Talk:Epact

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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)

[edit] 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.