Talk:Golden number (time)

The Article
This should not be merged with "metonic cycle." The term Golden Number is still commonly used in Anglicanism, and is printed in tables in the Book of Common Prayer, in reference to the computus of Easter, with no reference or correlation to the Metonic Cycle.

The Golden Number of any year is the same in both the Catholic and Anglican versions of the modern calendar. From a practical point of view, they are one and the same concept. —Preceding unsigned comment added by 75.24.76.3 (talk) 05:50, 5 April 2009 (UTC)

The years, months, days of the month, and days of the week in the English civil calendar are for all practical purposes identical to the like-named or -numbered years, months, days of the month, and days of the week in the Gregorian calendar. Even the discrepancy regarding whether Feb. 24 or Feb. 29 is regarded as the leap day in a leap year has been tidied up (IIRC, the Catholic Church took care of this several years ago; Feb. 29 is now the leap day). —Preceding unsigned comment added by 75.24.76.3 (talk) 05:55, 5 April 2009 (UTC)

Definition of Golden Number
An encyclopaedia should give the true definition. The UK Act and Prayer Book (q.v.) have words corresponding to GN := (Y+1) mod 19 ; if GN=0 then GN := 19 ; Of course, that and GN := Y mod 19 + 1 ; are fully equivalent, and the latter should also appear since it is the better way to calculate it. It's not clear to me whether Clavius gave either of those; he has a tabular method good for A.D. 1 to 899999999. 82.163.24.100 (talk) 20:14, 22 October 2008 (UTC)

On deeper scrutiny, the final paragraph of Clavius' Canon 1 does give, in words, the Act/Book method - Et fi ex divifione nihil remanet, erit Aureus numerus 19.. 82.163.24.100 (talk) 20:48, 22 October 2008 (UTC)


 * In the above quotation, I believe 'fi' and 'divifione' would better be rendered as 'si' and 'divisione', as the 'f' character in each word will be a 'long s' in the original printing. Fergus Wilde (talk) 09:10, 8 January 2016 (UTC)

Metonic cycle- golden number- another point of fact-Dr. N. N. Chandra.
I recently read that Metonic cycle was known to Brahmins from a very long period back. At least as far back as Kali Yuga i.e. 3102 BCE. The reference can be found in Cassini as quoted by Baily in his classic work "Indian Astronomy" published in 1787. As a matter of fact John Playfair in his book "Works of John Playfair" published in 1822 recalculates Cassini's method and concludes that the golden number of Brahmins was more accurate than given by Metonic cycle. Brahmins still use the number based on 19 solar years equal to 233 lunar years in dating festivals in their calendars. —Preceding unsigned comment added by 173.32.182.222 (talk) 15:48, 13 October 2009 (UTC)


 * John Playfair does not mention any golden number in his "Astronomy of the Brahmins", pages 91–175 of The Works of John Playfair (1822). Nor is any 19-year cycle mentioned. Nor does he attribute any cycle to either Bailly (Traité de l'astronomie indienne et orientale) or Cassini. He dismisses one cycle by stating "It is indeed remarkable, that we find no trace [in the Brahmin eclipse tables] of the period of 6585 days and 8 hours, or 223 lunations, the Saros of the Chaldean astonomers, which they employed for the prediction of eclipses" (p.171).


 * I assume that anonymous meant to write "19 solar years equal to [235] lunar [months]". I am not aware of any 19-year cycle in either the Hindu calendar or in its astronomical basis, the Surya Siddhanta. — Joe Kress (talk) 23:49, 15 October 2009 (UTC)

Hildegard of Bingen and the Golden Number
I have deleted the claim of Hildegard of Bingen's knowledge of the Golden Number. Although the "aureus numerus" is indeed mentioned in her Ordo Virtutum it has nothing to do with calendars but rather refers to the completion of the ten heavenly choirs. AstroLynx (talk) 12:38, 20 May 2016 (UTC)

Why?
They use the number for a 19 year cycle because... What is the point of this number? Ballchef (talk) 11:53, 19 December 2018 (UTC)


 * Good question; I think this edit provides its function and purpose. --SteveMcCluskey (talk) 01:46, 21 December 2018 (UTC)

Deleted section
I am pasting this section I deleted for being unsourced as the anglican-orthodox dialogue appears to not have mentioned anything about Easter or golden numbers in their published documents.

