Talk:Computus

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Contents

[edit] Name of the Article

I do not like the title of this page. It is too long and I never get the small words and capitalization quite right; the capital 'E' is un-Wikipedia anyway. I propose to re-name this "Computus", for the medieval term of this craft. -- Tom Peters 25-Jul-2003 21:52 UTC

  • What was the original title of this page? The term Computus is hardly known, even by those who take an interest in these things. The case-sensitivity of Wikipedia's search function (apart from the first word) is one of the major bugbears in its use.—Copey 2 13:42, 3 May 2006 (UTC)
"Calculating the date of Easter" still links here, but I believe other re-directs existed with a different capitalization of Date or easter; anyway, I never got it right. "Computus" is the technical term and has been used since the early middle ages. "Calculating ..." is a descriptive phrase. IMNSHO an encyclopedia should have lemmata of words, not awkward phrases. Tom Peters 18:01, 3 May 2006 (UTC)

[edit] iCalendar/RRULE

I'm working on an ical specification for easter and have been unable to find any notes on this. Since iCal is the standard method of recording events these days is there any chance we could add information about icalendar implementations of easter? Nickjost 23:57, 23 October 2007 (UTC)

Your meaning is not entirely clear to me. If a definition of the date is required, one cannot do better than the original British Calendar Act - that was inherited by the American colonies and will still be in force there unless replaced by later legislation. If an algorithm for the date is needed, then that derived by merlyn from the Act seems unlikelty to be beaten; but it can only be implemented for iCal by someone with a knowledge of an applicable language and with test facilities. 82.163.24.100 (talk) 11:34, 4 May 2008 (UTC)

[edit] Gauss's Algorithm

I found a source for Gauss's Algorithm, Blackburn & Holford-Strevens pp. 864–866. However, the Gregorian exceptions are described differently:

if M = 0, 3, 6, 8, 11, 14, 17, 22, 25, 27 and 19a + M (mod 30) = 29, d = 28.

if M = 2, 5, 10, 13, 16, 21, 24, 29 and 19a + M (mod 30) = 29, d = 27

Does anyone know if the exceptions are actually equivalent? They don't seem equivalent to me. Alternatively, which is right? --Gerry Ashton 17:14, 9 October 2006 (UTC)

I'm not sure what you mean: the algorithm provided on this page does not give a list of exceptions like H-S&B do, but provides a pre-computed table of (M,N) values that is identical with what H-S&B compute; and gives two heuristic rules. Do you have an example where the two descriptions give a different date? Tom Peters 21:00, 9 October 2006 (UTC)

Gauss spent several years on his definitive calculations for Easter and published three (similar) algorithms. I cant give a definitive source for this but Algorithm 1 presented here works for the 1980-2024 dates listed elsewhere and I had the impression always worked without exceptions. It looks quite similar to the algorithm posted on the page but precedes it by 150 years !

Numerator Divisor Quotient Remainder
year 19 A
year 100 B C
B 4 D E
8B+13 25 G
19A+B-D-G+15 30 H
A+11H 319 M
C 4 I K
2E+2I-K-H+M+32 7 L
H-M+L+90 25 month
H-M+L+month+19 32 day

A1jrj (talk) 13:17, 1 May 2008 (UTC)

I may have been misled here - a little research suggests that this algorithm was popularised in O’Beirne, T.H. “Chapter 10 Ten Divisions Lead to Easter” in Puzzles and Paradoxes. London: Oxford University Press, 1965. 158.234.250.71 (talk) 17:57, 1 May 2008 (UTC)

That happens to be correct for all years starting with Year 0. But it is not particularly quick.
Definitive algorithms should be directly traceable to the prime authority - that means Clavius or the Calendar Act, since those are what a Pope and a King authorised - or to the person whose algorithm it is said to be. To do otherwise introduces doubt. Faster algorithms may be preferred for actual use, but should be compared against something known good. For Easter, that means comparing for at least 5700000 years.
For use by people, Easter algorithms need to give Month and Day. But for computer purposes it is often better to give Day-of-March instead - h-m+l + 22 in this case - since that can be directly converted into such as a JavaScript Date Object or a VBScript CDate. And, correspondingly, it can be useful to have the Day-of-March indicated in comment if Month and Day are returned. Indeed, if the language provides an easy way of moving to the Sunday next following, it can be useful to have the Day-of-March of the Paschal Full Moon returned or indicated.
82.163.24.100 (talk) 17:52, 1 May 2008 (UTC)

[edit] References and Table

This article is weak in the way sources are cited. There are long passages of complex text that do not indicate which source they came from.

In particular, two edits have just occured concerning the epact table, but there is no indication which source the table was taken from, so one is forced to do some laborious calculations to see which version is right (unless you happen to be a computer programmer). --Gerry Ashton 22:14, 4 October 2006 (UTC)

I have found sources for the table in question and added appropriate footnotes --Gerry Ashton 23:13, 4 October 2006 (UTC)
The tables follow from the procedures as explained. The readers should be able to construct them themselves. The procedures come from the documents involving the Gregorian reform, which are not easily accessible: the site of Rodolphe Audette [1] appears to be the only reliable source on the Internet. I believe all computations are explained in sufficient detail that they can be checked, so no further reference needed; indeed, I've found nowhere in writing how the lunar calendar REALLY works, why things were done this way, and what all the consequences are. Much of the literature have not thought things through (including apparently Clavius!). The draft by Denis Roegel [2] comes closests but is very technical. Dr. H. Lichtenberg is misguided. Tom Peters 10:59, 5 October 2006 (UTC)
The Blackburn & Holford-Strevens source that I added explains the mechanics, but does not go into the accuracy of the result. The fact that the text is self-consistent is better than nothing, but the information in the article really should be verifiable. --Gerry Ashton 16:15, 5 October 2006 (UTC)

