The Century and the Millennium; Cardinalists vs. Ordinalists

SCULLY:  And besides, 2001 is actually the start of the new millennium.

MULDER:  Nobody likes a math geek, Scully.

X-FILES, "Millennium," 7x05, broadcast 11/28/1999


If you didn't know there was a year zero in astronomy, let me respectfully suggest you're not informed enough to tell others when to begin their centuries.

Steven Dutch, Natural and Applied Sciences, University of Wisconsin, Green Bay [note]

There are two kinds of people, those who think there are two kinds of people, and those who don't.

I am among those who think there are two kinds of people, and that they are people who think that the new century and millennium began on January 1, 2000, and those who think that they began on January 1, 2001.

A definitive discussion of this issue may be found in an essay of the late, great Stephen Jay Gould, "Dousing Diminutive Dennis's Debate (or DDDD=2000)," which is collected in Dinosaur in a Haystack [Harmony Books, 1995]. Gould, as in his defense of the name Brontosaurus ("Bully for Brontosaurus"), displays towering good sense. (For more on "two kinds of people," see "Psychological Types")

The advocates of "2001" usually say that since a century is 100 years, a millennium is 1000 years, and the calendar began with year 1, therefore all subsequent centuries will begin with a year 1 (e.g. 1901), and all millennia will begin with a year 1 (e.g. 2001). There is no year zero.

Fair enough. However, when calendars were invented that numbered the years, whether the regal years of Egyptian Kings or a continuous count like the Seleucid Era, the number systems used did not contain the number zero. There could be no year zero when there was no zero. Also, years were thought of as ordinals:  the first year of a reign was thus year 1. People who still think in these terms I will call "Ordinalists."

The number zero, conceived in India, was introduced into Western mathematics by the mathematician al-Khuwârizmî (c.780-850). The Arabs still call this system "Indian" (Hindî) numbers, while Europeans, etc., call it "Arabic" numerals. The number zero answers the question of cardinal numbers, "How many?" rather than the question of ordinal numbers, "Which one?" Mathematical questions are usually about cardinals rather than ordinals.

When we say that it is the year 1997 of the "Annô Domini" or "Common" Era, does this mean that it is the 1997th year of the Era ("Which one?"), or that 1997 years have elapsed ("How many?") since a Benchmark? Well, it can mean both. If it is the 1997th year of the Era, then the Era began on January 1st, 1 AD. On the other hand, if 1997 years have elapsed since a Benchmark, then the Benchmark was January 1, 0 AD. January 1, 1 AD, would mean that 1 year has elapsed since the Benchmark. That makes the calendar begin with the year 0 AD, not with the year 1 AD. People who think in these terms I will call "Cardinalists" [note].

If the question is about when the calendar really "begins," then of course the truth is that the calendar did not begin either in 1 AD or 0 AD. The Julian Calendar began in 46 BC, the Gregorian Calendar began in 1582 AD, and the "AD" numbering of the years was proposed, although not extensively used until later, by Dionysius Exiguus in the 6th Century AD. Even the calendar of the French Revolution was introduced in October 1793, a year and a month after the beginning of its own year "1" (September 1792), which was identified retrospectively -- and the calendar soon enough ceased to be used (Napoleon abolished it in year 12, or 1804, when he crowned himself Emperor). When a calendar or a reckoning "begins" thus usually says nothing about whether a calendar might be reckoned from a year 1 or a year 0.

The bald statement by "2001" partisans that "there is no year zero" is now, as a matter of usage, simply false. Calculations by astronomers and chronologists conveniently use zeros for years, months, and days. Perusing the Astronomical Almanac for the year 1997 [U.S. Government Printing Office & Her Majesty's Stationery Office, 1996], one finds days like "January 0." This is not surprising. Astronomers and chronologists do their calculations with Arabic numerals, which contain the number zero. This introduces a Cardinalist bias.