Modern-day use of the golden number
Following an initiative by Pope Francis in 2015, it has been proposed that the golden numbers, which are used by both eastern and western churches, form the basis of a common Easter date. Apart from its logistical convenience, it will bring to an end criticisms that in some areas Christ is still preaching while in others he is already crucified.

In 2022 an interdenominational discussion document prepared under the auspices of the International Commission for Anglican-Orthodox Theological Dialogue, (Metropolitan Athenagoras of Belgium, The Rt Revd Graham Usher, Bishop of Norwich, 22 pp), was lodged in the Cathedral Library at Norwich. Comments were invited (the Library is public, the document's title is The prospect of Whitby and its Call Number is 529.3).

Chapter 1 Early differences (page 1) notes:

A letter to the Church of Alexandria after the Council of Nicaea in 325 recorded:
 * We further proclaim to you the good news of the agreement concerning the Holy Easter, that this particular also has through your prayers rightly been settled: so that all our brethren in the East who formerly followed the custom of the Jews are henceforth to celebrate the said most sacred feast of Easter at the same time with the Romans and yourselves and all those who have observed Easter from the beginning.

The penultimate sentence of the chapter (page 2) notes:

"Constantine had admonished: 'Think, then, how unseemly it is, that on the same day some should be rejoicing at feasts, while others are still observing a strict fast.'"

On the same page, Chapter 2 Summary of developments (which was added on the express instruction of the International Commission) notes:

"664: Synod of Whitby. England aligns with Rome."

"4 December 1563: The Council of Trent authorises the pope to revise the missal and breviary (but not the calendar)..."

"1564: Pius V reserves to himself the sole right of interpretation of the enactments..."

"24 February 1582: Gregory XIII claims the right to unilaterally change the calendar and the date of Easter and does so. Anyone who does not fall into line will be excommunicated."

Page 3 notes:

"Queen Elizabeth's astronomical adviser...in 1582 advocated the 'astronomical Easter', an idea rejected by the pope..."

At the end of the sixteenth century the Orthodox church issued a series of anathemas against the Gregorian calendar. It is easy to see why:

(1) the Julian calendar is simple to operate. Easter jumps forward in years 3, 6, 8, 11, 14, 17 and 19 of the nineteen-year cycle. This is the same rule which applies in the Jewish calendar, although the Jewish cycle begins three years later. Easter is thus kept in lockstep with Passsover.

(2) the Julian calendar incorporates effective measures to prevent Easter being celebrated on [page 4] or before the Passover. These include: The Jewish calendar has a system of delays which prevent certain festivals being observed on certain days of the week. With only the first safeguard, the Gregorian Easter may fall a day or a month before the Passover. Eventually, Easter will fall a month before the Passover every year.
 * If the full moon falls on a Sunday Easter shall be the Sunday after
 * The month preceding Easter always has thirty days
 * The 'lockstep' safeguard referred to above

Method of calculating the date of Easter
Nineteen Julian years are slightly longer than 235 lunar months, while nineteen Gregorian or Revised Julian years are slightly shorter. Therefore, as time goes on, the eastern and western dates will coincide less and less, and in a few hundred years the western Easter will always precede the eastern one. The common ground is that, since the Synod of Whitby in AD 664, all churches agree that the "full moon" shall be observed on the fourteenth day of the lunar month. From this, the definition of Easter is derived:

"EASTER-DAY, on which the rest depend, is always the First Sunday after the Eighteenth Day of Miri, and if the Eighteenth Day of Miri happens upon a Sunday, Easter-Day is the Sunday after. All of which holds until the year 2099 inclusive, after which, on account of adjustments made every three or four hundred years in the calendar used in the calculation (of which Miri is the third month) the reference to the 'Eighteenth' day shall be replaced by a reference to the 'Nineteenth' day, and so on."

The date of the full moon is identified in the table below. Both the old (current western) and new (current eastern) methods are given, as they have been in the Breviary since 1582.

