Talk:Epact

Age of the Moon

User:Karl Palmen writes:

The section on the age of the moon is not aparently NPOV. So I have moved it here.

It asserts that the age of the moon equals the day of the lunation. Also the concluding paragraph contradicts the Catholic encyclopeadia article referenced and the end of the article.

I observe that an epact of "*" (0 or 30 or nulla) for a year, implies a 1st day of the lunar month on the 1st day of the year. If the epact is an age, this would mean that the age is 0 on day 1. Hardly consistent. All this involves the usual confusion between ordinal counting and cardinal (or real) numbers - people used to be "in their first year", nowadays your age is 1 year *after completing* your 1st year. So what is the age of the Moon on the 1st day of the month, traditionally? For that matter, what is the age of J.C. today? This is related to the milennium controversy (was 1 Jan 2000 or 1 Jan 2001 the start of "the" new milennium?).

And incidentally, the Catholic Encyclopedia can have it wrong too... -- Tom Peters 13:07, 15 Aug 2003 (UTC)

age of the Moon

The epact is often defined as the age of the Moon at the begin of the (solar) year. Now when a new lunar month begins on 1 January, the epact is 0. However we count the days of the lunar calendar as ordinal numbers, i.e. in this case the 1st day of January is also the 1st day of the lunar year and the 1st day of the lunar month. We can accordingly assign an age of 1 day to the Moon, if we follow the ancient convention that the lunar month starts when the New Moon is first visible. This is actually some time after the astronomical conjunction of Sun and Moon (also called Dark Moon), when the "astronomical age of the Moon" is 0. Indeed the lunar calendar used for Calculating the date of Easter in the Gregorian calendar has its months starting systematically a day after the astronomical New Moon. In this reckoning the astronomical opposition of Sun and Moon indeed usually falls on the 14th day of the lunar month, which is consistent with the tradition of having the Paschal Full moon on the 14th day of the spring month.

The epact can then be defined as the age of the Moon on the day before the begin of the (solar) year. This is not the same as the age of the Moon on the last day of the previous year, because the epact may be corrected by 1 at the start of the new year.

Karl August 15 10h UT

Oh well, how about this text then:

"The epact is often defined as the age of the Moon at the begin of the (solar) year. Now when the epact is 0, 1 January is also the 1st day (i.e. the day of first visibility of the lunar crescent) of the 1st lunar month. However age used to be expressed as an ordinal number, starting with 1 (a newborn baby was said to be "in its 1st year"). A supposed age of 0 of the Moon is translated to the 1st ordinal number, which is an apparent discrepancy.

Also there has been a historical change in the definition of "age". A baby that was said to be "in its first year", is now called "0 years old". Events used to be timed with a hierarchy of periods labeled with ordinals numbers (e.g starting point is 1st day of 1st month of 1st year). We now interpret time as a continuous variable starting from 0 at some specific moment, and count fully completed days and years for age. But calendar dates are labels that are still expressed the old way, as ordinal numbers. This is the underlying reason for the milennium controversy (start at 1 January 2000 or 2001?).

Also it has become custom to define New Moon at the moment of astronomical conjunction, which is at the same moment everywhere on Earth, and take that as the zero point for counting the (continuous) age of the Moon. In contrast the crescent Moon becomes first visible one or two days later, and the moment of first visibility depends on the place on Earth.

The epacts of the ecclesiastic calendar are usually still consistent with the age of the Moon in the modern sense, if interpreted in the following way:

1. define New Moon in the modern astronomical sense;
2. count age continuous from that moment;
3. define the epact as the age in the modern sense (i.e. count completed days) at midnight of 1 January.

"

-- 194.109.250.130 21:00, 15 Aug 2003 (UTC)

Tom has given here two alternative interpretations of the concept of age of moon, which are both different from the one normally used in the description of the Calculation of Easter.

1. Use Ordinal Numbers for Age. This is never done as far as I know in the West, but is done in the East. For example in China a new born baby is age 1 and becomes age 2 at the nexct new year.
2. Define the age of the moon as the number of days AFTER the day as the (reckoned) astronomical new moon.

Karl 18 Aug 2003 09h UT

Karl misunderstands. Age has always been counted in ordinal numbers of some unit of time in the West too (until the 19th cy. I think). Painted portraits for instance typically have a note "in aetas sui xxxxi", i.e. "in his 41st year"; nowadays we call that person 40 years old. Pertinent to this discussion: Dionysius always refers to "the 14th moon". Presumably the lunar month then started with the "1st moon", which was on the 1st of January when the epact is 0 ("nulla" with D.E.). There is however never an "0th moon". That is the inconsistency I point out when interpreting "epact = age of the Moon on 1 Jan." using that old (ordinal) definition of age.