There is a Reference to Weisstein, for PFM. That page is unexceptionable but trivial; it links to an Easter page, which is in error. It seems to me that the Weisstein material is no longer maintained, and is better not cited. 82.163.24.100 (talk) 12:29, 18 April 2008 (UTC)

In References + Links, I see nothing for the original authoritative materials. The Papal Bull and the Calendar Act give details of the new secular calendar (the Leap Year Rules), and give authority for, but no description of, the revised Easter rules : those were in Annexes. References and links are much needed. Clavius is imaged at http://mathematics.library.nd.edu/clavius/. For the Anglican version, I suggest the Preface to the printed Book of Common Prayer of the Church of England. 82.163.24.100 (talk) 12:29, 18 April 2008 (UTC)

I've Googled for "intermediate Years betwixt" which should appear in any true copy of the BCP, and found nothing authoritative ; "eskimo" has it, but has Gregorian material in a URL containing 1662. 82.163.24.100 (talk) 12:29, 18 April 2008 (UTC)

Google Books currently has, via http://books.google.com/books?id=zr8PAAAAIAAJ&printsec=frontcover&lr=#PPA24,M1, images of the relevant pages of the 1815 Prayer Book; see pp. 24 ff. It largely matches a c.20 copy of the Book (limited-period matter differs but corresponds). It can be considered as a including a faithful representation of the Annexe to the 1751 Act. Page http://justus.anglican.org/resources/bcp/ The Book of Common Prayer at the http://justus.anglican.org/soaj.html Society of Archbishop Justus has http://justus.anglican.org/resources/bcp/1789/Tables&Rules_1789.htm TABLES and RULES from the 1789 U. S. Book of Common Prayer, in HTML, matching the 1815 Book. I suggest that at least one of those should be a reference or link in the article, at least until/unless a good direct copy of the original Annexe itself is found on the Web. 82.163.24.100 (talk) 10:45, 22 April 2008 (UTC)

[edit] Algorithms: Meuss/Jones/Butcher (Gregorian)

Implementing this in a calendar program shows that it is correct, but the names of the variables on this page make it hard to understand what is actually going on. I've given it a try (read as: mostly guess-work) given my limited knowledge, maybe someone with more knowledge about Computus can fix my incorrect assumptions - and then put it into the article (I realise some of it is trivial, e.g. the century bit, but for completion):

a = golden_number
b = century
c = year_in_century
d = gregorian_cycle_number (as in, the howmanieth cycle it is)
e = gregorian_cycle
f = ?
g = ?
h = epact
i = gregorian_cycle_number_of_year_in_century - or basic attempt at figuring out a leap year?
L = gregorian_cycle_of_year_in_century - or basic attempt at figuring out a leap year?
m = ?

I've tried to wrap my head around the constants whilst trying to figure this out, too:

451 = ?
114 = MAX_EASTERDATE_AS_DAYOFYEAR - am I right that this is supposed to represent the 25th of April?
100 = YEARS_IN_CENTURY
19  = MAX_GOLDEN_NUMBER
32  = ?
30  = MAX_EPACT
25  = ?
22  = ?
15  = ?
11  = LUNAR_OFFSET
8   = ?
7   = EMBOLISMIC_MONTHS
4   = YEARS_IN_A_GREGORIAN_CYCLE
3   = ?
2   = ?

I would love to see my mistakes corrected and the bits I don't understand explained. I know this is not much to work with, but I'd really like to see the algorithm explained. Notably, I'm aware that often in purely mathematical calculations of dates, an "offset" has to be defined as a constant so the result is not shifted by some amount - so I realise that not all numbers used must neccessarily have another meaning but for, shall we say, 'error correction' in the algorithm; but even that, I find, ought to be documented.

-pinkgothic 14:35, 4 April 2006 (UTC)

There are 8 adjustments every 2500 years so that is where 8 and 25 come from. 15 represents the year 1500. We are counting adjustments from 1500. There are 3 adjustments every 400 years due to the Julian/Gregorian conversion. The number 114 represents April 19th. That means 95 represents March 31st and 96 represents April 1st. If we take this number, subtract 6, then divide by 30 (greatest integer), this will represent the month minus 1. 32 represents 32 adjustments every 10000 years. 10000 years is a complete adjustment cycle with the 8 every 2500 years and 3 every 400 years for the Gregorian/Julian conversion. 22 sounds like it's 25 minus 3. --Trust101 18:41, 28 May 2007 (UTC)

[edit] Whose mistake?

I wrote an Excel spreadsheet using Jean Meeus' formulae; it put this year's Gregorian Easter on 2 April, two weeks early, and the Julian Easter on 10 April, a Monday. I haven't found a mistake in my own copying. Could someone else please verify the Meeus algorithms given here? NakedCelt 16:45, 10 March 2006 (UTC)

Found the mistake in my Gregorian calculation, but the Julian Easter still seems to be on Monday.
There is currently a 13-day difference between the Julian and Gregorian calendars. April 10 Julian is April 23 Gregorian, a Sunday. Checking another source, I find that this is the correct Julian Easter for 2006. Indefatigable 20:57, 10 March 2006 (UTC)

[edit] Western Easter only?

Do I understand correctly that this page pertains only to the Western calculation of Easter? If not, the two methods need to be explained distinctly. If so, then this page should include this specificity very early, and a corresponding article be created explaining Eastern Easter computation. — Xiong熊talk* 05:57, 2005 August 18 (UTC)

The article does discuss both Easters, but not under the terms "Western" and "Eastern". Eastern corresponds to Julian, and Western to Gregorian. Perhaps an explanation of the different nomenclatures should be added. Indefatigable 16:46, 20 August 2005 (UTC)
There are in fact three cases of significance, at least - Gregorian Easter on the Gregorian Calendar (in general current use), Julian Easter on the Julian Calendar (used in Europe in the first half of the second millennium) and Julian Easter on the Gregorian Calendar (currently, I think, what Russians need). The calendar change is a simple function of the centade. 82.163.24.100 (talk) 21:47, 9 April 2008 (UTC)

[edit] Age and epact

Tom has changed the text on the assumption that the age of the moon must be real (not whole) number. This need not be the case in the English language at least. Applying this assumption causes the text to be more complicated as a result.

