UTC)

I don't want to push this, but in American English, "conventional" has the following meaning:

According with, sanctioned by, or based on convention: conventional spelling, conventional morality. --SteveMcCluskey (talk) 18:02, 7 July 2019 (UTC)

I don't think any modifier, conventional, declared, etc. is needed. The existing modifiers "ecclesiastical" and/or "paschal" are sufficient, especially after a couple of centuries had passed when the 365.25–365.2422 = 0.0078-day error per year in both the Alexandrian and Julian calendars had built up to more than a day, requiring Phamenoth 25/March 21 to be justified using ecclesiastical or paschal arguments, like Dionysius's AD 525 claim that the Council of Nicaea dictated the rules. — Joe Kress (talk) 20:20, 7 July 2019 (UTC)

Makes sense to me. Because the date is based on an ecclesiastical or paschal "equinox" date reads well, I don't see a need for a qualifying adjective now. I shall change, feel free to WP:BRD. --John Maynard Friedman (talk) 10:01, 8 July 2019 (UTC)

Easter Sundays in the Revised Julian calendar

Is there an algorithm to compute Easter Sundays in the Revised Julian calendar? —Jencie Nasino (talk) 02:38, 19 July 2019 (UTC)

It depends on what you want. If you want an algorithm for the method accepted by the 1923 synod, for Jerusalem time, then there is none because nobody uses it. All Orthodox Churches rejected it and almost all continue to use the Julian Easter, whose algorithm is in the article at Meeus's Julian algorithm.

However, if you really want the Synod's Easter then you would need to create the algorithm yourself. It must be done astronomically, similar to the Chinese calendar. Convenient equations that are sufficiently accurate are provided by Jean Meeus in his book Astronomical Algorithms. You will need the Jerusalem time/date of the vernal equinox and the true full moon immediately after it for some year. Then apply its computistic rules (Sunday after the instant of the full moon that is after the instant of the vernal equinox). Unfortunately, it is much more complex than that outline. The astronomical Easters for 2001–2025 using a slightly different rule developed in 1997 by the World Council of Churches (WCC) can be found at Easter#Table of the dates of Easter. All astronomical Easters are identical to the Gregorian Easter except for this year's Easter (2019) which was one month earlier. No one uses this new rule either. A much older astronomical Easter was used by German and Swedish Protestant Churches during the 18th century for the meridian of Tycho Brahe's observatory on the island of Ven which produced Easters that were only one week earlier about every 20 years (see the end of Computus#History). Joe Kress (talk) 21:39, 19 July 2019 (UTC)

A much simpler method is the table lookup method, similar to the tables used by medieval computists. Both the 1923 Synod and the 1997 WCC Consultation proposed that Easter be the Sunday after the instant of the full moon that is next after the instant of the vernal equinox at Jersalem. Time at Jerusalem for the Church of the Holy Sepulchre (35°.229793E = 35°13'47"E) is 2.348643 hours earlier than Greenwich or TDT – 2^h 21^m (TDT ignores leap seconds). The full moon instant can be on the same day as the vernal equinox instant but it must be after it. The next Sunday must be after the day of the full moon instant. The instant of the full moon can be found in the Six Millennium Catalog of Phases of the Moon by Fred Espenak. A corresponding list of vernal equinoxes for 1452–2547 are at Vernal Equinox by Ivan Smith. Both are accurate to the minute, and both use the algorithms of Jean Meeus (in TDT). I do not know the rules used by 18th-century Germany and Sweden except for the tables they used. Furthermore, we have at least three non-English (German and Swedish) accounts for what they did and those accounts disagree. Three good sources for Germany and Sweden are by Robert van Gent: Anomalous Easter Sunday Dates in the 18th and early 19th Century, Anomalous Easter Sunday Dates in Sweden and Finland, and Astronomical and Gregorian Easter Sunday — Joe Kress (talk) 22:37, 20 July 2019 (UTC)

To determine the Sunday after the full moon instant, zero the time leaving the date at midnight. Use the appropriate algorithm in Julian day#Julian day number calculation to find its JDN. Calculate (JDN + 1.5) MOD 7 (per Meeus). If the result is 0, the full moon instant is on a Sunday so 7 days must be added to its date to determine Easter Sunday. Add smaller numbers 6–1 for the other days of the week 1–6, Monday to Saturday. — Joe Kress (talk) 04:45, 21 July 2019 (UTC)

Items that need doing when cleanup is approaching stability

No article is ever finished but hopefully the present cleaning frenzy will ease off soon. I've already noticed one article that needs revising, there may be more. So this is the start of a 'to do' list:

• Easter (repeats the "first Sunday after the first full moon" and cites a questionable source).

Add more as and when you notice them. --John Maynard Friedman (talk) 20:42, 14 May 2019 (UTC)

• Easter by definition occurs on a Sunday. Have all calculated dates been verified to meet that criteria? Google Sheet's Day of Week formula suggests that 2031 is wrong.— Preceding unsigned comment added by Stephenenmo (talk • contribs) 15:17, 1 January 2020 (UTC)

  The Multiyear Computer Interactive Almanac from the US Naval Observatory uses the Gregorian Calendar, and indicates 13 April 2031 is a Sunday. Jc3s5h (talk) 16:48, 1 January 2020 (UTC)

Semi-protected edit request on 21 February 2020

Within the table for calculation of Meeus's Julian algorithm, several of the Gregorian dates for Easter are incorrect. Namely, 2008 should be March 23 and not April 27, 2009 should be April 12 and not April 19, and 2016 should be March 27 and not May 1. JoshB99 (talk) 14:21, 21 February 2020 (UTC)

@JoshB99: Not done: please provide reliable sources that support the change you want to be made.

None of the dates in the Gregorian calendar in Meeus's Julian algorithm are "Gregorian dates for Easter". They are Julian dates in the Gregorian calendar. All are 13 days after their corresponding Julian dates because the difference between the two calendars is now 13 days. We must give both dates because most Eastern Orthodox Churches use the Julian calendar to calculate Easter, but must announce those dates to their congregations in the civil Gregorian calendar used by their respective countries. — Joe Kress (talk) 17:11, 21 February 2020 (UTC)

 Not done: please provide reliable sources that support the change you want to be made. Eggishorn (talk) (contrib) 18:39, 9 March 2020 (UTC)

Discussion: is the computus a PRNG with a fixed seed?

