Talk:Computus

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-- 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)

Contents

[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)

[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)

[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)

[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)

[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)

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)

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