How old is Tom? What is Tom's age? 35.767 or 35? (not actual age).

So I think the age of the moon in days as a whole number is a valid concept (in English at least) and could be retained on this page for simplicity. Perhaps the Dutch language does not allow whole number for its equivalent to age. -- Karl 1-Aug-2003 09:45 UT

Uhm, where does this apply? -- Tom Peters 12-Aug-2003 21:07 UTC

I'm referring to the change on 31 July "TP: elaborations on epact<->dayte in lunar year<->age of Moon. Could be explained without reference to "age" (continuous real number), but only "day of month" (ordinal number).) " concerning the section Some Theory. I've just made a small change there that should clarify the moon age references. -- Karl 13-Aug-2003 09h UT

I disagree with your insertion "(moon age 0 at solar new year's day)". The intention is to start the lunar year at the same time as the solar year, i.e. the date (ordinal number) is 1. The epact is 0. The epact is the difference in date between the lunar and solar year. This is equivalent to the age of the Moon, but that is secondary. Anyway, the age of the Moon on 1 Jan. is 1, not 0 (hence the tedious explanation of epact as the age of the Moon on the day before the solar year starts). Think of it as the crescent Moon, which marks the 1st day (ordinal number) of the month, being already (at least) 1 day old. This is also what I state in the 2nd par. in the section on the Gregorian computus; your insertion is in conflict with that text. -- Tom Peters 12:31, 13 Aug 2003 (UTC)

I disagree with Tom's assertion that the age of the moon is 1 on new year's day when the epact is 0. This contradicts the first paragraph of the Catholic Enclopaedia article. Referecenced in Epact. Also the New Moon in this context is always the First Cresent and the astronomical new moon does not come into this. SeeTalk:Epact. -- Karl 15 Aug 11h UT.

[edit] Easter Sunday (Western)

If I am reading the Computus page correctly, it is stating that according to the Meeus/Jones/Butcher Gregorian algorithm, Easter Sunday will be April, 11, 2007. My 2007 calender has April 8, 2007 as Easter Sunday. On Jan. 1, I checked the page again and the correct date of April 8, 2007 was in the table named Worked Example Year(Y) = 2007

Did you look at the table with worked examples? The last three lines of the table give the results, and show April 8, 2007 as Easter, just like your calendar (and mine too). I entered the formulas in the table into Excel, and my results agree with the table. Notice that the formulas that appear in the section after the table are for Julian Easter, not Gregorian Easter. --Gerry Ashton 14:54, 30 December 2006 (UTC)

[edit] Chronology

This article has the potential to become a really great article for a complicated subject as the Easter calculation. First, I would discuss the Julian calculation BEFORE the Gregorian calculation.

The reason why I put it after the Gregorian one is that it is now obsolete and I thought people should not read through the old stuff before finding out how it is actually done now. Tom Peters 14:42, 29 March 2007 (UTC)
Julian Easter is a straightforward implementation of the basic principles. It uses a Spring Full Moon date of maximal regularity easily calculated from the Golden Number, then a move to the following Sunday. That, described in modern arithmetical terms, would be an easy summary introduction to the tabular methods (in either order) that were actually decreed. http://www.merlyn.demon.co.uk/estr-bcp.htm#JES. 82.163.24.100 10:36, 18 May 2007 (UTC)

Second, I would expand the article to include the epacts, new moon dates, and full moon dates in the same table.

I disagree. The article, which is already long in its current state, shows the general principle. The current page has the bare workable minimum of needed information, and all the rest can be constructed from that. No need to clutter the page with more and expanded tables; those can be found among the numerous references. Tom Peters 14:42, 29 March 2007 (UTC)

The Easter calculation is based on the Metonic cycle. That is, we assume there are 235 lunar months in 19 solar years. Because the Julian year has an average of 365.25 days, the lunar cycle drifts backwards with the Julian calendar by an average of one day every 312.5 years. Thus by 1582, the lunar cycle fell four days behind the Julian calendar over a 1250 year period of this calculation. Morever, the Julian calendar was too long by 10 days over those 1250 years. Thus, in 1582, 10 days were removed from the calendar to correct the Easter calculation, a new Gregorian calendar had an average of 365.2425 days, and new full moon dates were established for Easter. Thus, with the Gregorian calendar, the lunar cycle drifted later with the calendar by one day every 233 years, or 43 days every 10000 years. To compensate for this drift, the epacts were decreased by an average of 43 times in 10000 years using a specific pattern. The decrease in the epacts caused the lunar dates to appear later by one day except where full moon date April 18th was reset back one month to March 21st.

The Julian calculation really used epacts of 0, 11, 22, 3, 14, etc. but with a specific solar date of March 22nd and a full moon date 14 days later. I would show these epacts and the new moon dates along with the full moon dates on the same table.

When the Gregorian calculation was established, the specific solar date to use for the epact calculation became January 1st (and March 31st and April 29th). Thus the epacts for prior to 1583 were restated to 8, 19, 0, 11, 22, 3, etc. The full moon now came 13 days after the new moon. Thus the restated epacts still produced the same full moon dates. I would show this table for the Gregorian section. I would also show the epacts, new moon dates, and full moon dates from 1583-2599. Thus in 1583-1699, the epacts were 1, 12, 23, 4, 15, etc. In 1700-1899, the epacts were 0, 11, 22, 3, 14, etc. In 1900-2199, the epacts are 29, 10, 21, 2, 13, etc. In 2200-2299, 2400-2499, the epacts will be 28, 9, 20, 1, 12, etc. In 2300-2399, 2500-2599, the epacts will be 27, 8, 19, 0, 11, etc. I would show all these tables along with the new moon and full moon dates.