Personally I believe the computus should be classified as a pseudorandom number generator with a fixed seed, albeit a fairly biased one, or at least have a See Also link to the PRNG page. 2A02:C7F:72A6:5E00:1F9:3206:C626:66E2 (talk) 22:39, 12 April 2020 (UTC)

That is not how Wikipedia works. Personal beliefs, original research, etc. are all irrelevant. The only valid criterion for inclusion is what wp:reliable sources say. Unless and until you can produce such a source, the answer will be no. --John Maynard Friedman (talk) 11:01, 13 April 2020 (UTC)

Edit of Footnote (copied from User Talk)

Hi Steve McCluskey, after your undo of my change in Computus, the History section now shows again a literal "{efn|" and the footnote text intermingled in the main text. That was the actual issue I was trying to fix. --2001:4DD0:2192:0:6CA4:BC28:72B1:5499 (talk) 11:15, 12 September 2020 (UTC)

OK, I see what you were trying to do. I didn't catch the "{efn|" at the beginning of the text. If I were doing it, I'd delete the "{efn|" and let the comment stand in the text. It seems like it belongs there. I'll copy this to the computus talk page. --SteveMcCluskey (talk) 15:23, 12 September 2020 (UTC)

Ecclesiastical Full Moon

The lead includes the following passage after a discussion of the drift of the paschal "equinox" in the Julian Calendar. "The Catholic and Protestant denominations thus use an ecclesiastical full moon that occurs four, five or thirty-four days earlier than the eastern one." Three points:

The ecclesiastical full moon is computed for every month, so the notion of a thirty-four day discrepancy is inappropriate; it might be appropriate for a discussion of the Paschal full moon, which is the ecclesiastical full moon preceding Easter.

The drift of the full moons between the Julian and Gregorian calendar might account for a four or five day discrepancy, although there should be a discussion of the Gregorian reform of the lunar cycle, not just of the reform of the of the paschal "equinox" (better called the computistical "equinox"), a discussion which should be supported by citations.

For the moment I'll just flag it with a citation needed. --SteveMcCluskey (talk) 17:05, 10 November 2019 (UTC)

The article says: "Easter is traditionally celebrated on the first Sunday after the Paschal full moon, which is the first full moon on or after 21 March." This is false, though. The Paschal full moon is a cyclical value, while the full moon is an astronomical value and not cyclical. Ulrich Voigt (talk) 23:52, 28 December 2020 (UTC)

Mistake in the Nature version of the Anonymous Gregorian algorithm

It says

h = (19a + b − d − g + 15) mod 30 = 7 for year 2021

That is not correct, it is

h = 19 * 7 = 133 + 20 = 153 - 5 = 148 -7 = 141 + 15 = 156 MOD 30 = 6

Hence your final date will be the wrong date of 28 March. — Preceding unsigned comment added by 181.228.126.117 (talk • contribs) 23:22, 17 February 2021 UTC (UTC)

The article is correct. If you read the original Nature article, available on Google Books and cited in the article, you will see each step gives a quotient and a remainder, meaning that integer division is being done. Usually when someone comes to the talk page and complains that one of these algorithms is wrong, it's because they did a floating calculation. As an example, for Y = 1961, b must be 19, not 19.61. Jc3s5h (talk) 23:49, 17 February 2021 (UTC)

The error is in the 1961 "New Scientist" table. The table states that h = (19a + b − d − g + 15) mod 30 = 7 for year 2021 and it is NOT. It is 6. The table is wrong. I don't know if the error is in the New Scientist article or in the Wikipedia article.

The table states that for Y=2021: a=7 b=20 c=21 d=5 e=0 g=7

If these numbers are correct, then h = (19a + b − d − g + 15) mod 30 = 6, not 7 as stated in the table.

Step-by-step:

19*7 = 133 133+20 = 153 153-5 = 148 148-7 = 141 141+15 = 156 156 MOD 30 = 6

If you proceed with calculation of i, k, l and m using h = 6 you get wrong Easter date for 2021 as March, 28 instead of April, 4 which is the correct answer.

Nothing to do with floating calculations. — Preceding unsigned comment added by 181.228.126.117 (talk) 00:31, 18 February 2021 (UTC)

I see that there is indeed an error in the New Scientist calculation. I'll try to find which editor added that and notify him or her. Jc3s5h (talk) 01:59, 18 February 2021 (UTC)

Update: I looked up the original reference in New Scientist 30 March 1961, Page 829 and tracked down the error to the definition of g parameter. The error was that "c" parameter was used instead of fixed value 13 called for in the original table. Also, values for 1961 were NOT computed but entered as fixed values in the Wikipedia table. They were also wrong. I also fixed these values to correct ones. Values for 2021 are computed in the webpage and I also corrected the wrong formula for parameter g.

You can compare uncorrected Wikipedia table to the original New Scientist table in this picture: http://s000.tinyupload.com/?file_id=03708057782729020070

The Excel spreadsheet I used for calculations can be downloaded here: http://s000.tinyupload.com/?file_id=26488126244114132322 — Preceding unsigned comment added by 181.228.126.117 (talk) 05:06, 18 February 2021 (UTC)

The error might have propagated to parameters beyond "g" parameter in the calculation formulas used for 2021. Albeit numbers are correct now they might be wrong from 2022 onwards if formulas are not corrected before next year. I'll try my best to correct the formulas asap if original author can't be located. — Preceding unsigned comment added by 181.228.126.117 (talk) 05:16, 18 February 2021 (UTC)

Nice work. The original editor was Jayarathina who I have notified. Jc3s5h (talk) 15:21, 18 February 2021 (UTC)

Actually, I think it was my mistake. I've fixed the expr tags for the New Scientist version to properly compute the date so it should work properly for all years. Plkstn (talk) 07:25, 19 February 2021 (UTC)

Thinking about it, I suppose we could let it compute future dates as far in the future as we want, until the limits of the appropriate computing language are reached. But dates earlier than 1583 don't make much sense, and dates earlier than about AD 30 make no sense at all. Jc3s5h (talk) 17:34, 19 February 2021 (UTC)

Stopping people putting in negative dates (i.e., BC/BCE) is a bit right all wrongs but someone could seriously make a fool of themselves if they relied upon it when writing about, for example, 1492. Someone doing a history of the Pilgrims (Plymouth Colony) and inputting 1621 would get confused because they were still using the Julian calendar. But surely a footnote is enough? Wikipedia is not a reliable source. --John Maynard Friedman (talk) 19:34, 19 February 2021 (UTC)

Pope never source for date

This sentence "In late antiquity, it was feasible for the entire Christian church to receive the date of Easter each year through an annual announcement from the Pope" is nonsense (and shows no reference, of course). Popes never announced date of Easter for the whole of Christianity in late antiquity, as he had no authority of that kind. There were Quartodecimanists who celebrated of 14th of Nissan following Jewish calendar, and there were others who stuck to a Sunday. WIthout digging too deep, the decision came at the First Council of Nicea and set out the rule: First Sunday after Full Moon after spring equinox. Kipala (talk) 11:29, 30 March 2021 (UTC)

Please read page xx of the cited source. It states

But a cycle had at least two additional advantages: it diminished the possibility of recurrent con£icts over the correct date, and it meant that clergy everywhere could be assured that they were celebrating Easter in unity with their co-religionists without being dependent upon annual announcements from some distant authority. Such a system of annual announcementsfrom the Pope in Rome had functioned in late antiquity, but to an ever increasing extent, deteriorating communications made local responsibility for the calendar a necessity.