To use the table:

The date of Easter is found from numbers which are allotted to certain dates as indicated in the table. For any particular year, the number which is taken is the same as the remainder that is obtained when one is added to the year and the total divided by 19. If there is no remainder 19 is taken. If the number is in Group A, Easter falls on the Sunday following the date against which that number appears. If the number is in Group B, Easter falls on the Sunday of the week commencing with the date against which that number appears.

If the number is in Group C, the date against which it appears is to be treated as a day of March, and Easter falls on the day after the Saturday following that date.

Rules for updating the table

The boundary between Group A and Group B is usually set between 18 and 19 April, but if there are numbers against both 18 and 19 April (as in the 21st century) it's set between 17 and 18 April. The boundary between Group B and Group C is always set between 19 and 20 April. The numbers are moved from time to time, and when they do move it's before Easter in years which are exactly divisible by 100. There are two separate movements:

1. The 'solar correction': the numbers move DOWN a day every time a centennial leap year is dropped (eg 2100)

2. The 'lunar correction': the numbers move UP a day in years giving remainder 200, 500, 800, 1100, 1400, 1800, 2100 and 2400 on division by 2500 (eg 2100).

Sometimes the corrections cancel out - thus in 2100 the numbers stay where they are. For Orthodox Easter the instructions for Groups B and C are ignored. Easter is, from the last lunar correction in 1800 to the year before the next lunar correction in 2100, the Sunday after the Wednesday following the date given by the table current for the relevant century. From 2100 until the year before the following lunar correction (in 2400) replace 'Wednesday' by 'Tuesday', and so on.

Example calculation

On what date does Orthodox Easter fall in 2023?


 * 2023 + 1 = 2024
 * 2024/19 = 106 remainder 10
 * Sunday Letter for 2023 is A
 * 10 stands against 5 April
 * The nearest 'A' day is 2 April.
 * Therefore, 2 April is Sunday and 5 April is Wednesday
 * The following Wednesday is 12 April
 * The following Sunday is 16 April
 * Orthodox Easter is 16 April.

What the prospects are for this method being implemented
Page 5 of the document notes:

"In the middle east even the Latin rite Catholics and Protestant churches have been observing Orthodox Easter since 1975, and in January 2016 Bishop Mouneer Anis (as he then was) reaffirmed this for Anglicans in Arabia (including the Gulf States), Cyprus, Egypt with North Africa and the Horn of Africa, Iraq, Israel (including occupied territories), Jordan, Lebanon, Persia and Syria."

Page 6 notes:

"In 1900 the Macedonian-born academic Maksim Trpkovic published at Belgrade his Reforma Kalendara (Calendar Reform). Based on Barnaba Oriani's proposed reform which became the state calendar of Greece [references cited] it featured epact calculations for the twentieth century and new paschal limits in the 19-year cycle of golden numbers, after which the dates of the new moons repeat."

"In 1903 the Holy Synod of the Greek Orthodox Church wrote to the Oecumanical Patriarch stating that the Julian calendar would be preserved."

Page 8 notes:

"The Congress deliberated in May and June 1923. Advocating his solution astronomer Milutin Milankovic said that with the proposition of the Serbian delegation (which had previously advocated the newly-introduced state calendar of Greece) the Orthodox Church would have the most precise and most scientific calendar in the Christian world, so it could [page 9] confidently enter any negotiations on the calendar question with Western Churches.   An astronomical Easter was adopted, calculated for the meridian of the Church of the Holy Sepulchre in Jerusalem."

There follows Chapter 6 Changes in church law are reversed following rejection by the people. It includes the following on page 9:

"Alexandrian patriarch Photius had told the Oecumenical Patriarch on 15 January 1924 (old style) that '...we reject every addition or any change of the calendar before the convocation of an Ecumenical Council, which alone is capable of discussing this question, concerning which Ecumenical Council we propose a speedy convocation .'"

Chapter 7 A light at the end of the tunnel (page 11) notes:

"A proposal was made in 1997 to impose something very similar to the 1923 agreement on all churches...Under it, Easter would have to break its canonical limits, leaving the way open for Shrove Tuesday to clash with Candlemas [reference cited]. At the end of the explanation the dates of the astronomical, Gregorian and Julian Easters are tabulated for the years 2001-2025 along with the Vernal full moon astron. reckoning and the date of Passover [reference cited].   In eight of those 25 years the full moon at Greenwich fell on the day before the Passover..."