No please don't: too much information can confuse too. Tom Peters 14:42, 29 March 2007 (UTC)

--Trust101 04:38, 29 March 2007 (UTC)

[edit] Traceable Easter Sunday Date Calculation

The true authorities for the Date of Easter Sunday are :-

  • In the British/Anglican tradition - the annexe to the Calendar Act (now on the Web), and the copy in the Prayer Book;
  • In the Roman Catholic tradition - as far as I know, just the Explicatio of Clavius, expanding the Papal Bull.

The Explicatio is some 500 pages of 16/17th century Church Latin, and the Web copy at ND.EDU seems in poor focus. It is likely that the Parliamentary advisers of the mid-18th Century were good at Latin, and had a better copy. And it appears certain that the method decreed by the resulting Act of Parliament gives results nowhere disagreeing with the Roman Catholic practice.

Granted that we have the algorithms presented by Zeller, Gauss, Richards, Oudin, Butcher, Meeus, Feather, USNO, Mallen, and others; and that bug-free implementations of those all agree within the range of the internal arithmetic used. Nevertheless, it seems desirable that there should be an algorithm directly traceable to the ultimate authorities; and sufficient that it be done from the Prayer Book or the Act annexe.

Such an algorithm is derived and presented, in Javascript, in Web page http://www.merlyn.demon.co.uk/estr-bcp.htm, and tested in that page and in http://www.merlyn.demon.co.uk/estrdate.htm - it can be shown by test forms on those pages to agree with several other algorithms for the whole of a 5,700,000 year cycle. Or more.

Tables I & II in the Prayer Book are for the years 1600 to 8500 etc. The pattern of Table I, for the Sunday Letter, is obvious. The pattern of Table II is not obvious; guidance from other sources implies a simple form fitting the data given. A corresponding expression, valid in perpetuity, can thus be derived from each of those Tables; and Table III can also be reduced to an expression.

One of the implementations on the cited site should cover all years, positive and negative, for which the integer range suffices - ±9E15 in Javascript; another covers only the 32-bit unsigned range, and is rather fast. They are shorter than ones written for simple calculators.

With a copy of the pre-1753 Prayer Book, it should be easy to generate corresponding algorithms for Julian Easter.

82.163.24.100 21:43, 5 May 2007 (UTC)


That Julian Easter algorithm has now been included. It is deduced, rather than traceably derived from proper authority; but tracing should be easy once authority is located.

The work of Zeller deserves a mention in the main page; a link would suffice.

82.163.24.100 11:18, 29 August 2007 (UTC)

[edit] Logical Basis

May an ignoramus say, I came to the page wanting to understand why the date of Easter is so variable, and so complicated to compute. I think it would help other ignorami if this could be set out here. And why it is so important for the title of this page to be such an obscure word.

Afterbrunel (talk) 22:04, 6 January 2008 (UTC)

[edit] Reversion of Excel date for Easter

I have removed the Excel formula for the date of Easter that was added on January 15. I compared it to values given on two pages of the United States Naval Observatory. It matched the dates given from 1980 through 2024 at http://aa.usno.navy.mil/faq/docs/easter.php but when I tried the year 3055 in the form at http://aa.usno.navy.mil/data/docs/easter.php the USNO gave the date of Easter as April 8, while the Excel formula gave April 1.

This formula has been added once before, and somone reverted it without a detailed reason. Now that a detailed reason has been given, I believe I have established that the site http://www.cpearson.com is not a reliable source and algorithms from that site should not be added to this article. --Gerry Ashton (talk) 15:40, 15 January 2008 (UTC)

It is valid for 1900 to 2099 only; see http://www.merlyn.demon.co.uk/vb-date2.htm#ESu. The source of that page contains a valid function for 1900-2199, and another for all years, which could presumably be used in Excel, and indicates where their derivation from an authoritative source may be found. 82.163.24.100 (talk) 12:20, 20 March 2008 (UTC)

Note that Anglican and British Easter are technically only defined up to 8599, the limit of Table I in the Church of England Book of Commpn Prayer, authorised by the Calendar Act. Continuation of the Table can however be deduced using other sources. http://www.merlyn.demon.co.uk/estr-bcp.htm refers. 82.163.24.100 (talk) 12:20, 20 March 2008 (UTC)

[edit] Eastern Orthodox Easter and Passover

I just removed a phrase asserting that Eastern Orthodox Christians "observe the additional rule that Easter may not precede or coincide with the first day of the Jewish Passover." This bit of folklore is widely believed among Orthodox Christians, but it is spurious. The canons clearly prohibit us from taking the Jewish Passover, as currently calculated, into account. (The Jews adopted a new method of determining the date of Passover sometime around the fourth century, and Christians were instructed to ignore the new Jewish practice.) BALawrence (talk) 05:25, 30 March 2008 (UTC)

[edit] The "on or after" saga

The web is littered with mistakes on the definition of Easter dating. This article, however, is of a very high standard in my view.

One of the most frequent mistakes is to abbreviate "on or after March 21" to "after March 21", which of course leads to incorrect results.

In fact, I've just corrected one of these mistakes in this very article!

I advocate that we change all "on or after March 21" phrases to "after March 20", to avoid perpetuating this mistake, and seek your views on this.

NO. We do not have the authority to rewrite the Calendar Act or Papal Bull Annexes, even without change to meaning. Your suggestion would have been acceptable in 1582 or 1751. 82.163.24.100 (talk) 16:33, 17 April 2008 (UTC)

I think this is consistent with the change in meaning of the word "after" from use up to about 300 AD where it meant "including and afterwards", then through an ambiguous phase up to aroung 1750 when it needed clarification, to modern use where it is well understood to mean the same as "following".