The book is published by Liverpool University Press. The author, Faith Wallis, is a history professor at McGill University. This certainly looks like a reliable source to me. Jc3s5h (talk) 12:18, 30 March 2021 (UTC)

WP:COMMONNAME

How does this article title comply with WP:COMMONNAME? Why is it not Date of Easter which is the obvious article name? DeCausa (talk) 15:25, 5 April 2021 (UTC)

I've often wondered that myself and I know of individuals who had told me of not being able to find a Wikipedia article about the date of Easter.

Mayhap a renaming proposal should be initiated. Vincent J. Lipsio (talk) 15:31, 5 April 2021 (UTC)

I don’t think it would be controversial to move it (but you never can tell on WP!) I think I’ll just leave this thread open for a few days and if no one disagrees, move it then. DeCausa (talk) 15:53, 5 April 2021 (UTC)

On second thoughts, in the archive someone was vociferously objecting to a name change 9 years ago. So I’ve begun a requested move (below) to be on the safe side. DeCausa (talk) 16:30, 5 April 2021 (UTC)

Requested move 5 April 2021

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: There's consensus to move. Most editors argue that "date of Easter" is a more recognizable name for this topic. A split can be discussed later to see if it has consensus. (non-admin closure) (t · c) buidhe 18:21, 12 April 2021 (UTC)

---

Computus → Date of Easter – The current title fails WP:CRITERIA on Naturalness and Recognizability. Clearly, the WP:COMMONNAME, while maintaining WP:CONCISE, is “Date of Easter”. DeCausa (talk) 16:27, 5 April 2021 (UTC)

• Strong Support: The present name has always struck me as, at best, unintuitive and arcane; unsurprisingly, I know of individuals who had told me of not being able to find a Wikipedia article about the date of Easter. Vincent J. Lipsio (talk) 16:40, 5 April 2021 (UTC)
• Support. In case of strong opposition, there should be two articles - one on actual dates of Easter in various churches (and judaism), and another on whatever it is so important to have under the title "Computus".--Nø (talk) 16:43, 5 April 2021 (UTC)
• Strong oppose. This article is about the calculation of the date of Easter, not just the date itself. For the best part of a thousand years, this was a serious astronomical and mathematical problem and the cause of serious doctrinal disputes (such as the one that meant, for example, that it took the British Empire nearly another 200 years to adopt the Gregorian calendar). However I appreciate the intent of the proposal, which is a valid one: the problem is just that the wrong solution is being proposed. Therefore I agree with Nø's solution: create a new article called "Date of Easter" which will satisfy the requirements of casual visitors who don't want or need to see the long answer. This new article would

1. give the simple version of the algorithm ("Easter-day, on which the rest depend, is always the first Sunday after the Full Moon which happens upon or next after the 21'st Day of March; and if the Full Moon happens upon a Sunday, Easter-day is [always the first Sunday after the second Saturday in April]." (Book of Common Prayer, 1752)), and refer readers to the Computus article for the exceptions.
2. give a table of the dates of Easter Sunday for the next 20 years (and may the last 20?).

An article about the Date of Passover is something completely different and needs its own article. --John Maynard Friedman (talk) 18:38, 5 April 2021 (UTC)

Point 2 already exists: List of dates for Easter. That’s not the issue. The issue isn’t the scope or content of this article. It’s that the article title doesn’t comply with WP policy. If, as you say, the article is “about the calculation of the date of Easter’ then, per WP:CONCISE the title “Date of Easter” is entirely adequate, and leads to no confusion. DeCausa (talk) 18:46, 5 April 2021 (UTC)

"Computus" (one word) is rather more concise than "Date of Easter" (three words). The word "Computus" with the specific meaning "computation of the date of Easter" has a history going back to the eighth century and that is its wp:common name in any material that goes into any significant detail on the subject. WP:CRITERIA says "Article titles are based on how reliable English-language sources refer to the article's subject" – the proposal fails on the very basis it gives for proposing the change, because its subject is the mechanism of computing the date, not the date itself.

The reason you give for wanting this change can fully be met by changing the redirect target of Date of Easter from this article to List of dates for Easter. Your anecdote confirms the average visitor just wants to know what date is Easter this year and next, they don't want complex theological/mathematical/astronomical analysis. Indeed your anecdote supports this supposition: assuming your acquaintance entered "Date of Easter", they were redirected to this article and it failed to answer their question – because that is not its purpose. --John Maynard Friedman (talk) 23:06, 5 April 2021 (UTC)

It wasn’t my acquaintance - another editor made that point. But I only found this article (I was looking for how the date was calculated) by searching for “Date of Easter”. So I would strongly oppose changing the redirect. I think if you took that away this article would be virtually unread. The current title is , for the vast majority of readers, arcane and unrecognisable and for that reason is very definitely contrary to Wikipedia policy. I don’t see any possibility that a reader will be misled by what “Date of Easter” means. The List of dates for Easter should clearly be a split from this article, and visibly so, in keeping with WP:SUMMARYSTYLE. But we’ll see what others think. DeCausa (talk) 08:00, 6 April 2021 (UTC)

Yes, that makes sense. So another way to deliver the intent of the request is to add a hatnote along the lines of This article is about the method by which the date of Easter is calculated. For the dates of upcoming and recent Easters, see List of dates for Easter. But early days, none of the real experts on this subject have contributed to this discussion yet, let's wait for more voices. --John Maynard Friedman (talk) 10:21, 6 April 2021 (UTC)

Well, it’s not another way. The article title still should change because it fails Recognizability and Naturalness. The hat note would always be useful though. DeCausa (talk) 10:34, 6 April 2021 (UTC)

An Internet search for "Computus definition" commenced with these 3 results:

Lexico prefixes the definitions with "historical" and gives 2 definitions, the first irrelevant to what this article is concerned with and the second, while not mentioning "Easter", states "A set of tables used in medieval times for calculating astronomical phenomena and the movable dates of the calendar; a calendar."