But nowadays we do count age from 0, and as a continuous variable rather than an ordinal number (even when counting only completed days or years). This causes 3 other problems:

• you have to define where this 0-point lies;
• you have to define when you evaluate the age, in case you wish to assign a single age to a whole day;
• in any case the traditional tables of epacts may match age starting from 0 at the time of first observation of the lunar crescent, but then the "1st moon" has age 0.x, and the "14th moon" has age 13.x, which is as confusing as the original inconsistency as I noted above.

So the statement "epact = age at 1 Jan." is valid only if we interpret the concepts in the way I specified in the proposed paragraph.

-- 167.202.196.71 12:50, 18 Aug 2003 (UTC)

So it seems that the concept of age of moon is far from clear-cut. Therefore, in discussions about such things as epacts or Easter Calculations, it is better to use something else, such as day of moon (defined to begin with new moon) or number of days after new moon. -- Karl 19 Aug, 13h UT.

Epacts in Book of Common Prayer

In the Preface in the Book of Common Prayer of the Church of England, in a section decreed by the Calendar Act, there is a page listing the Moveable Feasts for about 40-50 years. Its third column contains Epacts. The Act and Book do not seem to have any definition of the Epact. Just what formal definition does the Church use?

Note that such a table is in Statutes at Large 1765, but not in the database which represents the Act as amended to date.

I suggest that the Article should contain a short section explicitly answering this point.

82.163.24.100 (talk) 10:01, 3 May 2008 (UTC)

Lilian (Gregorian) epacts

The current article text under "Lilian (Gregorian) epacts"

• (a) seems to get it just right where it comes to the actual rules of the solar equation and lunar equation; but
• (b) it also contains a quantity of material that seems completely unsupported, and at best dubious, where it comes to the 'Metonic relation', 'pure' or otherwise, and to the unit called the 'tithi'.

I suggest that the relevant sources here are those that refer to the actual work that culminated in the Gregorian reform of 1582, especially the papers given in the 1983 commemorative conference. These sources (primarily the papers by O Pedersen, J D North, G Moyer and A Ziggelaar) appear to show that the lunar equation in the Lilian system of epacts was a systematic empirical adjustment, intended to reflect the fact that the Moon's mean rate of motion had turned out to be just a little faster than the expectation embodied in the traditional form of 19-year cycle. In the second half of the sixteenth century, full moons were occurring much sooner than the dates indicated on the traditional tabular basis (which by then had been in use for over a thousand years). According to the text of "Inter gravissimas" the paschal full moons needed to be "put back in place" from a deviation of something more than 4 days ("et XIV paschalem suo in loco, a quo quatuor et eo amplius dies hoc tempore distat, reponendam".) Lilius' periodical adjustment was intended as a correction to bring the tabular epact value closer to the real age of the Moon, and prevent any repeat of the long-term divergence which had been seen with the traditional tables.

A temporary 'patch' had been applied in the 1568 edition of the Breviary, namely, to move the Golden Numbers up four places and to warn that they would need to be reviewed again and moved every 300 years or so. But the text of "Inter gravissimas" complains that previously-proposed solutions were not long-term ("neque perennes erant"), and it praises Lilio's effort for providing in principle a perpetual arrangement to restore "all the things in the calendar that had got into disarray" so that there would be no future "mutation" ("omnia quæ in calendario collapsa sunt, constanti ratione et sæculis omnibus duratura, sic restitui posse ostendit ut calendarium ipsum nulli umquam mutationi in posterum expositum esse videatur.").

In all of this there seems to be no reference to Metonic relations or tithis. It seems appropriate to take out the material about these factors, unless good sources are given for their relevance to the 16th-century work. Terry0051 (talk) 01:01, 4 December 2009 (UTC)

Terry, I notice your edit a bit late. I think you misunderstand. Your text does not explain why the reformers bothered to have both a solar equation and a lunar equation, instead of just 43 epact adjustments evenly spread over 10000 years. The only explanation I can think of is that they tried to undo the effect of the skipped Gregorian leap days, and then adjust the ratio of the synodic month to the (Julian) calendar year. But as explained, if this was their intention, then it is mistaken. It is a mathematical fact, as explained in my text in 2 different ways, that Lilian epact corrections are 1/30th of a synodic month, and not full days on average. Unfortunately, both in the Canons and in his explicatio, Clavius explains the use of the epacts but is vague on the reasons and background of the construction. Likewise the commemorative conferences spent much attention to the tropical year and the solar calendar and the history of the computus, but lacks a thorough analysis of the lunar calendar.