The astronomical and calendrical use of 0, however, began in the very first days of modern science. When the Gregorian calendar was introduced in 1582, it involved a rule for determining when certain leap days of the Julian Calendar should be skipped. The rule was that 3 Julian leap years (i.e. the years of the AD era evenly divisible by 4) every 400 years should be common years in the Gregorian calendar, and those years would be years evenly divisible by 100 but not evenly divisible by 400. Years evenly divisible by 100 are conveniently called "century years." 2000, not 2001, is thus a "century year." Now, advocates of 2001, the Ordinalists, can say that "century years" end a century rather than begin a century. That will work, but then we have to ask how they are going to apply the Gregorian calendar to the year 1 BC. "1" is not evenly divisible by 100, but it is the end of the first century BC and is the year immediately before 1 AD. For mathematical convenience in the usage of the Gregorian calendar, 1 BC must be identified as 0 AD. Then the division works: 0 is evenly divisible by 100 and so is a century year (and evenly divisible by 400 and so a leap year, like 2000 itself). But then we do indeed have a year 0 AD, which the Ordinalists do not want to admit. And 0 AD is, oddly, the actual first year of the AD era, since by (questionable) tradition Jesus was born on December 25th, 8 days before January 1, 1 AD. It would sound peculiar indeed to say that Jesus was born in the year 1 "Before Christ." So 0 AD "begins" the AD Era [note].

Even though traditional usage for years was ordinal, while modern mathematical and scientific use tends to be cardinal, there is one common numbering usage that is cardinal: the numbering of personal age. When someone is born in the United States, they may be starting their 1st year, but they are not already "1 year old." That comes a year later. Age is thus seen as elapsed time, starting from 0. That a different usage is possible should be obvious. Indeed, the traditional Chinese reckoning of age is ordinal, so that "1 year old" means the 1st year of life. This can be very confusing in places where both Chinese and Western reckoning may be used along side each other, as in Hawaii.

The real choice between 2001 and 2000 is an aesthetic preference: 2001 is consistent with tradition and thus the conservative, traditionalist choice. 2000 is the natural result of the introduction of the number zero, which made the mathematical power of science possible, and thus the modernistic, progressive choice. There is no particular reason why one should be seen as really superior to the other, if we are to honor both tradition and innovation in human affairs. It would be appropriate to celebrate both to indicate that we both look ahead (2000) and look back (2001) in our worldview.

On the other hand, the worst thing about the Ordinalists is their customary dogmatism and arrogance: they just know that there was no year zero, which means that people who begin the century with a zero are vulgar, ignorant, and can't add the number 100 (I've had at least one completely indignant, rude, hostile, and blockheaded correspondent display this attitude -- I think he wished he could have me arrested). "Vulgar" is a significant component of their judgment, since their pronouncements are often delivered with a sneer and a lofty, superior air (if not the aforesaid hostility). The cognitive psychologist and linguist Steven Pinker says that some things are "gotcha! material for pedants and know-it-alls (the kind of people who insist that the millennium begins January 1, 2001)" [Words and Rules, Basic Books, 1999, p.54]. Indeed, Ordinalists use the issue to prove how superior they are compared to the gaucherie of everyone else. For this they should, at least about this turn of the century, be savagely ridiculed. They seem to be among the mathematical illiterates who have never heard of actually using the number zero. Or perhaps they are racists who don't want to use some newfangled thing that comes from India or the Arabs. Such charges would at least serve to drive them out of their arrogance, if not silence them completely (since we know that anyone accused of being a racist, who denies it, therefore is a racist).

Sadly, the great libertarian economist Walter Williams, who always displays towering good sense much more than Stephen Jay Gould on economic and political issues, nevertheless has revealed himself to be an Ordinalist (cf. "Feelings are more important than facts," Conservative Chronicle, November 3, 1999, p.31). Although he can cite the U.S. Naval Observatory in his defense, Williams nevertheless betrays his unfamiliarity with the chronological use of zero on a issue unrelated to the century and the millennium:  He says that "the new millennium starts at 12:01 a.m. 2001." Saying that the day starts at "12:01" is natural for an Ordinalist, and perhaps also for someone just using a 12 hour clock. Anyone using a 24 hour clock, especially a digital clock, knows, however, that the day starts at 00:00, "zero hundred hours" -- at 00:01 a minute has already passed. This betrays for us the characteristic Ordinalist lack of attention, or familiarity, with the modern use of zero.