All input welcome within Wiki guidelines ;-) Ron Mallen (talk) 13:12, 15 April 2008 (UTC)

Good catch. I assume your AD 300 limit refers to Roman inclusive counting. But that phrase did not exist before AD 300, nor did it exist until much later. I suspect it is a modern phrase meant to succinctly state the original rule given either in tabular form or in more verbose terms. We do not know what the equivalent Greek term was because no Alexandrian texts survive from that period, only tables. The next earliest description is in Latin by Dionysius Exiguus in 525 (I discount Victorius of Aquitaine's confused description in 457). But he did not describe lunae XIV at all—he only gave a few argumenta on how to calculate each parameter, not what they meant. The first thorough analysis is by Bede in 725. Moreover, your suggested change from "on or after March 21" to "after March 20" is not appropriate for Wikipedia because we must use the terminology found in the literature. We are not allowed to invent new terms because this is an encyclopedia, a digest of known knowledge, not a research paper. Any such change is original research forbidden on Wikipedia. — Joe Kress (talk) 22:13, 15 April 2008 (UTC)
I don't agree with Joe Kress that there is a difference between "on or after March 21" and "after March 20". We are writing in modern English and may use any ordinary English phrase with the appropriate meaning. Now, if we were to make up a neologism for the concept of "on or after" as it applies to dates that are not tied to any particular time zone, that would be inappropriate. --Gerry Ashton (talk) 22:24, 15 April 2008 (UTC)
Correct Joe, on the reference to 300 AD Roman inclusive counting; also I agree that historic text uses the "on or after" phrase, I believe due to the need to clarify the ambiguous and changing meaning of the word "after".

However, I agree with your view Gerry, that we need to write this Wiki reference in modern and clear text. We have abundant* evidence that the phrase "on or after March 21" is misused, and I'm strongly in favour of replacing it with "after March 20" to prevent perpetuation of this simple but serious mistake.

  • A check now on Google returned 10,400 references to "Easter" and "after March 21", which includes only 717 references to "Easter" and "on or after March 21" (I hope it's not really that bad!)

I propose that we, as a group, let this topic run for a few weeks, then review collective input. I'll refrain from further comment for now to promote that input. Ron Mallen (talk) 01:13, 16 April 2008 (UTC)

Your Google count is flawed because Easter is indeed "after March 21"—only its Paschal full moons or lunae XIV are "on or after March 21". — Joe Kress (talk) 02:55, 16 April 2008 (UTC)

[edit] Structure of Article

Perhaps the Article should be more clearly subdivided :-
  • 1 Considerations leading to the Rules
  • 2 About the actual, official Rules annexed to Bull and Act, and how they are decreed to be used
  • 3 Algorithms derived from the Rules, suited to modern use, with particular reference to efficient, traceable ones
  • 4 Consequences of the Rules each subdivided into Dionysian (Julian) and Gregorian.
In each case, Julian should precede Gregorian; and the introduction should say so.
If copyright permits, there should be legible images of the necessary material as in the Book of Common Prayer : for Gregorian, that amounts to one paragraph plus three pages. The paragraph is EASTER-DAY (on which the rest depend) is always the first Sunday after the Full Moon which happens upon, or next after the Twenty-first Day of March ; and if the Full Moon happens upon a Sunday, Easter-day is the Sunday after. The pages are the one defining the Golden Number, and the two containing Tables I to III. Images too small to be read, but recognisable, of those three pages are under 33 and 38-39 in http://www.merlyn.demon.co.uk/estr-bcp.htm .
82.163.24.100 (talk) 16:33, 17 April 2008 (UTC)
Perhaps, between section 2 The Official Rules and 3 Algorithms, one could have a section on rules equivalent to the official rules as an aid to understanding and seeing that the following algorithms are correct. The March 20 rule could be put there if deemed necessary. Karl (talk) 08:12, 18 April 2008 (UTC)
Call it pro tem "Section 2.5, Alternative Expressions". IMHO, any mention of March 20 will lead to confusion. Those who cannot understand "on, or next after" are beyond hope. The formal statement above is now imaged on the cited page. The Sunday Letter, given by Table I and explanation, can be readily found from a larger, but simpler, Table, needing less explanation, loc. cit.. It should be noted that the Epact, while no doubt considered in the construction of the Tables, plays no part in the use of the Tables; it exists in my copy of the Book merely as an unexplained column of page 35. Immediately adjacent to the first use of "Full Moon", the description "ecclesiastical" should appear; that is sufficient to indicate that it is not exactly the one in the sky. 82.163.24.100 (talk) 11:38, 18 April 2008 (UTC)

[edit] More on References and Links

(That's a new division. 82.163.24.100 (talk) 11:59, 23 April 2008 (UTC))