"On 12 June 2015, at the World Retreat of Priests at the Basilica of St John Lateran in Rome, Pope Francis observed that 'we have to come to an agreement' for a common date on Easter. Lucetta Scaraffia, writing in the Vatican newspaper L'Osservatore Romano, explained that the Pope is offering this initiative to change the date of Easter 'as a gift of unity with the other Christian churches.'"

Use of golden numbers for Easter
When possible, more sources need to be added for the date of Easter section. I am still not sure what the scope of the interdenominational discussion document is, what churches are involved and what the prospects are for this method being implemented.

Suggestion
I think unless another source comes out specifically talking about the use of golden numbers to calculate Easter or a final agreement, this information would be better added to Reform of the date of Easter. This website claims that they are trying to reach a final agreement by 2025 so presumably more information should come out soon regarding different methods — Preceding unsigned comment added by Safes007 (talk • contribs) 13:29, 2 January 2023 (UTC)
 * Introducing the discussion document on 3 November 2020 and commending the proposals the International Commission stated that it:

"...blends the political realities of ecclesiastical and state politics, particularly in the Christian East, with the mathematical reasons why varying astronomical calculations cause such confusion on the dates for religious festivals...the celebration of Easter on different days and...the loss of the link with Passover is to be lamented...'"

The Commission points out that it is the very opposite of a proposal for "Reform of the date of Easter." The joint proposal by the Oecumenical Patriarch and the pope was floated in 2015. Justin Welby told the British government to get ready to implement it in January 2016 and the Catholic Herald wrote:

"When the Archbishop of Canterbury rationalises such a momentous decision by pointing to difficulties over school holidays one has to ask: what is the biggest influence here? Christian unity or relatively frivolous secular concerns? If the latter is a motivation then such a move - to borrow the Holy Father's words - could also prove to be a scandal.'"

Yet the discussions reported in Zenit are presented as completely new. Although they say astronomers will be consulted there is no explanation of why, after eight years, this has yet to happen. The controversial claim that the date of Easter is not a religious matter but a scientific one is presented as fact. The fact that reform of the date of Easter is not on the agenda of the Orthodox Church, and many Orthodox churches have severed relations with the Oecumenical Patriarch on this account is nowhere mentioned. 79.79.43.32 (talk) 18:11, 7 January 2023 (UTC)

"Modern day usage"
The claimed source is a document in the Cathedral Library at Norwich. An ISBN, call number, or other unique identifier would be helpful. Elizium23 (talk) 11:27, 29 December 2022 (UTC)

Section on Calendar reformation, etc.
The textual majority of this article now seems to essentially serve as the personal project of a single unregistered user, beginning late last year. As regards that text, the greater part of is either mere at-length quotations from a single Anglican document, or (For the most part, at least) unsourced claims that must represent either original research or reproduction of the propositions of the aforementioned document. These claims, along with the editor's responses to attempts at revising the article, are often and have often been bewildering.

Given the repeated reverting of proceeding revisions to the article, those reverts being by the aforementioned user, I suppose that some further arbitration is needed. As something encyclopedic, the article as it now stands is unacceptable. Zusty001 (talk) 18:24, 2 September 2023 (UTC)


 * Not sure why you think that a project which has been of interest to the whole Church for the last 442 years is "the personal project of a single unregistered user."  This division is the most pressing issue that the Churches face today.   The point was taken, and the reportage was restricted to the subject of this article - the arrangement of the Golden Numbers in the calendar.   Then out of the blue one editor claims "vandalism - addition of unsourced content."   A lot of effort was made to provide detailed sourcing, only to be dismissed with the edit summary "repeat vandalism - again."   The editor responsible does not engage in dialogue with other editors - he has not engaged on his talk page for a year.   Another editor alleging "vandalism" has not engaged on his talk page for four years.   The absence of a user page also indicates lack of communication.
 * The reportage is fair and there has been input from (among others) the Bishop of Norwich (on behalf of the Church of England), Rev Joseph Iannuzzi, Doctor of Divinity, Pontifical Gregorian University, Rome (on behalf of the Catholic Church), and Vassula Rydén (on behalf of the Greek Orthodox Church). 93.96.9.14 (talk) 18:32, 11 January 2024 (UTC)