The Merriam Webster Dictionary also has two definitions, the first similar to Lexico's second definition (but also not mentioning "Easter") and the second irrelevant to what this article is concerned with.

Wiktionary does, however, give as its first definition "The calculation of the date of Easter in the Christian calendar" but methinks that to be derived from its usage here on Wikipedia. Vincent J. Lipsio (talk) 22:53, 6 April 2021 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Non-verbose algorithm?

Surely there is a step-by-step algorithm for computing the Gregorian date of Easter that could be explained in a non-verbose manner. That would be a useful addition to this article.2601:200:C000:1A0:7810:5C16:30F4:BB8B (talk) 19:57, 17 January 2021 (UTC)

Like this? http://almanac.oremus.org/easter/computus/ I won't add any link from here because it's a page I maintain so I'm not neutral enough to judge the value! Simon Kershaw (talk) 13:38, 22 April 2021 (UTC)

Template:Dates for Easter‎

I still believe I was correct to move the Dates for Easter template to the top of the article, where it is readily accessible to visitors who just want to know the date of Easter (given that is now the title of this article). But for visitors on mobiles, it takes a lot of space before any text arrives. At Template talk:Dates for Easter‎, I invite comments on producing a shorter version. --John Maynard Friedman (talk) 11:45, 10 May 2021 (UTC)

On second thoughts, I wasn't right to have moved it, I should have removed it completely since the opening hat note points to list of dates for Easter. I have done so now. Maybe there is a case for a very small infobox giving this year, last year and next year? --John Maynard Friedman (talk) 18:54, 10 May 2021 (UTC)

Comments invited at talk:Islamic calendar

Would regular editors of this article care to add a comment to talk:Islamic calendar#Delete whole section "Converting Hijri to Gregorian date or vice versa", please? --John Maynard Friedman (talk) 12:03, 31 October 2021 (UTC)

Gauss' 1807 correction

I'll put this here since I just did the math and don't have a source (and it's too nerdy for even an endnote):

The two conditions (11M + 11) mod 30 < 19 and a > 10 are equivalent only when d has the value 28. The first condition is either true or false for 1-3 centuries at a time while the second looks like it could vary between one Metonic cycle and the next -- but it works out that for a given set of solar and lunar corrections, any Paschal full moon on April 18 (d=28) will be on year 11 of the cycle or later (and will need to be corrected to April 17 (d=27)) if and only if the first condition is true. Note that it's not given that there will be such years for a given value of M -- but if there are, every 19-year cycle in such centuries will have one.

Also Gauss only corrects the dates when e=6 -- subtracting one from the value of d at an earlier stage would be more in line with keeping the Paschal full moons on different dates (and with the epact table), even if the end result is the same. The system is not designed to keep the date of Easter from repeating within a cycle; on the contrary, because the Dominical letter often repeats after 11 years (3 of 4 cases when not crossing centuries) then after moving one Easter from April 26 (d=29, e=6) to April 19 you may get a "natural" April 19 after 11 years (d=28, e=0), as happened in 1981/1992. Lhmathies (talk) 17:27, 13 December 2021 (UTC)

Tables of dates

Some of the lists available on the internet are this one from the US Census Bureau, this one from the Astronomical Society of South Australia and this one from T Larsen The first one looks like a reliable source even if the others are less so. They all give the date of Easter 1750 as 29 March. As this one from Petko Yotov's website shows, that is the date of the Catholic/Western Easter in the Gregorian calendar. As this 18th-century Book of Common Prayer shows, Easter in that year was actually celebrated on 15 April (Julian calendar) in England (and associated places - I do not want to get into a discussion here about Scotland, Wales, Ireland and the colonies). I note that 29 March in places which observed the Gregorian calendar was the same day as 18 March in places which observed the Julian calendar. As that date is too early for Easter, the Julian Easter fell a lunar month later on 15 April Julian, which was also 26 April Gregorian. Would it be worth noting this somewhere in the article? Alekksandr (talk) 21:06, 20 March 2022 (UTC)

Epact in Julian calendar

I don't understand the epact in the Julian calendar. According to what our article says (and the Swedish table with runes), the epact for golden number equal to 1 must be 8, which gives Paschal full moon on April 5. But then how did the Gregorian get to epact=29 when goldenn number=1? It decreased by 1 in 1700 and 1900, so it was 31, that is 1, at the time of the reform. It should have been 10 less than what it was before the reform, so that should have been 11, not 8. This is confirmed by the tables "Tabula æquationis cycli epactarum perpetui" and "Tabella cycli epactarum perpetua" in Canon 2 of Clavius. The table also seems to say that the initial epact was increased in AD 320, 800, 1100, and 1400. The initial epact was 8 back before AD 800. So what's goin' on? Are the Eastern Orthodox still using the value from before AD 800, in spite of what the table of Clavius says? Did the Roman Catholics do lunar corrections in AD 800, 1100, and 1400 which the Easterners didn't do? Eric Kvaalen (talk) 11:25, 12 May 2022 (UTC)

It's a long article. Please rewrite your questions so that every time you mention what our article says, someone reading your question can easily find the exact spot in the article that you are referring to. Jc3s5h (talk) 13:42, 12 May 2022 (UTC)

@Jc3s5h: The fact that the epact for golden number equal to 1 must be 8 is based on the fact that the ecclesiastical full moon is given as 5 April in the table introduced by the sentence "This is the table of paschal full moon dates for all Julian years since 931". If the full moon is on April 5, then the new moon, 13 days earlier, is on March 23, which, as shown in the table higher up, corresponds to epact viii (8). That's the only place where I referred to what our article says. Eric Kvaalen (talk) 08:16, 22 May 2022 (UTC)

@AstroLynx and Jc3s5h: According to this 1980 article (p. 157), "By the 16th century, the actual equinox was falling on the 11th March (10 days before the assumed equinox) and to return the equinox to the 21st March, 10 days were dropped from the calendar. Also the actual full moons were falling four days after the calculated full moons and a similar adjustment was made in the Lunar Calendar to correct this error." So apparently in the Gregorian reform they decreased the epact by 7 (from 8 to 1 for golden number 1, or from 4 to 27 for 1583) rather than by 10. — Preceding unsigned comment added by Eric Kvaalen (talk • contribs) 16:49, 22 May 2022 (UTC)

my english is poor ...

But in my opinion the literal meaning of

In 1807 ... stated that 26 April is always replaced with 19 and 25 April by 18 April in the circumstances stated.

is that there were TWO errors in the original formulation (that in p and the miss of this statement). Perhaps he simplified a previous statement.

Is it known the reason for the restriction to those two centuries? It seems a partial fix of the error in p.

