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Notes to Excel formulas

Both formulas on article page work correct only from 1900 to 2203 in the 1900 date system and provide only the Gregorian Easter Sunday dates

Calculate Gregorian Easter date

The actual state is a reduction to <100 characters with full functionality from 1900 to 9999

Excel community: http://www.online-excel.de/fom/fo_read.php?f=1&h=58861&bzh=72926&ao=1#a123x

The Gregorian Easter period began 1583 and not 1900 - and that's why it must be enhanced (1900 date system).

Notice: This formula provides the same results like Gauss from 0001-9999, you could enhance it again with starting =TEXT(A2,"0000")&...
17:42, 23 June 2013 (UTC)

Calculate Julian Easter date

As date: The following works from years 1900 to 9999 (1900 date system)

As text: The following works from years 0001 to 9999 (1900 date system)

Combination of Julian/Gregorian Easter date

As YYYY-MM-DD text: The following works from years 0001 to 9999 and any breakpoint from 1 to 9999 (here it is 1583), taking 1900 date system

Frank Schneider, 08:55, 5 November 2013 (UTC)--

First two Excel formulas of main page have a lot of restrictions - is it possible to replace them? 22:10, 30 September 2013 (UTC) — Preceding unsigned comment added by 85.199.76.112 (talk)

I added the universal formula. Frank Schneider, 08:55, 5 November 2013 (UTC)--

Addition to table, claiming regular pattern

Is the table addition in this edit by User:Q5968661 comprehensible and sufficiently connected to the remainder of the article that readers will understand why it is included? Is this table useful to readers, and therefore merit inclusion? Is "regular pattern" a correct and useful titile for that portion of the table? Jc3s5h (talk) 19:54, 3 March 2013 (UTC)

• Simplify or explain. The table is confusing, but if additional explanation were offered it would make more sense. Alternatively, the article could include a simplified walkthrough of what all of those dates mean for a single year. Andrew 19:21, 5 March 2013 (UTC)

  This makes sense. Perhaps split into two tables preceded by explanations? Comparisons should still be easy enough for reader, if tables are in proximity to each other.  — daranz 20:35, 14 March 2013 (UTC)

Mental arithmetic

>> step1 needs to be bracketed to clarify it is the +29 that is conditi0onal on y mod 19 = 5 or 16. >> and some clarification is also needed on what mod 30 really means here, since mathematically it should be in the range 0-29 or (sometimes) -14..15 but in the samples 55 mod 30 = 25 but 88 mod 30 = -2. A1jrj (talk) 14:01, 19 May 2013 (UTC)

Step one: using 45 - (y mod 19 × 11) mod 30 + 29, if y mod 19 = 5 or 16, to determine the date of PFM (PFMd).

Step two: using (y mod 100 + + c + PFMd) mod 7 to determine the day of PFM (dPFM).

Step three: using PFMd + 7 - dPFM to determine the date of Easter (if the result > 31 the month = April).

where c = 3 for years 1900 ~ 1999, c = 2 for years 2000 ~ 2099, and c = 0 for years 2100 ~ 2199.

Take a few examples:

• The year 2000 mod 19 = 2000 - 1995 = 2000 - 2000 + 5 = 5 hence 5 × 11 mod 30 = 55 - 30 = 25, so PFMd = 45 - 25 + 29 = 49 (Apri 18), and 2000 mod 100 = 0 hence dPFM = (0 + 0 + 2 + 49) mod 7 = 0 + 0 + 2 + 0 = 2 (Tuesday), so Easter Sunday = 49 - 31 + 7 - 2 = 18 + 5 = 23 April.
• The year 1992 mod 19 = 16 hence 16 × 11 mod = 26, so PFMd = 45 - 26 + 29 = 48 (April 17), and 1992 mod 100 = 92 hence dPFM = (92(8) + + 3 + 48) mod 7 = 1 + 2 + 3 + 6 - 7 = 5 (Friday), so Easter Sunday = 48 - 31 + 7 - 5 = 17 + 2 = 19 April.
• The year 2117 mod 19 = 2100 - 2090 + 17 - 19 = 2100 - 2100 + 10 - 2 = 8 hence (8 × 11) mod 30 = 88 - 90 = -2, so PFMd = 45 - (-2) = 47 (April 16), and 2117 mod 100 = 17 hence dPFM = (17 + + 0 + 47) mod 7 = 3 + 4 + 5 - 7 = 5 (Friday), so Easter Sunday = 47 - 31 + 7 - 5 = 16 + 2 = 18 April.