 * More unsourced claims. How serious can one take a calendar reform which uses the following month names: Harriet, Ronan, Miri, James, Eloise, Thomas, Nicholas, Catherine, Richard, Emma and Paul? AstroLynx (talk) 22:18, 11 January 2024 (UTC)


 * For the most part, not a response to anything. Use of and extrapolation from a single (Unusually sourced) Anglican document; The (Appendant?) creation of "Golden Number" tables by the user themselves that are both left unexplained and, as regards page history, have been historically spurious (See various available sources for calculating "Golden Numbers" for the Latin calendar both retroactively, before the Gregorian revisions, and otherwise); And more related to and following from these all remain the same and unaddressed, such as the use of unsourced or strangely sourced quotations, strange claims without sourcing either proper or present, etc. Responses remain as absent or as bewildering as before this Talk section was made. I once again recommend further arbitration, especially as I am not here frequently enough to review the seemingly vast amounts of content which have been added by the editor in the course of his attempts to combat the removal of (What appears to be) his older claims and creations.
 * Zusty001 (talk) 07:51, 12 January 2024 (UTC)
 * (Replying to myself given formatting of editor's reply)
 * More lengthy yet odd replies. Comment on the spuriousness of table as regards what it purports to give, and the interpretations appended to in in text, refer, as said, to the original version made by the editor, - that they have made what is basically a new table since then should also be noted - the new table lacks any of the "explanatory notes" (However fallacious) of the original.  Anyone interested should look for freely available tables that accurately reflect the Latin calculation (Such as in archived Latin breviaries or sites with explanatory notes like kalendar.beda.cz).
 * Old revisions of the editor were made under a previous IP address. Zusty001 (talk) 23:28, 12 January 2024 (UTC)
 * There is absolutely no change in the golden numbers - they track the moon and there has been no sudden disturbance of the moon's orbit.  To demonstrate this, if you open the Book of Common Prayer at the March/April page you will see them in the left hand column with the date and the Sunday Letters, and everything is identical to the supposedly "historically spurious" revision.   If you disregard 17 and 6 (which are peculiarly squashed against 9 at the foot of the list) they are marked as follows:

14 - March 22; 3 - March 23; 11 - March 25; 19 - March 27; 8 - March 28; 16 - March 30; 5 - March 31; 13 - April 2; 2 - April 3: 10 - April 5; 18 - April 7; 7 - April 8; 15 - April 10: 4 - April 11; 12 - April 13; 1 - April 14; 9 - April 16.

These mark the "paschal full moons" (the fourteenth day of the month), but traditionally they marked the first day, and the traditional format was agreed. Making the change involves subtracting 13 days (14 - 1 = 13), placing them as follows:

14 - March 9; 3 - March 10; 11 - March 12; 19 - March 14; 8 - March 15; 16 - March 17; 5 - March 18; 13 - March 20; 2 - March 21; 10 - March 23; 18 - March 25; 7 - March 26; 15 - March 28; 4 - March 29; 12 - March 31; 1 - April 1; 9 - April 3.

These are the exact dates the numbers appear against in the table. Possibly the attack on the names was made because no technical deficiency in the system was found. There is a reference to them in the source document at page 19:

To assist this, key months have been given the names of Biblical personages and (in one case) the name of a Roman Catholic pope.

The provenance is as follows:


 * (1) Harriet is a diminutive of Henrietta.  Wife of Charles I, she was the ancestor of several monarchs.
 * (2) St Ronan was a key figure in the implementation of a common Easter date at the Synod of Whitby in 664.
 * (3) Miri is a contraction of Mariam, the given name of the Mother of God.
 * (4), (6), (12) James, Thomas and Paul were apostles.
 * (5) Héloïse was an abbess who reached a rank equivalent to that of Bishop.
 * (8), (9) Nicholas and Catherine are well-known saints.
 * (10) Richard I, known as Coeur de Lyon, was instrumental in recovering the Holy Land from the Saracens.
 * (11) Emma was the mother of Edward the Confessor.
 * (13) Paul II was Ecumenical Patriarch of Constantinople 641-653, and a Pope of that name reigned 1464-1471.