The info in these few lines is not time-ordered. If you give me safe info on the above two points, I will propose here a time-ordered form. pietro 151.29.59.56 (talk) 08:39, 3 July 2022 (UTC)

thanks

I do not know who has removed the vandalism that prevented my italian translation of the gauss method. In any case, thanks. pietro. 151.29.59.56 (talk) 22:37, 14 July 2022 (UTC)

I propose to delete the details section

This section has been tagged as needing more sources for nearly two years. I don't know if it was ever correct, but the absence of sources makes it impossible for editors patrolling this page for vandalism or incompetence to quickly assess if a new edit is correct or not.

The following error discredits the whole section and warrants its removal:

So the Gregorian Easter dates repeat in exactly the same order only after 5,700,000 years, 70,499,183 lunations, or 2,081,882,250 days; the mean lunation length is then 29.53058690 days.

But Richards (2013, full citation in article) page 599 states:

The entire calendar involves a cycle 5700000 years containing 2081882250 days, which are equated to 70499175 lunations.

So the unknown editor Tom Peters who added these numbers in 2003 disagrees with the reliable source about the number of lunations in a cycle.

In addition to being wrong, the whole section is rambling and has no clear point.

It appears Richards should have put "of" between "cycle" and "5700000" but that's how it is in the book. Jc3s5h (talk) 16:03, 17 June 2022 (UTC) with the editor who made the original edit added 18 June 2022 21:44 UTC.

The numbers cited in this section are found in NAAE1931 (p. 744) and ESAA1992 (p. 582) and are also found in the various editions of Calendrical Calculations (CC1, p. 54; CC2, p. 122; CC3, p. 117; CC4, p. 148).

They could all be copying these numbers from each other but it is also possible that Richards made an error here. AstroLynx (talk) 10:38, 19 June 2022 (UTC)

The earliest reference to these numbers appears to be a 1837 treatise on the Gregorian Easter reckoning by Magnus Georg Paucker. AstroLynx (talk) 10:52, 19 June 2022 (UTC)

My name was mentioned so I need to jump in. I was one of the first authors of this page who put a lot of time into this.

First, about the number of 70499175 lunations in the 5.7 Myr Gregorian cycle as mentioned in the 3rd edition (from 2013 - after I wrote this page) of the Explanatory Supplement to the Nautical Almanac p.599 . It was 70499183 in all earlier sources mentioned here; the change is not explained. I speculate that it is the truncated value obtained by dividing the 2081882250 days in 5.7M Gregorian years, by 29,53059 which is a rounded value for the current mean length of the synodic month: so it would NOT be the actual number of lunations counted in the Gregorian calendar, which is what the section on this page is about. In any case the last two editions (1992, 2013) of the Expl.Suppl. are very poorly edited and are full of errors, often in the numbers, sometimes very serious: the list of errata is long (https://uscibooks.aip.org/explanatory-supplement-to-the-astronomical-almanac-3rd-edition-list-of-errata/). So much for relying on authorative sources in print. The computation of the number of lunations in the Gregorian calendar is explained on this Wiki page, so rely on your brain instead.

User:Jc3s5h questions the relevance of these details. But people have been excommunicated over the details of the computus. Easter dates jump around all over the solar calendar, and it is of general interest to do stats on the dates and explain why this happens. The old Julian computus had a cycle of only 532 years; the Gregorian cycle is much longer and needs explanation. The Gregorian lunar calendar is a complex beast not generally well understood. Misguided statements picked up from secondary literature pop up all the time. The information on this page is not readily obtained elsewhere - hidden in Latin or otherwise obscure sources. I think an encyclopedia must be a compendium of the best available sources. That it is complex or not relevant to every user is a poor argument. I have a PhD in science, but many of the mathematics pages in Wikipedia are beyond me - but I do not go around deleting them because I don't understand them or find them not useful.

That said, elaborating on the exact number of lunations in the 5.7Myr Gregorian cycle: the overall computation assumes that the net epact changes make a correction of a neat lunation of 30 days that can be subtracted from the total. They do not. In 2003 I wrote a program to follow the Gregorian rules exactly, and evaluated them over the 5.7 million year period. The epact changes sometimes cause lunations of 1, 59, or 58 days, which screws up the statistics. Lunations of 28 and 31 days also occur, those of 31 days frequently by including a leap day. The epact 19 with Golden Number 19, which happened to appear in the first Golden Number table after the Gregorian reform, causes a lunation of 59 days in dec./jan.; this happens 10000 times over the 5.7Myr cycle. The calendar reformers cared enough to fix this with an exception rule, even though it has no influence on the date of Easter. This is explained on this Wiki page. It is in the canon and if they cared enough, we should care to put it in Wikipedia.

With that exception rule, I counted 70500000 lunations. The number of 70499183 I can obtain when other exception rules are implemented, so that any remaining 1-day lunations are absorbed into a preceding or following lunation; and the remaining 58- and 59-day lunations are somehow split into two lunations. So as far as I can tell, with the documented canonical rules, the Gregorian lunar calendar counts 70500000 lunations and not 70499183, and the mean lunation length would be 29.53024468 days - much too short. But the books say 70499183 lunations. Saying otherwise would be "original research" - I get that accusation a lot.

Tom Peters (talk) 17:30, 11 August 2022 (UTC)

I am very much opposed to deleting that section, which I found very interesting. And it's obvious that we have the correct number of lunations in 5,700,000 years -- if there were no solar and lunar corrections, it would bee 5,700,000/19*235, which is 70,500,000, but every 10,000 years there are corrections amounting to 43 unit changes of epact (as explained in our article), or 43 lunations every 300,000 years. There are 19 such periods in 5,700,000 years, so the number of lunation in total is 70,500,000 minus 43*19, in other words 70,499,183! Eric Kvaalen (talk) 20:08, 20 June 2022 (UTC)

Astrolynx has cast considerable doubt on the number of lunations from Richards 2013. Eric Kvaalen has provided an explanation to support the number of lunations, although I am not able to follow it in detail. It turns out calendar days per lunation rounds to 29.53059 no matter which is correct, so no value change is needed in the article. But I have changed the citation to Richards 2013 just before the phrase "This corresponds to an error of less than a day" to a citation to Dershowitz and Reingold 2008.

I also checked Richards 1998 and it does not address this issue.

I still feel the details section is a mess and we should get rid of it. Jc3s5h (talk) 20:44, 20 June 2022 (UTC)

How can I say this? If you don't like reading about the details, then find something else to do! :) Really, don't get rid of things that other people appreciate. I do agree that there are a couple things that need fixing, which is what I tried to do last week. ````— Preceding unsigned comment added by Eric Kvaalen (talk • contribs) 11:59, 21 June 2022 (UTC)

I refer you to Wikipedia:What Wikipedia is not, especially the section Wikipedia is not an indiscriminate collection of information. What are the things about the date of Easter that might be worthy of putting in an encyclopedia?