So it is very easy to determine the date of Easter! --Q5968661 (talk) 10:06, 8 March 2013 (UTC)

Hello !!! Try it the other way around. I'll give you the dates: 22 March and 25 April, and you determine the year (the last and the next occurrence). Thanks. :–D 195.91.110.132 (talk) 16:07, 23 March 2014 (UTC)

Still confused

I am still confused as to why the golden number (date of the full moon) can be only 19 different days when a month is 30 or 31 or 28 (or more appropriately a lunar month is 29 or 30 days). Are there some days in the range of Mar 21 - April 20 or whatever that cannot be a full moon? (The golden number of any Julian or Gregorian calendar year can be calculated by dividing the year by 19, taking the remainder, and adding 1). This leaves only 19 possible days for a full moon out of 29 or 30.

The golden number is note a date; I don't have time to explain right now. Vincent J. Lipsio (talk) 19:09, 17 April 2014 (UTC)

In the Julian computus, there are only 19 dates in each 29-or-30-day cycle that the full moon can occur on. By the time of the Gregorian reform, those dates were about 4 days in error compared to the actual moon. In the Gregorian computus, in any given century there are only 19 dates possible for a full moon, but at the start of some centuries those dates shift ahead or back by one day because of the "solar correction" and "lunar correction" components of the formula for the epact. Indefatigable (talk) 19:13, 19 April 2014 (UTC)

I don't know all the details of the computus, but I do know this much. First, don't confuse the actual astronomical events with the calendar. Predictive calculation of astronomical events was not possible when computus was first created, nor even when the Gregorian reforms occurred. One could only tell when these events occurred through observation of the occurrence, at or after the fact. But the church needed to predict the Paschal moon in order to tell when Pascha was supposed to be celebrated, and only after that date was set could it know when to begin preparations for Pascha, the season that developed into Great Lent. They needed not only to be predictive, but up to two months in advance! The church was practical. It used the calendar as the best means then known to look ahead. Then it set up the computations based on the calendar. And in earliest times, that was the Julian calendar in the west, and the Alexandrian in the east (at least for the easterners who weren't depending on the Jews to make determinations of when Passover occurred, on the basis of the Hebrew calendar. (See the issue about that which was considered at the First Council of Nicea.)

Ancient observations of what had occurred historically were much more sophisticated than is normally supposed today, and records had been kept over centuries of time. Alexandria's famous library was a primary repository for much of such ancient knowledge, and that is why Julius Caesar went there to consult the best astronomers in constructing the Julian calendar in the first place, and why that calendar was a practical breakthrough in calendar quality. (The Alexandrian one was no slouch either.) But the ancients knew that it took 19 years for the moon to run through a whole number of lunar cycles within a whole number of years, and that is what the 19 is about in the computus. Computus also has to consider what days of the week the Paschal moon falls on, since Pascha must come on a Sunday following that moon (not on that moon). The reason in the Gregorian computus that there are only 19 dates possible in a given century (if that's really true), would have to do with the fact that in the Gregorian calendar, only one century year out of four is a leap year (unlike the Julian calendar). The computus accounts for leap years, because it is based on the calendar, and you have to account for that in order to keep the days of the week right.