Unfortunately for the Ordinalists, everyone celebrates the New Year at the stroke of Midnight, not at 12:01, and, much worse, the meaning of 00:00 hours January 1, 2000 was hightened by anxieties and fears about the damage that could be done by the Y2K computer bug. It was thought that various essential public services could stop because older computers might lock up when their internal clocks showed the year as 00 and this was interpreted as 1900 rather than 2000. A made-for-television disaster movie anticipated riots and anarchy, and doomsday theorists were ready to take to the hills with enough supplies to surivive the End of Civilization. It was especially of concern that the Russians might lose control of their nuclear missles. Few expected the Russians to upgrade their computers in time to be free of any possible Y2K bugs. As it happened, little or nothing went wrong at Midnight of January 1, 2000, either where the day began, in the western Pacific, in Russia, or anywhere else. But there was not going to be anything like same kind of anxiety about 2001.

When 2000 was upon us, there was a sense of newness and strangeness every time I had to write "2000" or say the date. It had been 700 years (since 1299) since the year of the AD Era did not have a "teen" in it, and, of course, a thousand years since there were three zeroes. Now that we are past even 2001, this strangeness, of course, continues. The Ordinalists had their parties for January 1, 2001, but they faced the disappointment that few considered it as big a deal. Only about a quarter as many people turned out in Times Square as for 2000. In 2001 the British closed, not opened, the "Millennium Dome"; and Pope John Paul II sealed the Holy Year door of St. Peter's Basilica. Nevertheless, they stuck to it. On January 1, 2001, Peter Jennings calmly announced on the ABC evening news the "beginning of the century," as though there were no question about this; and even the less confident news personalities admitted that the "more mathematically precise" reckoned the century to have just begun. I don't think I ever saw the Cardinalist case actually presented, or even acknowledged, in the media. But this is typical of the "objective" news reporting of our day. By 2001 the presence of this page on the internet for four years didn't seem to have made much difference. No one even bothered to solicit the opinion of Stephen Jay Gould, who was a high profile public intellectual in his own right. Perhaps Peter Jennings had never read his books.

Traditional English Names of Full Moons, and the "Blue Moon"

Philosophy of Science, Calendars

Philosophy of Religion

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Copyright (c) 1997, 1999 (MCMXCIX), 2000 (MM), 2001 (MMI), 2006, 2009, 2010 (MMX), 2011 (MMXI), 2014 (MMXIV) Kelley L. Ross, Ph.D. All Rights Reserved

The Century and the Millennium; Cardinalists vs. Ordinalists; Note 1

Since 1999 Dr. Dutch has had a generally excellent webpage posted about the millennium.

Unfortunately, despite an insightful and helpful discussion, the page is marred at the end with the following diagram, which I reproduce:

199 BC    99 BC    4 BC     3 BC       2 BC      1 BC  |   1 AD   2AD
  +---------+----...-----+---------+---------+---------+---------+....
-200 -150 -100    -2.5  -2  -1.5  -1  -0.5   0   0.5   1   1.5   2
               | Year -2 | Year -1 | Year -0 | Year +0 | Year +1 |
  |Century-1|          Century -0            |     Century +0

Here we see the year 1 BC identified as "Year +0," 2 BC as "Year -0," 3 BC as "Year -1," and 4 BC as "Year -2." However, "+0" and "-0" are not different numbers (adding or substracting 0 does not change any number). What comes before the number 1 in the sequence of integers is 0, and what comes before 0 is -1. Thus, while 1 BC is indeed 0 AD, 2 BC is already -1 AD, 3 BC is -2 AD, and 4 BC is -3 AD.

I have brought this problem to Dr. Dutch's attention, and he insists that this is correct because the "0" refers to the integer portion of the decimal, while, with the numbers listed in the middle of the diagram (showing years and half-years), 2 BC does begin with -1.

Now, such a construction is reasonable enough, with a zero point at the boundary between 1 BC and 2 BC, but it is confusing and does not clearly represent the way years are actually numbered in historical usage, whether Ordinalist or Cardinalist. Or, for that matter, centuries, where the 1st century AD and the first century BC are not helpfully labeled "+0" and "-0" any more than the years.