• The significance of Easter to Christians and why they care about the date it's celebrated
• Rules Christians considered important for acceptable Easter dates
• Various methods of calculation in various areas and sects
• How this calculation was one of the main calculations done in Europe for a number of centuries
• How developments in mathematics and the import of mathematical ideas from Arabia and India affected the calculation

But how is the distribution of Easter dates relevant? Where is the evidence that how frequently Easter occurs on certain dates is important to Christians, or anyone else affected by Easter (such as candy makers)? Jc3s5h (talk) 13:37, 21 June 2022 (UTC)

I installed a version of Lisp on my computer and loaded the calendar package from Calendrical Calculations Ultimate edition (that is, 4th edition). So far I have compared 1 January 1600 with 1 January 5,701,600 and found, as expected, that January 1 falls on a Friday for both years, and Easter falls on 2 April for both years. I also confirmed that when I compute the Rata Die for 1 January 5,701,600 and subtract the Rata Die for 1 January 1600 I obtain 2,081,882,250 which is what the sources indicate it should be. I have not yet computed the number of lunations. Jc3s5h (talk) 13:20, 23 June 2022 (UTC)

If you go to the Book of Common Prayer, there is a helpful table which allows you to compute the Sunday Letter for any year. You add one quarter (omitting fractions) and the number at the top of the column (in this case 2), divide by 7 and note the remainder. The Sunday Letter is then found against that remainder. In the case of 1600, the calculation is 1600 + 400 + 2 = 2002. 2002/7 = 286 remainder 0. Sunday Letter is A. But that's not the whole story. Although irrelevant to the calculation of Easter, in January and February of a leap year (such as 1600) the Sunday Letter is one up in the series, i.e. B. So 2 January (against which B is marked) was Sunday and 1 January was Saturday, not Friday. For Easter, A is marked against 2 April, confirming your date. 82.46.116.18 (talk) 10:37, 10 August 2022 (UTC)

Duh, the average Gregorian year is 365 days + (100-3) leap days in 400 years, so 365.2425 days per year; times 5,700,000 years is 2,081,882,250 days. You don't need a Lisp program to compute the silly Reingold.Dershowitz day numbers, a scientific calculator would do. Tom Peters (talk) 17:40, 11 August 2022 (UTC)

Frequencies of the dates of Easter

@AstroLynx and John Maynard Friedman: AstroLynx, you ask why I think the original graph was wrong, giving the frequencies of the dates of Easter. Very simple -- the reason that April 19 is more commonn than most of the others is that April 17 is twice as common as other dates as the date of the ecclesiastical full moon, because that's the date if the epact is either 25 or 26, whereas for other dates there's only one epact which gives that date. Now, Easter will fall on April 19 when the ecclesiastical full moon is on April 12, 13, 14, 15, 16, 17, or 18. Since the 17th is twice as common (in the long run), it's as though April 19 gets eight "votes", whereas a date such as April 16 gets only seven (April 9, 10, 11, 12, 13, 14, and 15). But the same thing goes for April 18! Easter is on the 18th when the ecclesiastical full moon is on April 11, 12, 13, 14, 15, 16, or 17. Again, since the 17th is twice as common as others, April 18 gets eight "votes" rather than seven. So both April 18 and April 19 are about eight sevenths as common as the dates from March 28 to April 17. The reason the ratio is not exactly 8/7 is that the date of Easter depends both on the epact of the year in question and on its dominical letter (actually the dominical letter for the latter part of the year, after February), and the seven dominical letters are not all equally common. In a 400-year cycle, two of them occur 56 times, two occur 57 times, and three occur 58 times. Easter falls on April 18 only when the dominical letter is C, which occurs 14% of the time (56/400), whereas it falls on April 19 only when the dominical letter is D, which occurs 14.5% of the time. So April 19 is slightly more common than April 18. (I actually made a mistake in my spreadsheet and had the dominical letters shifted by one, so my graph was off, but I have now corrected it.) Eric Kvaalen (talk) 08:16, 22 May 2022 (UTC)

This is all nice and well but the original graph is already properly sourced by two references. Several more could be added but I do not think that this will be necessary. AstroLynx (talk) 08:29, 22 May 2022 (UTC)

@AstroLynx: Are you referring to the 1944 article in Popular Astronomy and the 1980 article in The Irish Astronomical Journal? I can't access them. Can you? Eric Kvaalen (talk) 13:24, 22 May 2022 (UTC)

When I browse to the links provided by Eric Kvaalen at 13:24 UTC I see, on the right side of the window, a box that says "FULL TEXT SOURCES" with two icons, which offer two presentations of the scanned images of the articles. Jc3s5h (talk) 13:41, 22 May 2022 (UTC)

@AstroLynx and Jc3s5h: All right, thanks. I understand now, based on the 1980 article. There's a complication that we don't have in our Wikipedia article. In fact, the ecclesiastical full moon falls on April 17 only 27/19 as often as on most of the other dates, and on April 18 it falls 30/19 times as often as on those other dates. So for Easter, April 18 gets only 7 and 8/19 "votes", April 19 gets 8, and April 25 gets 30/19. That gives the distribution shown in the graph presently in the article. Eric Kvaalen (talk) 16:49, 22 May 2022 (UTC)

@AstroLynx and Jc3s5h: I want to redo the edit I did a couple weeks ago, but more correctly. I'll say here what I want to do so that it won't get reverted:

I want to add the complication (which I mentioned above) that is missing from our article, having to do with when the epact is 25.

I want to shorten the paragraph which I myself added earlier about the accuracy. I hadn't noticed that the accuracy is discussed further down, and in a more precise way.

I want to put in my graph of the distribution of the date of Easter during the period 1900 to 2199, because it's much different from the long-range distribution. People may get the impression that April 19 is more common than other dates NOW, which is not true. (One could also make a graph for the long-term distribution if we were to stay with the present series of apacts, but in fact we will stop using the present series in 2200.)