Both calendars, over a sufficient number of centuries, and the Julian calendar more so, contain "inaccuracies" compared to actual astronomical events. They accumulate those inaccuracies over time, and eventually the discrepancies add up to a certain number of days. Within the last 50 years we have become able to calculate astronomical events, both observationally and predictively, with such accuracy that we can notice fractions of seconds (today, even microseconds or less) of differences. And we know that unpredictable astronomical events can and regularly do introduce tiny fluctuations in all these measures. We even adjust for those on a fairly regular basis now - perhaps you've heard of the "leap second". Suffice it to say that no calendar will ever be able to make predictions with complete accuracy if you project it far enough into the future. Computus survives because, in principle, it is still practical. Hope this helps some. Evensteven (talk) 20:01, 19 April 2014 (UTC)

Also, this year in Illinois the Vernal Equinox was Mar 20th. The equinox happens at a certain instant and in Illinois it was on Mar 20 but in Tokyo it was already Mar 21 since they are like 12 hours ahead of Illinois. What time zone do they use for equinox?

The meridian of Jerusalem by default; there was no knowledge of the problem (of longitude) when this algorithm was devised. Vincent J. Lipsio (talk) 19:09, 17 April 2014 (UTC)

Since the authors of the Gregorian calendar were working in Italian cities, I expect their tables were calibrated to the observations of local Italian astronomers. Indefatigable (talk) 19:13, 19 April 2014 (UTC)

One last question. Is Passover always in the middle (14th) of a month (often coinciding with Easter but occasionally almost a month ahead due to the extra month added sometimes to the year)? So is Passover always on a full moon? — Preceding unsigned comment added by 63.84.231.3 (talk) 17:58, 17 April 2014 (UTC)

The month (Nisan, IIRC), and all other months on the Jewish calendar, start at a new moon, so the 14th of the month is, therefore, a full moon, Vincent J. Lipsio (talk) 19:09, 17 April 2014 (UTC)

Drift in ecclesiastical full moon

It would be more helpful to tweak the wording, rather than nuke the section entirely. The value of delta T over 2,000 years has reached about 3 1/2 hours. The shift in the time of full moon over the same period is much the same. So the one cancels the other out. 156.61.250.250 (talk) 10:44, 14 May 2015 (UTC)

The deleted section appears to be largely based on "original research" which doesn't belong here. AstroLynx (talk) 10:50, 14 May 2015 (UTC)

(ec)My mistake. I see the objection is not to this bit, it's to the bit above. Nobody claimed it was badly written when it was part of a stable version five years ago. 156.61.250.250 (talk) 10:54, 14 May 2015 (UTC)

You said it was badly written. Now you claim it's original research. You seem to be making this up as you go along. The fact is that the change in delta t and the secular acceleration of the moon has been known for years. 156.61.250.250 (talk) 10:58, 14 May 2015 (UTC)

Actually it is both (original research as there is no reference and it is badly written - the cited numbers 84 and 19 come from nowhere). The fact that it was there five years ago is not relevant - it was evidently removed for the reasons which I mentioned just now. Changes in Delta T and the secular acceleration of the moon are indeed well known but you do not provide references for your claim. AstroLynx (talk) 11:03, 14 May 2015 (UTC)

It was removed as part of a batch by an editor claiming the article had been edited by a sockpuppet. The content was never questioned. 156.61.250.250 (talk) 11:45, 14 May 2015 (UTC)

Then why is it unsourced and badly written (see my earlier comments). Such content does not belong in WP. AstroLynx (talk) 11:54, 14 May 2015 (UTC)

I don't see it's badly written. Lichtenberg theorised a mixture of 200 and 300 - year correction steps. The actual error to be compensated is one day in about 210 years, so there will be many more 200 than 300 - year steps. The actual ratio turns out to be 84 to 19, but that's a side issue that doesn't affect the structure of his scheme. 156.61.250.250 (talk) 12:09, 14 May 2015 (UTC)

If the section which I deleted comes from Lichtenberg's paper this should be indicated more clearly. Still I do not feel that this level of detail belongs here, perhaps it should be moved to Reform of the date of Easter. AstroLynx (talk) 12:26, 14 May 2015 (UTC)

The consensus is that this level of detail does belong here. 156.61.250.250 (talk) 13:45, 14 May 2015 (UTC)

Kindly provide some proof of your claim. AstroLynx (talk) 13:58, 14 May 2015 (UTC)

It was a stable version five years ago. 156.61.250.250 (talk) 15:21, 14 May 2015 (UTC)