The following links provide some original material:
— Joe Kress (talk) 20:53, 18 April 2008 (UTC)
Good links, but :
  • Inter Gravissimas lacks the Easter details
  • Coyne seems to lack the exact Rules
  • Audette seems to lack the exact Rules
  • Opera may lack a straightforward exact statement of the Rules; we know Gauss got it wrong
  • Healton's cited page is limited; pages after 347 are needed
  • BCP 1815 pp. 24-30, corresponding but not equal to the c20 Prayer Book, has the exact rules and must match the original Act of 1751
The BCP material is from the NYPL; might they have the *original* Act, as passed in about 1751?
Since the BCP of c20 has the same Rules as the 1815 BCP, the derivations in http://www.merlyn.demon.co.uk/estr-bcp.htm are now known to be traceable, using only the Web, to Authoritative Rules - but note that the BCP does not truly define the Lunar Correction outside 1600-8600.
82.163.24.100 (talk) 16:07, 19 April 2008 (UTC)
I mistakenly appended my links to #Structure of Page when they should have been appended to #References and Table. They provided "orginal material"—I never said that they gave the rules.
  • The papal bull lacks the rules only because virtually all editions of it lack its attached canons, which contain the rules.
  • I said that Coyne has "historical material", not rules.
  • Audette has the exact rules as stated by the Roman Catholic Church because he includes the canons containing the rules. He has links to both the original Latin and a French translation of them at Les canons. The first five canons define the terms, whereas the sixth canon calculates Easter.
  • Because the complete text of the papal bull, including its attached canons, appears in the preface of volume V of Opera Mathematica, it also has the rules. Each page of Opera Mathematica can be magnified by left-clicking on the desired page. Gauss failed to account for the 2500-year period of lunar corrections in his first algorithm, specifially its last 400-year sub-period, but he corrected it in a later publication.
  • The 1751 Act and its tables can be found in all law libraries in numerous editions of the (British) Statutes at Large. Modern editions differ from the original Act principally by removing the morning and evening prayers (lessons) next to every day of the year. — Joe Kress (talk) 07:39, 22 April 2008 (UTC)
I believe the Papal Bull to be what Gregory XIII issued in 1582; it suthorises, but does not include, its Annexed material. Clavius and Audette have the full material (alas not in English), but I've not yet located in it a part which could be described as "just the complete algorithm". 82.163.24.100 (talk) 11:21, 22 April 2008 (UTC)
You will not find any modern algorithm within the canons because they were written to find Easter via tables, not via mathematical calculation. — Joe Kress (talk) 08:32, 23 April 2008 (UTC)
I meant "algorithm" liberally. The Act and the Book contain a tabular algorithm. I've not located a section of Clavius which provides the method for answering a question such as "What date will Easter Sinday be in AD 5000" and does not contain much other material. 82.163.24.100 (talk) 11:59, 23 April 2008 (UTC)
By the way, I know enough about Latin and Catholicism to say that, while the English translations of the Bull that I have seen do largely give the sense of the thing, they use less than ideal wording - but I don't know enough to remedy that properly. The task needs a Learned Catholic Scholar. Even http://isotc.iso.org/livelink/livelink/fetch/2000/2122/138351/138352/1311683/4020763/2015225/8601RevN005_Inter_Gravissimas.pdf?nodeid=2179035&vernum=0 is just a copy of what was done before. 82.163.24.100 (talk) 11:21, 22 April 2008 (UTC)
That translation was a group effort with input from several Latin scholars. I trust it, except for the comment at the end about the Florentine year, which is wrong because contemporary bulls did not consistently use any March 25 year, even though "Inter gravissimas" was supposedly signed "in the year of the Incarnation of the Lord 1581" ('Incarnation' implies a March 25 year). But it was printed a few days later on March 1, 1582 (IIRC). — Joe Kress (talk) 08:32, 23 April 2008 (UTC)
Being trustable is not the same as being a properly elegant rendition such as a Pope would wish to disseminate. I could, within a day's work, myself verify that the English reflects the intent of the Latin Bull; but I can see that it's imperfect. 82.163.24.100 (talk) 11:59, 23 April 2008 (UTC)
Re the 1751 Act : be careful. Working libraries will have the Act as subsequently amended, since they need to give the current state of the Law. Only 18th century paper, or an image of it, can really be trusted. Also, Law Libraries are not readily accessible to the average web user. 82.163.24.100 (talk) 11:21, 22 April 2008 (UTC)
Not true. All university law libraries I have consulted (which teach law) have numerous editions of the Statutes at Large from the 17th, 18th, 19th, and 20th centuries. Google Books has the 1765 edition of the Statutes at Large containing An act for regulating the commencement of the year; and for correcting the calendar now in use and especially its complete set of Easter tables. — Joe Kress (talk) 08:32, 23 April 2008 (UTC)
I think that you live where university law libraries are affluent. Ordinary people generally don't have ready access to such. Indeed, all the books I could possibly want are within what I would once have considered as walking distance; but that does not help me now. Obviously you are better at searching than I am; that's a valiable link, which I suggest should be added to the article. 82.163.24.100 (talk) 11:59, 23 April 2008 (UTC)
If possible, I do like to live near large university libraries (although I do not at the moment). But I have been known to travel a considerable distance to a library which has what I want in its catalog. It didn't take too long to find that Google Book. I first tried "Statutes at Large", but found too many results, most of which weren't British. I then entered the first half of the exact title of the Act in the Google Book search feature ("An act for regulating the commencement of the year") but none of the results were acceptable, so I removed the quotes. I found the cited book on the fifth page of the new results.
Surprise! While repeating the above sequence to make sure I remembered it correctly, I discovered that Google Books has the very rare book The ecclesiastical calendar: Its theory and construction by Samuel Butcher (1877), no doubt containing his famous algorithm (at least famous to computists). I also found the site containing the Act at the national archives of the UK in its revised statute form, including all tables, but not in its original form. The Act and at least some of its tables also appear on a Ministry of Justice page. Both indicate ommissions made by acts subsequent to the original act. — Joe Kress (talk) 03:13, 24 April 2008 (UTC)