It is of note that although the seventh month of the secular calendar bears the name of a Roman dictator alleged to have bribed his way to power, and the eighth commemorates a dictator who gained lifelong power while claiming to have given full democratic power to the Roman senate, no objection to it is raised on that account. The existing system has fallen into disrepute not least because, although the Book of Common Prayer claims Easter falls on the Sunday following the full moon following the vernal equinox, it frequently doesn't, and the squishing of the golden numbers at the end of the table means the error can be very large. 93.96.9.14 (talk) 18:07, 12 January 2024 (UTC)

I've accessed the site mentioned, but it's in a language I don't understand. We originally provided an explanation of how to use the golden numbers to calculate both the occidental and the Orthodox Easter, and there is a competent explanation also in the linked article Date of Easter. With the complaint that the section was too long, we concentrated on explaining how the new table is used to give Orthodox Easter. In view of your comment, we can add the information back, and this is the suggested wording:

To calculate the date of occidental Easter, proceed as follows:

1. In the calendar, locate the date of 14 Miri (which is the "paschal full moon").

2. If it falls on or before 17 April, Easter is the Sunday following. If it falls on 18 April and no golden number is marked against 6 April, again Easter is the Sunday following. If it falls on 18 April and a golden number is marked against 6 April, Easter falls on 18 April (if Sunday), and if 18 April is not Sunday Easter falls on the following Sunday.

3. If the paschal full moon falls on 19 April, Easter falls on 19 April (if Sunday), and if 19 April is not Sunday Easter falls on the following Sunday.

4. If the paschal full moon falls on 20 April or later, the date of the paschal full moon is to be treated as a day of March, and Easter falls on the day after the Saturday following that date.

One reason for dispensing with the occidental Easter was that sometimes the instructions direct the festival to be observed on the day of the Jewish Passover, which the ecumenical councils do not permit to happen. 93.96.9.14 (talk) 17:14, 13 January 2024 (UTC)


 * This whole discussion appears to revolve around a mysterious 22-page pamphlet published in 2022 with the title The Prospect of Whitby, also the name of a famous London pub and the title of an 1948 overture by Robin Orr, which is not listed in Jisc Library Hub Discover or in WorldCat but is claimed to be in the Norwich Cathedral Library.


 * However, the online catalogue of the Norwich Cathedral Library seems to be unaware that it has this pamphlet on its shelves and unless more substantial proof for such a publication is provided I think that we can safely assume that it does not exist.


 * Even if it does exist outside the imagination of the OP it appears to have a notability of virtually zero and can therefore be safely disregarded in any discussion about the Golden Number or the Easter computus. AstroLynx (talk) 13:13, 14 January 2024 (UTC)


 * You're linking to book catalogues.  To give an analogy, the British Library publishes many pamphlets which can be picked up from the information desk or mailed out on request, none of which is listed in their book catalogue.   The pamphlet in question is put out by the International Commission for Anglican Orthodox Theological Dialogue.   You will have no difficulty in obtaining it from Norwich Cathedral Library if you ask for a copy, but it is of course held in other libraries as well. 93.96.9.14 (talk) 15:38, 14 January 2024 (UTC)


 * A 22-page pamphlet is quite substantial and if it exists it would have been mentioned in a library catalogue or online somewhere. Apart from your postings nobody anywhere appears to refer to it, so even if it exists it has not had any impact. Unless you can provide better evidence that it actually exists I am bowing out of this pointless discussion. AstroLynx (talk) 20:30, 14 January 2024 (UTC)


 * The first ten pages of the British Library catalogue list "books", "journals", and "scores".  As a control I requested details of one of the "books" and it said it had "90 pages".   If you can find an example of a "book" with 22 pages please let me know.   Also, this is not an "end-product".   Published reports customarily list the documents consulted in the course of preparation but we are not at that stage yet.   WP:AGF is a relevant guideline.   The Papal Nuncio, Miguel Maury Buendía, has seen the document and you can email him for confirmation.   An update has already been published - it's a four-page pamphlet titled Sundays 2023 - 2026, which was published on 13 September 2023. 93.96.13.97 (talk) 18:04, 15 January 2024 (UTC)