That is a very long time ago. So apparently nobody objected to its deletion five years ago? You still have not given any evidence that the deleted section is from Lichtenberg's paper. AstroLynx (talk) 15:42, 14 May 2015 (UTC)

Obviously it's not word - for - word because that would be plagiarism. As for your other point, doubtless many editors objected to the loss of their work when Jc3s5h arbitrarily turned the clock back. 156.61.250.250 (talk) 15:55, 14 May 2015 (UTC)

Lichtenberg describes the replacement of solar equations (common centennial years) and lunar equations (drift of one tithi in 312 1/2 years) with a unified correction cycle which provides the same number of epact corrections over the cycle. — Preceding unsigned comment added by 156.61.250.250 (talk) 16:20, 22 May 2015 (UTC)

You must be referring to another paper by Lichtenberg or someone else. I have read the Lichtenberg (2003) paper twice and I don't see anything which matches your claim. AstroLynx (talk) 10:44, 23 May 2015 (UTC)

He most certainly does use unified corrections (200 and 300 year steps). How do you claim he makes the adjustments? 156.61.250.250 (talk) 12:49, 23 May 2015 (UTC)

Lichtenberg's (2003) paper indeed discusses the lunar and solar corrections which are necessary to compute the correct lunar age but the section which I blanked is not a part of his paper as you claim. If you think that the blanked section (which I repeat here)

Using a more accurate leap year rule (218 leap years in 900 years with AD 2500 a leap year) the present system has a "lunar jitter" of 2.60 days. The unified correction cycle repeats every 22500 years starting in 1 BC. In this period there are 175 Gregorian solar corrections and 72 lunar ones for a net correction of 103 days. There are nineteen 300 - year correction periods interspersed among eighty - four 200 - year ones. These numbers are unforgettable - 84 is the number of years in the British epact cycle before the Synod of Whitby and 19 is the number afterwards. The 300 - year periods end in 1100, 2400, 3500, 4800, 5900, 7000, 8300, 9400, 10700, 11800, 13100, 14200, 15500, 16600, 17700, 19000, 20100, 21400 and 22500. In the first three millennia of the Christian era the lunar jitter is 3.16 days, which cannot be reduced by moving corrections which would otherwise occur in leap years. The cycle is furthest behind the moon in the 11th century and furthest ahead in the 22nd century.

is a part of his paper, please indicate where. AstroLynx (talk) 13:57, 23 May 2015 (UTC)

That's not what I asked you. My question was, does he or does he not make use of unified corrections in spaced out 200 - and 300 - year intervals to replicate the 43 epact corrections in 10 000 years? 156.61.250.250 (talk) 14:16, 23 May 2015 (UTC)

You're sidestepping the issue. The issue is the section which I blanked because it is unsourced and you keep on trying to put back. Up to now you have not be able to provide a verifiable source. AstroLynx (talk) 14:26, 23 May 2015 (UTC)

It's you who is "sidestepping the issue". I happen to know that's exactly how he did it. 156.61.250.250 (talk) 14:43, 23 May 2015 (UTC)

Provide a verifiable source then. AstroLynx (talk) 14:58, 23 May 2015 (UTC)

The verifiable source is obviously the paper itself. 156.61.250.250 (talk) 15:03, 23 May 2015 (UTC)

Sorry to puncture your balloon, but as I already indicated above the blanked section is nowhere to be found in Lichtenberg (2003). How long do you want to keep on this farce? I can keep up just as long as you can. AstroLynx (talk) 15:08, 23 May 2015 (UTC)

As your parachute deflates, you can ponder that there is no requirement that ideas should be reported in the precise words of the person who originates them.156.61.250.250 (talk) 15:20, 23 May 2015 (UTC)

The problem is that most of the numbers and years listed in the blanked section are nowhere mentioned in Lichtenberg's (2003) paper. Nor is the Synod of Whitby anywhere referred to in the same paper. How can you claim that your text is a selective rephrasing of Lichtenberg's paper? I am seriously beginning to doubt whether you have ever read the Lichtenberg paper you are claiming to cite. AstroLynx (talk) 15:38, 23 May 2015 (UTC)