I want to add the following (corrected) explanation of the long-term distribution:

However, the distribution is quite different over the long term. The date of Easter in a given year depends only on the epact for the year, its golden numer, and its dominical letter, which tells us which days are Sundays (more precisely, the dominical letter for the part of the year after February, which is different in leap years form the letter for January and February). (The golden number only matters when the epact is 25, as explained earlier.) If we go forward 3,230,000 years from a particular year, we find a year at the same point in the 400-year Gregorian cycle and with the same golden number, but with the epact augmented by 1. Therefore, in the long term, all thirty epacts are equally likely. On the other hand, the dominical leters do not all have the same frequency  – years with the letters A and C (at the end of the year) occur 14% of the time each, E and F occur 14.25% of the time, and B, D, and G occur 14.5% of the time. Taking into consideration the complication having to do with epact 25, this gives the distribution shown in the second graph. April 19 is the most common because when the epact is 25 the ecclesiastical full moon falls on April 17 or 18 (depending on the golden number), and it also falls on these dates when the epact is 26 or 24, respectively. There are seven days on which the full moon can fall, including April 17 and April 18, in order for Easter to be on April 19. As a consequence, 19 April is the date on which Easter falls most frequently in the Gregorian calendar, with a frequency of 29/750 (about 3.867% of the years). April 18 is the second most common, because of the extra times that the full moon is on the 17th. 22 March is the least frequent, with a frequency of 29/6000 (0.467%).

I will use the 1980 article as reference.

Eric Kvaalen (talk) 11:40, 31 May 2022 (UTC)

@AstroLynx: You reverted my edit with the comment "reverted (original reseach - we only describe the current situation, unsourced suggestions for improvements do not belong here". I did not make suggestions for improvement! I did what I wrote above, and gave you two weeks to react. Why did you revert my whole edit? That's not correct behavior. Eric Kvaalen (talk) 15:24, 17 June 2022 (UTC)

I don't know what AstroLynx would say, but I have issues with several parts of the edit.

• Describing the distribution for the complete 5,700,000 cycle as "ill-defined" is wrong. The rules are well known.
• "the present system of calculating the date of Easter will not be accurate over many thousands of years" is true, but involves advanced topics such as the increasing length of the day and advanced orbit calculations. Such a statement should not be given without a reliable source. The article contains the statement "This corresponds to an error of less than a day in the phase of the moon over 10,000 years, but in fact the length of a day is changing (as is the length of a synodic month), so the system is not accurate over such periods." This statement should have a citation and I have added a citation needed template. I need to check if the other numbers in that paragraph have appropriate supporting citations.
• "It would be possible to get a similar level of accuracy with a much shorter period.<ref>For example, a period of 18,000 years would be possible by resetting the golden number to 1 when the year is divisible by 18,000." There are far to many cranks constantly trying to get the calendars they invented into Wikipedia. The no original research policy should be enforced with the highest degree of strictness and vigor when it comes to editor suggestions for calendar improvements. Jc3s5h (talk) 15:38, 17 June 2022 (UTC)

On the first point, what I mean is that the frequency distribution depends on which mapping from golden number to epact is in force. Each such mapping last for between 100 and 300 years. So the frequency distribution is "constantly" changing. The only way to get a true frequency distribution, as I wrote in the next paragraph, is by looking at the whole 5.7-million-year cycle. But that of course is ridiculous beccause the system will certainly not be used for anything like that much time! So even though the mathematical problem is well defined, the actual frequency distribution is not well defined.

On the second point, it's well known that the system is not accurate for many thousands of years -- as you admit yourself. It's easy to find a reference in one of our other articles. What I don't like is when people revert an edit because of statements they know are true, just because there is not a reference, instead of improving the article by finding a reference. I remember a guy once who wouldn't let me write a formula in a less ambiguous way, just because I didn't have an explicit reference! I think he knew that I was right.

On the third point, I didn't mean to "get a calendar I invented into Wikipedia". I was just motivating the next sentence, by saying (or implying) that it's not because the cycle is so long (millions of years) that it's not accurate in the long term -- we could use a much shorter cycle like 18,000 years but it would still be too long to be accurate. I put that example of an 18,000-year cycle in a footnote just so people can check whether the statement is true that there are shorter cycles with similar accuracy to that of the system we use. It's easy to check that it gives a month length very close to the present true value (from "Year 0" to AD 18000 there are 6574365 days and 222629 lunations, giving an average length of 29.53058676 days).

When I wrote what I wrote here yesterday I thought AstroLynx had reverted the edit I had described on this Talk page, but in fact he just reverted the subsequent edit I made in which I clarified some things and corrected a couple sentences. I hate it when people revert a whole edit just because of one little thing they don't like. And then they often start arguing about other things and we get bogged down in arguing instead of improving the article!

Eric Kvaalen (talk) 06:19, 18 June 2022 (UTC)

@User:Jc3s5h: For crying out loud, this is getting silly. You demand a reference for the statement "This corresponds to an error of less than a day ... over 10,000 years". Immediately before it is said that the value is accurate to 5 decimal places (which can be verified by comparing it to the length of the synodic month already mentioned with reference under "Theory"), so 0.00001 days. So it is trivial arithmetic that the error is 1 day after 1/0,00001 = 100,000 lunations, or of the order of 10,000 years. Tom Peters (talk) 20:11, 11 August 2022 (UTC)

The amount of error is not the point. The point is that the edit in question seemed to be proposing a specific reform to improve the Gregorian calendar. Improvement proposals from Wikipedia editors should not appear in Wikipedia articles. Jc3s5h (talk) 20:22, 11 August 2022 (UTC)

@User:Jc3s5h: I am surprised that you are reading that in that section. I make a statement about the accuracy with which the Gregorian calendar approaches the (current) lunation length: but point out that this (or any) calendar can not be accurate over such long timescales (because the universe changes). This is not a call for calendar reform. BTW there is evidence (discussed in the article) that the reformers anticipated additional corrections in the future. In any case in your comment you explicitly asked for a citation of the accuracy statement, which does not exist because it trivially follows from the established real and calendar lunation lengths already referenced. Tom Peters (talk) 05:34, 12 August 2022 (UTC)

The [ edit in question] was by Eric Kvaalen and part of it added a reference, which was actually an explanatory footnote, which stated "For example, a period of 18,000 years would be possible by resetting the golden number to 1 when the year is divisible by 18,000. The epact will then always be 8 in such years." I viewed that as a suggestion for reforming the Gregorian calendar. — Preceding unsigned comment added by Jc3s5h (talk • contribs) 14:08, 12 August 2022 (UTC)

@User:Jc3s5h: OK, now I understand your point. Tom Peters (talk) 21:26, 12 August 2022 (UTC)

"Computus" listed at Redirects for discussion

An editor has identified a potential problem with the redirect Computus and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 September 8#Computus until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Veverve (talk) 15:31, 8 September 2022 (UTC)

Definition rewording proposal

There are loopholes in the current definition given in the article’s very first paragraph:

"Easter is celebrated on the first Sunday after the Paschal full moon, which is the first full moon on or after 21 March (a fixed approximation of the March equinox)."