It did not add to Dr. Dutch's explanation when he wrote to me that this was like "0oN" and "0oS" latitude -- when in fact 0o latitude is the Equator, and there is no difference between North and South there. Again, he was apparently using this construction to mean the integer portion within the first degees of latitude, North and South, despite the confusing way that will appear. A location at 30' (minutes) North latitude will be identified as 30'N, or 0o30'N, or 0.5oN, never as just "0oN." That is no actual, specific location of latitude -- except as equivalent to the Equator, where the "North" part is moot.

It is a bad idea to employ "+0" and "-0" as though they are different numbers, when they are not, especially where readers might get the idea that the year before 0 AD is "-0 AD" and that 4 BC corresponds to -2 AD rather than -3 AD. The way that Dutch uses these numbers, while it may be reasonably motivated and explicable, displays a prima facie numerical fallacy and is far too easily misunderstood or misapplied. When the problem of the century and the millennium is that the Ordinalists don't use zero at all, it doesn't help to introduce a usage where we see more zeroes than there actually are in the sequence of integers.

Come to think of it, I'm going too easy on Dr. Dutch. Since +0 and -0 are not different numbers, it is wrong to use them as though they are, whatever the explanation. And if the explanation for this involves decimals, this is also bad, since calendars use integers and fall under discrete or modular mathematics -- a whole branch of mathematics -- with deals with integers alone. If Dr. Dutch doesn't approve of this, I can just see him trying to lecture Gauss, who substantially developed that form of mathematics and who wrote modular formulae for calendars.

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The Century and the Millennium; Cardinalists vs. Ordinalists; Note 2

Ordinalism has its own permutations. When the Julian Calendar was instituted in 46 BC, with the rule that a day should be added every fourth year, a curious misunderstanding ensued. The priests (pontifices) in charge of the calendar inserted the leap day every three years, not every four years. They did this because they were counting "inclusively," i.e. the fourth year from the previous cycle counted as the first year of the next. This kept up from 46 BC to 9 BC, when the error was realized. The Emperor Augustus then brought things back in order by omitting sixteen leap years until 8 AD [cf. E.J. Bickerman, Chronology of the Ancient World, Cornell U. Press, 1968, 1980, 1982, p.47].

Ordinalists now tend to count ordinals "exclusively," as Augustus began doing in 8 AD, counting the first year of the cycle as the one after the fourth year. This practice, however, in effect leaves the fourth year of the cycle as the zero year of the next, which means that inclusive counting is really more conformable to ordinals, while the exclusive counting of ordinals is commensurable with cardinals.

The inclusive counting of ordinals can also be found in the Bible, where Jesus is said to have risen on the "third day" after his burial [Matthew 16:21, Mark 9:32, etc.], i.e. Easter Sunday. Once I saw an evangelist on television (I think it was Herbert W. Armstrong, 1892-1986) who protested that Jesus could not have been crucified and buried on a Friday and resurrected on a Sunday, because that was only two days later, not three. It is, of course, the third day if you count Friday as the first. Of such stuff are heresies and schisms made.

Inclusive counting is something also seen in music. The "octave" (octava, "eighth") is the next note in the scale of the same kind. Thus, beginning with C, we go through D, E, F, G, A, B, and finally C again. One notices, however, that there are only seven notes. To get eight going from C to C, one must count inclusively. This is the case with other intervals on the scale, the second, the fifth, etc.

Thus, ordinal counting includes varities of practice that may not trouble the cardinalists.

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The Century and the Millennium; Cardinalists vs. Ordinalists; Note 3

the Four Stephanitic Games,
the 75th Olympiad
0481 BCZero Year, -480 AD
1480 BCJuly-AugustOlympic Games
2479 BCJuly-AugustNemean Games
478 BCApril-MayIsthmian Games
3July-AugustPythian Games
4477 BCJuly-AugustNemean Games
476 BCApril-MayIsthmian Games
1July-AugustOlympic Games
An interesting case concerns the Olympic Games. The diagram shows the cycle of four years around the 75th Olympiad in 480 BC. The games are supposed to have begun in 776 BC. Within the four year cycle we see the other four sets of "Panhellenic Games," which are discussed
elsewhere.

How do we calculate what Olympiad it is? If we multiply 75 by 4 (=300) and substract from 776, we get 476, which is not 480 BC. What went wrong? We are confusing cardinals with ordinals. The 1st Olympiad, in 776 BC is not four years (1x4) after the First Olympiad. We can multiply 75 by 4 and subtract it if we use the "0th" Olympiad, which would be 780 BC:  780-(75x4)=480.