As I say, it doesn't have to be exact. To say that "most" of the years are different is not good enough. Please list specifically the years which you find to be different. 156.61.250.250 (talk) 15:44, 23 May 2015 (UTC)

OK, which table or page lists the years 11800 and higher? Where is the Synod of Whitby mentioned? Where are the values for lunar jitter mentioned? Unless you can provide specific page numbers from Lichtenberg's (2003) paper mentioning these numbers, I can only conclude that it is unsourced. AstroLynx (talk) 16:02, 23 May 2015 (UTC)

As I pointed out, Lichtenberg does the calculation over 10,000 years so you wouldn't expect to see years 11,800+ appearing in his data. You can still provide the data for earlier years. 156.61.250.250 (talk) 12:09, 24 May 2015 (UTC)

So you finally admit that most of the numbers and years listed in the blanked section are not found in the Lichtenberg (2003) paper but are based on original research (probably yours?). I still seriously doubt whether you have actually read Lichtenberg's paper.

As I became interested in the reason why you persist in having this section restored I had a closer look at the original edit on 10 June 2010 by IP 94.194.22.179, one of the known London-based sockpuppets of Vote (X) for Change.

Comparing the latter's editing behavior (and that of his numerous sockpuppets) with yours has been very insightful and revealing - it explains so much. AstroLynx (talk) 12:57, 24 May 2015 (UTC)

What a load of rubbish! I drew attention to the "sockpuppet" issue earlier in this thread. The section was declared kosher five years ago so you have a high bar to overcome to remove it. You're creating a diversion by throwing mud around in the hope that some will stick. If you're not prepared to justify your position by detailing the "discrepancies" you allege you can be dismissed as just a troll. I object to people removing good content for spurious reasons. This subject was extensively discussed in the archives - I suppose Karl Palmen, Tom Peters and the rest are all sockpuppets as well. 156.61.250.250 (talk) 13:17, 24 May 2015 (UTC)

Despite your whining you still have not provided a verifiable source for the blanked section - original research doesn't belong in WP. The blanked section never was 'declared kosher' five years ago as you claim - it was repeatedly removed after your sockpuppets tried to put it up again and again.

If I were you I would also start worrying about your recent additions to Iranian calendars. I have noticed that you have added quite a lot of unsourced text in recent days. If you do not start adding verifiable sources soon I will remove most of it - including the sections which appear to be original research. AstroLynx (talk) 15:24, 24 May 2015 (UTC)

Nah, it was added once and there it stayed. I think we can assume from your reticence that the dates in the first ten thousand years are in agreement with those in the paper. 156.61.250.250 (talk) 15:36, 24 May 2015 (UTC)

Why don't you check yourself - you claim to have read the Lichtenberg paper. AstroLynx (talk) 15:43, 24 May 2015 (UTC)

Information like that is not something you would commit to memory. 156.61.250.250 (talk) 09:00, 27 May 2015 (UTC)

You should have kept notes. If you had access to the Lichtenberg paper five years ago, you should be able access it again now. AstroLynx (talk) 09:49, 27 May 2015 (UTC)

This is typical of your attitude. Looking at your editing history I see you've tried this trick before. When someone wants to do an end run around Misplaced Pages policy it's they who have to do the legwork. We have a verified stable version which you want to change. In the previous incident you were trying to skate round WP:V. Editors pointed to sources which they wanted to include in an article and you pointed to a book which you claimed supported your viewpoint. Asked to support this by quoting the relevant passage you said you didn't have a copy and would order it through the library if the editor used "the magic word". Later, when an editor referred to the book you quoted from it instantly, thus proving that you had had a copy of it all the time. You exhorted the editor to get a copy of the book so as to quote from it "to prove wrong." That's not what good faith, collegial editing is all about. The incident related to an attempt by you to exclude the other editors' sources from a description of a picture of Muhammad. You have this picture on your web profile. You are arguably obsessed with it. 156.61.250.250 (talk) 10:55, 27 May 2015 (UTC)

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