Tom Peters (talk) 10:22, 20 February 2010 (UTC)

definition of epacts

I see the quality of the article has eroded since 2007. First, someone "cleaned" the prose of my translation of the original verbose Latin quote for style, and then removed the original text altogether. Then it was claimed that this text from the Gregorian calendar Canon was the first to define epacts as the excess of the solar over the lunar year: but it was only an explanation, not a formal original definition, of a concept that had been widely known among computists for over a millennium before the reform. Then Terry picked up the definition of "age at 1 January" from the paper by Perdersen in the commemorative conference: he defines it as age at 1 January, and shows that epacts were introduced in the computus with the latercula of 354: Terry here incorrectly assumes that the "1 January" is then the older, original definition. However from the very name it is obvious that the "excess" definition is the original one of the concept of epacts, and Pedersen only uses the equivalent "1 January" definition for computist convenience. Moreover, as you could have seen on this discussion page in the thread from 2003, the "1 January" definition is problematic, and therefore is best avoided. Also see the first sentence in the lemma on epacts in the Catholic encyclopedia, which succinctly supports my view: http://www.newadvent.org/cathen/05480b.htm . So I am inclined to revert this article back to its 2007 version! Tom Peters (talk) 19:28, 20 February 2010 (UTC)

Sorry, I only just noticed this. This looks like a matter on which not only sources are important but also careful reporting of their content and area of application. The 'added days' definition does not look at all compatible with the usages of 'epact' that have been current for the last few hundred years e.g. in the Prayer Book and other easter-calendar uses; these current usages appear clearly to refer to 'age of the moon on day x', generally January 1. Maybe, in the current lead para text, 'original' could be disputed, but the cited source shows that the 'age on day x' usage is clearly older by a few centuries than the Dionysian easter calculus. It clearly goes back to a time when the records can scarcely be expected to be more than fragmentary, so it seems unlikely that an earlier specimen of the etymological usage could be found.

The older state of the article (I don't know if this includes 2007) contained material about time units in relation to epact (especially Gregorian epact) that seemed to be unsourced, unreliable, and anachronistic if not also irrelevant. A proposal just to wind the clock back on the article text to 2007 therefore looks to be highly undesirable from the point of view of article reliability and quality. But I'd agree that the 'added days' etymology seems to have some claim to early mention in the lead paragraph as long as it is differentiated from the recent and current 'age on day x' usage which also needs to be explained there. A considered amendment along those lines might strengthen the quality of the article usefully. Terry0051 (talk) 00:29, 28 March 2010 (UTC)

Late response (it's getting tedious to repair mistakes again and again in Wikipedia).

1) The Catholic encyclopedia says: "The surplus days of the solar over the lunar year; hence, more freely, the number of days in the age of the moon on 1 January of any given year." So The "1 January" definition is a supposedly equivalent definition for computistic convenience. Mind that in the Middle Ages many "styles" for the start of the year were used, 1 January has become a standard recently. Epacts were used before the Dyonisian computus of 525 (which made them unnecessary for the computus): Pedersen as quoted states that they were introduced by some Augustalis (possibly) in the early 3rd century, and he mentions 1 January, but since the table itself apparently has not been preserved, it is not completely clear if Pedersen explains the concept using current practice, or that we actually know that Augustalis used 1 January already. Anyway the current description does not explain the etymology. So the initial text of this page should be changed to something more like the original one.

I have to add that the"age of the Moon at 1 January" is problematic or simply wrong. "Age of the Moon" is a problematic concept when used with a calendar counting ordinal days, on a round world with a dateline. Moreover consider the following: in Judeo-Christian computus the 14th day of the lunar month is the day of the Full Moon. The 1st day of the month has always been that of the first visible crescent, since the Babylonians unto present-day muslims: so not that of the conjunction, which has the astronomical age 0.0, and precedes the Full Moon by almost 15 days. Now an epact of '*' = day 30 or equivalently day 0. A year with epact * has the first day of the lunar month, the ecclesiastic New Moon, on 1 January: not the 30th or 0th day. So the epact is the age of the Moon on 31 December of the preceding year, not the age on 1 January.

Like it or not, but the Gregorian reformers did not define the epact in a way that you can conveniently quote in Wikipedia. They presented tables and how to use them, and definitions must be deduced from them. The "age at 1 January" is bogus, whatever the Catholic Encyclopdia and Pedersen say. If you use that definition you get the wrong Easter dates.

2) The second statement of the introduction (that the epacts differ by 11 days from year to year BECAUSE a solar year is longer than a lunar year) is a false interpretation of the quote from the canon of the Gregorian calendar. It says that epacts are CALLED this way because the solar year exceeds the lunar year by so many days, which also is why I think it should go into the initial definition. This is also a matter of perspective: epacts deal with reckoning solar years and lunar YEARS, where the lunar year is central and the solar year is deviant. The way it is put now, the solar year is central, and there is some funny number mysteriously related to the Moon that changes by 11 days every year for a reason that does not become clearly apparent.

3) The fact remains that Lillian / Gregorian epacts, in contrast to the original "Dyonisian / Julian" expacts" are NOT measured in days, even though the reformers apparently were not aware of that (and apparently many modern calendrists still do not either). This has already been pointed out by Viete around 1600, and why this is was explained and self-evident in the original Wiki text, but the current addition dropped all that and contines the confusion by implying that Lillian epacts are days. This section must be repaired.

Tom Peters (talk) 08:46, 15 August 2010 (UTC)