How do we determine which year is the first year of the Olympiad? 480 is convenientaly divisible by 4. But dividing by four leaves a remainder of zero, while we might be prefer to have a remainder of 1 for the first year. No problem. All we need to do is use dates in the AD era. 480 BC is -479 AD, as 1 BC is 0 AD. The previous year, -480 AD (481 BC), is now evenly divisible by 4, which means that the first year of the Olympiad is -480+1=-479 AD=480 BC, which is what we are looking for.

The "0th" year of the "0th" Olympiad is -780 AD. We can get the zero year of any Olympiad by adding 4 times the number of the Olympiad to this year. Or we can substract this from the zero year of any Olympiad, divide by 4, and get the number of the Olympiad.

Using years of the AD era means that we can conveniently calculate modern Olympiads. 2008 is evenly divisible by 4 (it is a leap year on the Julian and Gregorian calendars), which means that:  2008-(-780)/4=697. 2008 is the zero year of the 697th Olympiad. The Olympic Games would be in 2009, the first year of the Olympiad. 2011 is the 3rd year of the Olympiad.

Oh, Oh. The Modern (Summer) Olympic Games were in 2008, not 2009. The Modern Olympic Games use the zero year of the Olympiad! Where were the Ordinalists when we needed them? But perhaps the creators of the Modern Olympics simply didn't know that years evenly divisible by 4 in the AD era would also be the "0th" year of an Olympiad.

Since 1994, the Winter Olympics (which have been held since 1924) have been offset two years from the Summer Olympics. They are thus like the Pythian Games, at Delphi, which were held two years after the Olympic Games -- which now puts the Winter Olympics in the 2nd rather than the (Pythian) 3rd year of the Olympiad. The Nemean and Isthmian Games were held every two years and were less prestigious.

Greek historians like Polybius dated events using Olympiads, but the system was never used as a continuous era, like the Seleucid Era, in a Greek civil calendar.

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Traditional English Names of Full Moons,
and the "Blue Moon"

The traditional English names of the Full Moons that occur during each year were coordinated to the seasons. The seasons are defined by the equinoxes and solstices. Each season can also be evenly divided into three zodiacal periods according to the longitude of the sun. A Full Moon usually occurs during each zodiacal period and is given a name specific to that period, starting with the "Moon after Yule" for the Full Moon that occurs while the Sun is in Capricorn. This may occur in the December of the previous calendar year, so it should be kept in mind that the "year" defined by the seasons is slightly offset from the calendar year.

While the division of the year is similar to the calendar of the French Revolution, where the year begins with the Autumnal Equinox, the French months were conventionally set to a length of 30 days each.
Full MoonZodiacal
Period
Starting DateLength
Yule, Winter Solstice89d
1. Moon after Yule CapricornDecember 2229d
2. Wolf Moon AquariusJanuary 2030d
13. Blue MoonThe third Full Moon of any Season with four
3. Lenten Moon PiscesFebruary 1930d
First Day of Spring, Vernal Equinox92d
4. Egg Moon
(Paschal Moon)
AriesMarch 2130d
5. Milk Moon TaurusApril 2031d
13. Blue MoonThe third Full Moon of any Season with four
6. Flower Moon GeminiMay 2131d
The Long Day, Summer Solstice94d
7. Hay Moon CancerJune 2132d
8. Grain Moon LeoJuly 2331d
13. Blue MoonThe third Full Moon of any Season with four
9. Fruit Moon VirgoAugust 2331d
Summer's End, Autumnal Equinox90d
10. Harvest Moon LibraSeptember 2330d
11. Hunter's Moon ScorpioOctober 2330d
13. Blue MoonThe third Full Moon of any Season with four
12. Moon before
Yule
SagittariusNovember 2230d
The zodiacal periods do not have conventional lengths but instead mark astronomical periods based on 30 degree increments in the Sun's longitude on the ecliptic (the apparent path of the Sun in the sky). In the table at right, the dates for the beginning of the zodiacal periods, and their lengths, will not be accurate for every year. Each zodiacal period may start a day earlier, as the year is reset by the addition of a leap day and then runs slightly fast for three years. Thus, while March 21 is the traditional date of the Vernal Equinox, the equinox actually occurs on March 20 three years out of four. The periods and seasons are so different in length because, according to Kepler's Second Law, the Earth travels faster the closer it is to the Sun. Between January 2 and 4, the Earth reaches Perihelion, its closest approach to the Sun, and travels the fastest. Winter in the Northern Hemisphere (89 days) is thus shorter than Summer (94 days).