 * Please draw the attention of your parish priest and congregation to this initiative during the Week of Prayer for Christian Unity which begins on Thursday.  See Vassula's specific message of 6 January 2024 at .   Join her in an Ecumenical Prayer Meeting on Sunday at 8 PM (GMT) at . 5.66.120.5 (talk) 15:15, 16 January 2024 (UTC)


 * The videolinks are unimportant.  The relevant policy reads:

"Source material must have been published, the definition of which for the purposes of Wikipedia is made available to the public in some form."

Are you aware of this policy? 93.96.38.91 (talk) 17:58, 21 January 2024 (UTC)

On the Byzantine Forum, in a post dated 27 February 2023, "ajk" makes unsubstantiated allegations about the neutrality of the article. It correctly summarises all points of view, and his real objection is that he wants it to mention only his point of view (that the Orthodox Church should adopt the Gregorian calendar and with it the Gregorian Paschalion). The discussion is dominated by him and Mockingbird - perhaps Mockingbird could go there and explain our neutrality policies to him? 93.96.44.214 (talk) 12:52, 9 March 2024 (UTC)

Golden number in the Calendarium Parisiense
A better explanation of the page is needed. Currently, our caption just briefly mentions the leftmost column. It appears that the second column shows the Sunday Letter, but that seems different from the deleted. The third and fourth column obviously show the day in the Roman fashion. Here is a transcription of these columns:

3	A	Ianuarius b	4	N′ 9	c	3	N′ d	2	N′ 19	e	Nonas	N′ 8	f	8	Id′ g	7	Id′ 13	A	6	Id′ 2	b	5	Id′ c	4	Id′ 16	d	3	Id′ 5	e	2	Idus f	Idus	Idꝰ 10	g	19	Kl′ A	18	Kl′ 18	b	17	Kl′ 7	c	16	Kl′ d	15	Kl′ 15	e	14	Kl′ 4	f	13	Kl′ g	12	Kl′ 12	A	11	Kl′ 1	b	10	Kl′ c	9	Kl′ 17	d	8	Kł 6	e	7	Kl′ f	6	Kł 9	g	5	Kl′ A	4	Kl′ 14	b	3	Kl′ 3	c	2	Kl′

It would be nice to have transcription and translation of introduction and fifth column, as well. Most pertinent for this article, however, is the leftmost column, which poses a number of questions:
 * 1) Why does the number 11 not appear? As I understand the caption, “each year” should be represented. Was that an oversight in this otherwise so meticulously crafted calendarium?
 * 2) Why are there only 25 days between the two occurrences of number 9? Was the moon's orbit particularly fast then? 😀
 * 3) For which years was that table accurate? If my computation is correct, the whole pattern should shift by a day after 19/(2h4′58″/24h) ≈ 19/0.086782 ≈ 219 repetitions, i.e. 219 years. Since there should be 21 days marked, the event of a single new moon date shifting by a day should on average occur after 219/21 ≈ 10 years. (That would tell us how accurate the calendarium was - or, if it turns out to have been very accurate, even hint at a more exact creation date than just a quarter century.) ◅ Sebastian Helm 🗨 09:26, 27 March 2024 (UTC)

Upon further research on point 2, the discrepancy seems to be no outlier. E.g. the year 1396 has, according to the modulo formula, the golden number 10 (in this table at 19 Kl′) and the year before has the golden number 9， for which there are two entries: at 3 N′ and at 5 Kl′. A synodic year before 19 Kl′ of January 1396 was January 25…26 (depending on rounding error), 3…4 days before the 5 Kl′ of this table. You might say they weren't so exact in the middle ages, but this computation requires no more than simple addition, subtraction and multiplication, and the observation of half a week difference to a full moon, so one should think that they could have done better. Or am I missing something? ◅ Sebastian Helm 🗨 12:59, 27 March 2024 (UTC)