I cannot see the actual full contents of Butcher at Google - can you? Looking at the expanded contents list, I see that his wording there about 2698 is not quite perfect. J & G Easters of the same year number will last coincide then; but after about 50,000 years coincidences of day between Easters of different years will start.
The cited merlyn site has for a year or so had a link to statutelaw. I think the content of opsi is a mere copy. The opsi site has provision for showing the original material, but the relevant stuff is not (yet?) present.
IMHO, the present Prayer Book more closely represents the intent of the 1751 Parliament than the Database does.
82.163.24.100 (talk) 11:59, 24 April 2008 (UTC)
I have not had time to study Butcher, but the blue underlined entries in the table of contents do not work when viewing a Google Book online (they do not exist in a downloaded PDF version). Instead, type in the indicated page number in the box immediately above the image.
The opsi site has more original content because it provides a few hyperlinks to footnotes—the statutelaw site does not. Both are copies of the printed version. Provision is made at the opsi site to display the original version, but those before 1837 are not yet available. — Joe Kress (talk) 19:36, 24 April 2008 (UTC)
Clicking the Statutes at Large link you provided above shows me the contents of a "Read this book" tab; but clicking the Butcher link above shows just the About this book tab. You seem to be privileged. FYI, Butcher's algorithm, via Montes, is tested at merlyn, which also now has traceable Julian Easter. 82.163.24.100 (talk) 12:21, 25 April 2008 (UTC)
There do seem to be two different presentations. For both books I see two tabs at the upper left, "About this book" and "Read this book". For both books, "Read this book" is active after clicking on the talk page link I provided. For both books there is a "Contents" entry in the right column, which, when expanded, only provides a link to the title page for the Statutes at Large, but provides links to all entries within the Table of Contents that are highlighted when expanded for Butcher. Clicking on any expanded entry immediately displays that page (for Butcher, the TOC words don't appear on the actual page). But when the "About this book" tab is clicked for Butcher a "Contents" section appears below the title page, which can be expanded ("more >>") to show all entries, all of which, when clicked, show the actual page. Also on Butcher's "About this page", two buttons appear immediately below the title page, "Read this book" and "Download PDF" (the latter is 9.2 MB). The only distinction between your presentation and mine I can think of is that Harvard, the source of Google's Butcher, or Google itself restricted its full use to within the United States, which seems unlikely given that its copyright expired long ago in all countries. — Joe Kress (talk) 18:21, 25 April 2008 (UTC)
The algorithm in this Wikipedia article has virtually nothing in common with Butcher's algorithm, so cannot be attributed to him. Because both calculate the Gregorian Easter, I'm sure that the Meeus algorithm given here (which is virtually identical to that given by H. Spencer Jones in General Astronomy (1922) page 73) can be derived from Butcher's, who states that his algorithm is substantially the same as that given by Delambre in Histoire de l'astronomie moderne (1821) (Tome i. pp.24-25). Butcher explains his algorithm on pages 197-210 (articles 135-143), including worked examples, with the Gregorian algorithm itself on pages 204-5 and the Julian on page 209. — Joe Kress (talk) 07:31, 27 April 2008 (UTC)
Delambre was presumably a Roman Catholic, and Meeus may well be. Although Meeus is undoubtedly right, that's a rather long and tenuous chain of traceability to the Papally-blessed document; and also unsatisfying to Anglicans. Simon Kershaw has derived a distinct algorithm; see http://www.oremus.org/liturgy/etc/ktf/app/easter.html and link. It's one of the faster ones. 82.163.24.100 (talk) 19:24, 27 April 2008 (UTC)
FYI: I can see Delambre's text, but not that of Spencer Jones. 82.163.24.100 (talk) 19:24, 27 April 2008 (UTC)
If you have access to a high-speed connection, you may be able to download the PDF versions:
— Joe Kress (talk) 21:09, 28 April 2008 (UTC)
Both give me a "404" message. IMHO, article citations of Google Books should be marked to show whether full, partial, or no text view is offered, and whether those are available to all. 82.163.24.100 (talk) 10:02, 28 April 2008 (UTC)
All Google Books are marked as "No preview available" (nothing viewable), "Snippet view" (only a few scattered sentences are shown), "Limited preview" (many pages viewable, but certain critical pages are not), or "Full view" (all pages are viewable, with a PDF version). I never cite a Google Book unless it is flagged as "Full view" or is flagged "Limited preview" and I have been able to view the specific page containing the citation. Your situation appears to be an individual exception which no one who cites a Google Book can know about. — Joe Kress (talk) 21:09, 28 April 2008 (UTC)
I wrote that the citations should be marked; that means here in Wikipedia. I could not see the text at the Public Library either; perhaps instead it is you who is especially favoured. FYI, I skimmed through the first volume of Delambre; but really I am mainly interested in testing computer-algorithms and in deriving them from original authority - Explicatio and Calendar Act, or representations thereof. 82.163.24.100 (talk) 21:29, 28 April 2008 (UTC)
After anonymously linking to this talk page at a medium-sized university library and at a medium-sized county public library, I had no trouble accessing any hyperlink on it, either the page views or the PDF downloads. Thus I don't have any special privilege, rather your access appears to be restricted in some manner. I can think of two more possibilities, neither likely: Either your browser in damaging the link provided or your country is restricting your access to some URLs for political reasons and these links are caught in the dragnet. — Joe Kress (talk) 02:02, 1 May 2008 (UTC)
For completeness, here are the PDF links for the other Google Books referenced:
— Joe Kress (talk) 06:27, 28 April 2008 (UTC)
Two in Mainland Europe report seeing only one tab : one in France, seeing it in French, and one in Austria, seeing it in English. 82.163.24.100 (talk) 17:58, 17 May 2008 (UTC)
Recently noted on HASTRO-L, The History of Astronomy Discussion Group: "Irritatingly, Google is operating a policy of geographic selective availability, and the full publication is not available for download from Europe". Although this refers to a 1982 publication that is still in copyright, it may apply to these old books. —Joe Kress (talk) 03:56, 30 May 2008 (UTC)