Here is a rewording proposal:

"Easter is celebrated on the first Sunday after the Paschal full moon, which, in the Julian or Gregorian calendar, is a movable date that is an approximation of the day on which occurs the first full moon occurring on or after 21 March, a fixed date which itself has been chosen as an approximation of the day on which the March equinox occurs."

You might find it’s a mouthful, but hear me out. Here are arguments for the wordiness:

• The Paschal full moon is not a phase of the moon nor an astronomical event or instant, it’s first and foremost a "date" which approximates a certain "day". The day is the smallest unit of time relevant for computus.
• 21 March is not the date of the March equinox, but only an approximated and fixed date for that astronomical event. The verb "chosen" insists on the "conventional" or arbitrary nature of the date. And it is put in the present perfect passive tense, "has been chosen", to imply that the choice of that date is ancient, which explains why, in the case of the Julian calendar, the equinox approximation has now become very loose (13-14 days).
• As for the (real) "full moon" and "March equinox", they actually are astronomical events or instants that do happen on some day, hence the verb "occur" and phrasing "the day on which X occurs".
• There’s a notable difference in the two "approximation" days: the Paschal full moon is a "movable" date in the (Julian or Gregorian) calendar while 21 March is a "fixed" date. And the phrase "Julian or Gregorian calendar" is explicitly stated in the definition because, while the Paschal full moon is movable in those two solar calendars, it is fixed (14th day or 14 Nisan) in the ecclesiastical calendar and in the Jewish calendar on which it is based, both of them being lunisolar.

Knowing how many misleading definitions are floating around the Internet, I’m of the opinion that Wikipedia’s definition should sacrifice brevity on the altar of precision. Wikipetzi (talk) 04:21, 26 March 2023 (UTC)

I would rather shorten the sentence in the first paragraph to: “Easter is celebrated on the Sunday after, nominally, the full moon on or after the March equinox.” All caveats and explanations belong into subsequent paragraphs and sections. — Christoph Päper 08:43, 27 March 2023 (UTC)

Calculation of Orthodox Easter

From past experience, doing anything about this myself is unrealistic, so would a regular editor take up the challenge? The deficiency that needs to be made good is coverage of the Orthodox calculation. (The opening sentence asserts 21 March without qualification, but that it is only true for Western Christendom.) The only coverage that I can see is a seriously tl;dr section, Date of Easter#Julian calendar.

As I understand it

• Western Easter Sunday is the first Sunday after the first full moon on or after 21 March Gregorian.
• Eastern Easter Sunday is the first Sunday after the first full moon on or after the northern spring equinox (most often 20 March Gregorian, 7 March Julian).

Except...

In 2023, that first full moon was on 6 April Gregorian (23 March Julian) and the first Sunday thereafter was 9 April Gregorian (26 March Julian). So surely that should have meant that both traditions celebrated Easter on the same day, this year – but they haven't: Orthodox Easter is a week later. This BBC article explains why not: the Western tradition ignores Passover but the Eastern tradition does not. Passover ends 13 April Gregorian so Orthodox Easter must be delayed to the following Sunday. Since Passover starts on 15 Nisan and Nisan starts on the full moon after the equinox or even a month later due to intercalation, surely the "except" clause must be invoked more often than not?

See also Passover#Date and duration.

Any volunteers? 𝕁𝕄𝔽 (talk) 15:48, 13 April 2023 (UTC)

As I understand it, all the churches that later divided into Catholic, Orthodox, and Protestant denominations agreed on using the Easter tables of Dionysius Exiguus by the end of the first millennium. This calculation always treated March 21 as the equinox, and the time zone was not considered, so that automatically made it un-astronomical. In addition, the references to the moon were not to the real moon, but a tabular moon so that people in scattered outposts with little knowledge of astronomy could still do the calculation. Even after the denominations separated, they kept the same Easter calculation.

The Gregorian calendar changed the calculation for the Catholic church, and this calculaiton was eventually adopted by Protestant churches and some Orthodox churches. There is the well-known change of dropping some days from the calendar and changing the leap year rule. There is also a change in the tables for calculating where the moon is. The equinox is still March 21 and time zones are still ignored. It's important to realize that the Easter calculation is part and parcel of the Gregorian calendar, even though people who use the Gregorian calendar for secular purposes usually ignore the lunar/Easter part. Jc3s5h (talk) 16:21, 13 April 2023 (UTC)

The notion of 'must be after Passover' appears in a lot of not-quite-technical discussions of Orthodox Easter, but it's not actually a feature of the tabular algorithm. Possibly Dionysius engineered that idea into his tables when he constructed them? It would be interesting to know if Orthodox Easter has actually been after Passover every single year since those tables were adopted. Indefatigable (talk) 17:02, 13 April 2023 (UTC)

Although I don't have time just now to explain in detail, I do understand it well; in 1980 I wrote a Fortran program which generated the Eastern Paschalion, which was well received by several Orthodox bishops who saw the print-out.

The Eastern algorithm does use 21 March as the equinox; however, that is 21 March on the Julian calendar, which in this century is 3 April Gregorian. Also, it uses the Metonic 19-year lunar cycle which is astronomically incorrect and places the full moon later than it actually is.

This year, the Eastern calculation places the full moon late enough that Pascha is 3 April Julian, a week later than the Western Pascha. Vincent J. Lipsio (talk) 17:46, 13 April 2023 (UTC)

The last coincidence of the first day of Passover with Orthodox Easter Sunday was in AD 783.

The last coincidence of the first day of Passover with Gregorian Easter Sunday was in AD 1981, the next occurrence will be in AD 2123.

After AD 7485 such coincidences will not occur again for a very very long time.

For details, see section IV of Perpetual Easter and Passover Calculator. AstroLynx (talk) 19:32, 13 April 2023 (UTC)

Thank you all for your responses. I'm afraid that it seems that I failed to explain the issue properly and compounded it with a poor attempt at a solution. So let me restate it more clearly: the lead as it stands gives a succinct statement of the computus as determined by the Western Church. It fails to provide the equivalent for the Eastern Church. So my request is simply for such to be written. --𝕁𝕄𝔽 (talk) 23:23, 13 April 2023 (UTC)

Something very weird happening on this page

User:Eric Kvaalen posted a new thread to this page to which I answered. But this poage doesn't seem to show that thread plus the existing threads. Not sure what's going on. DeCausa (talk) 20:29, 10 September 2023 (UTC)

Here, I fixed it -- it was because of the footnote, for some reason: Eric Kvaalen (talk) 20:34, 10 September 2023 (UTC)