[edit] 14th Day or Full Moon?

Consider the second paragraph of the Article, before the History section.

The Book of Common Prayer of the Church of England, in a Preface section decreed by the Calendar Act, does not use the fourteenth day as such; it refers to the Full Moon. I suspect that Catholic sources do explicitly refer to the fourteenth day.

It seems inappropriate to say that the canonical version uses the fourteenth day, without qualification. I suggest a transposition to : The canonical rule is that Easter day is the first Sunday after the nominal full moon (the 14th day of the lunar month) that falls on or after 21 March (nominally the day of the vernal equinox).

82.163.24.100 (talk) 19:58, 20 April 2008 (UTC)

There are at least two "canonical versions", the 1751 Anglican version already quoted and the original 1582 Catholic version, which is the first sentence of the sixth canon attached to the papal bull [3]: "Pursuant to the order of the holy Council of Nicaea, Easter, on which other movable feasts depend, is to be celebrated on Sunday immediately following the fourteenth day of the first month (the Hebrews called the first month the lunar month in which the fourteenth day coincides with the vernal equinox, i.e. March 21, or the nearest following)." Other canonical versions probably appear in the German and Swedish laws implementing the Protestant reformation astronomical and Gregorian Easters. — Joe Kress (talk) 07:39, 22 April 2008 (UTC)
Then let The canonical rule is that be omitted : Easter Day is the first Sunday after the nominal full moon (the 14th day of the lunar month) which falls on or after 21 March (nominally the day of the vernal equinox). 82.163.24.100 (talk) 10:26, 22 April 2008 (UTC)

[edit] Tabular Methods

The current Tabular Methods section describes the historical arguments by which the dates of Easter were decided. As far as I know, the detailed authority in the Catholic tradition is in the Explicatio of Clavius.

But, for the British Empire and (then) Colonies, the authority is the Calendar Act Annexe of 1751; and, as its method is required by the Act to be in the Prayer Book, that seems also to be the general Anglican authority. Naturally it is chosen to agree with the Catholics.

So, in practice, the method of determining British (and American, etc.) Easter from Authority is quite different from what is currently described in the Article. In general, one determines the Golden Number, then uses three Tables to determine the Sunday Letter, a Cypher, and the date of the Paschal Full Moon, from which the date of Easter Sunday follows; but a simpler Table can be used for 1900-2199. Clavius' details were employed in the construction of the method, and play no subsequent part in its use.

British Easter before 1753 was also defined by a Table in the Prayer Book, the use of which is not described in the Article.

http://www.merlyn.demon.co.uk/estr-bcp.htm, in deriving an algorithm traceable to the Book, verifies its processes by computing matching Tables; but assumes that a description of how to use them is at hand.

I don't yet know whether there is, on the Web, a nicely-legible representation of the Easter material in a current C of E Book of Common Prayer.

  • It might be held that such methods do not fall unter the title Computus; but they should at least be mentioned herein. Perhaps Computus should be reserved to be (mainly) for material from before, say, 1750, with another page on calculation and consequences.

82.163.24.100 (talk) 12:07, 26 April 2008 (UTC)

On page 240 Butcher states that before 1662, the English Prayer Book did not have a definition for Easter day. On the next page he states that in 1662 [through 1752] the Prayer Book included the definition: "Easter Day is always the first Sunday after the first Full Moon which happens next after the one and twentieth day of March. And if the Full Moon happens upon a Sunday, Easter Day is the Sunday after." He notes that this is wrong because it does not allow Easter to occur before March 23—it does not allow the Full Moon to occur on March 21. — Joe Kress (talk) 07:31, 27 April 2008 (UTC)
I cannot swear to "not before 1662", but what I've heard supports that. The Prayer Books of 1662 & 1683 do have the bad version. The Act (in S@L 1765) cites in S.III the bad version as being in the then-current Book; its Annexe gives, for inclusion in the Book, the correct words, used to this day.
The Books of 1662 & 1683 have a Table indexed conventionally by Golden Number and Sunday Letter giving the Easter date; Mar 22 is at XVI,D and Apr 25 at VIII,C. The merlyn page reproduces that by calculation using the JPFM algorithm deduced from other sources, amd. has a copy of its instructions. 82.163.24.100 (talk) 18:57, 27 April 2008 (UTC)

[edit] Calendar Act and Prayer Book Method

Proposed part for Article

The Tabular Methods section describes the historical arguments and methods by which the present dates of Easter Sunday were decided in the 16th century.

In Britain, then still using the Julian Calendar, Easter Sunday was defined, from 1662 to 1752, by a simple Table of dates in the Anglican Prayer Book (Act of Uniformity 1662). The Table was indexed directly by the Golden Number and the Sunday Letter, which were presumed to be already known.

For the British Empire and Colonies, the new determination of the Date of Easter Sunday was defined by the Calendar (New Style) Act 1750 with its Annexe. The method was chosen to give dates agreeing with the Gregorian Rule already in use elsewhere. It was required by the Act to be put in the Book of Common Prayer, and therefore is the general Anglican Rule. The original Act can be seen in Statutes at Large 1765.

The method is quite distinct from that described above. For a general year, one determines the Golden Number, then uses three Tables to determine the Sunday Letter, a Cypher, and the date of the Paschal Full Moon, from which the date of Easter Sunday follows. A simpler Table can be used for limited periods, such as 1900-2199, during which the Cypher (which represents the effect of the Solar and Lunar Corrections) does not change. Clavius' details were employed in the construction of the method, but play no subsequent part in its use.

Page http://www.merlyn.demon.co.uk/estr-bcp.htm, in deriving an efficient computer algorithm traceable to the Prayer Book and the Calendar Act, verifies its processes by computing matching Tables; but assumes that a description of how to use the Tables is at hand.

If the above is considered satisfactory, after adjustment if necessary, please signify that by putting it in the Article.

ASIDE : The original Calendar Act and the Prayer Book tabulate, but do not define, the Epact. What algorithmic definition of the Epact is there applied?

82.163.24.100 (talk) 17:53, 4 May 2008 (UTC)