This strict positioning of phases of the Moon in relation to the actual longitude of the Sun is also characteristic of the Chinese Calendar, though it positions New Moons, which mark the beginning of the Chinese year and months, rather than Full Moons. The first New Moon after the Vernal Equinox was also the basis of the Babylonian calendar; but the Jewish calendar, although similarly starting each month with the New Moon, was structured to position the month of Niisân so that its Full Moon would be the first Full Moon after the Vernal Equinox. This set the date of Passover and was inherited by Christianity in the determination of Easter. If the "Egg Moon" is allowed to occur on the Vernal Equinox itself (rather than, for instance, only after), then it is equivalent to the Paschal Moon defined for Easter. Easter calculation, however, always defines the Vernal Equinox as March 21, so there may be some years, when the Equinox is on March 20, that the Paschal Moon differs from an astronomical calculation. Although the "Egg Moon" may be pre-Christian, it does suggest Easter eggs, and the prior Full Moon, the "Lenten Moon," definitely shows Christian influence. A popup window with this table, for reference, can be created with this link.

Every two or three years thirteen Full Moons will occur from one Winter Solstice to another, and two of these will necessarily occur in the same zodiacal period. Wherever four Full Moons occur in the same season, the third is called a "Blue Moon." Seven such moons will occur in a nineteen year period -- the "Metonic" cycle of the Babylonian, Jewish, and Chinese calendars.

The detailed workings of this system had become very obscure knowledge until recently. A "Blue Moon" is now commonly said to be a second Full Moon in a calendar month, though this means that in some years, as in 1999, there are two months, January and March, with Blue Moons, while February contains no Full Moon at all. This leaves only 11 non-Blue Moons in the year to which the 12 standard moon names would need to be assigned. If the moon names are all assigned by calendar month, then presumably the absence of a Full Moon in February would mean that there is no "Wolf Moon" -- though that loss of such an omnious name might be seen as auspicious. Assigning the "Egg Moon" always to April, on the other hand, severs its relationship to the Paschal Moon. In 1999 the Paschal Moon is on March 31 (with Easter on April 4), but the April Full Moon falls on April 30, a month later. In 1999 the Paschal Moon itself would be, by the calendrical month rule, a Blue Moon, and the Lenten Moon would coincide with, indeed, the astronomical Lenten Moon on March 2.

The recent meaning of "Blue Moon" occurred because the old moon names have mostly fallen out of use, and even been forgotten. Although I have found close to accurate definitions of the "Harvest Moon" and "Hunter's Moon" in a 1962 World Book Encyclopedia and in the 1997 Microsoft Encarta Encyclopedia (using almost the same language), and I had long heard that such traditional names existed for all the Full Moons of the year, I never saw a list of all of them until an article on "Blue Moons" in the March 1999 issue of Sky & Telescope magazine ("Once in a Blue Moon," by Philip Hiscock). That article contained an inset by Donald W. Olson and Roger W. Sinnott, "Blue-Moon Mystery Solved?", where they reproduced a page from the 1937 Maine Farmer's Almanac (see at right), that identified the Full Moon occuring on August 21, 1937 as a "Blue Moon" and provided a list of all the moon names. This was mysterious to them because the Full Moon on August 21, 1937 was not a second Full Moon in the month, and the Almanac really didn't explain why this particular Full Moon was a Blue Moon. The list of moon names, however, clearly established their astronomical character, and the only explanation for August 21 is the astronomical one. Both Sky & Telescope pieces reveal, however, how obscure the matter has become and how difficult it has been to find older references. The encyclopedia articles, also, don't seem to get it quite right. The World Book said that the nearest Full Moon to the equinox was the "Harvest Moon," while Encarta said that it was the one right before the equinox. The interpretation of the Almanac, however, requires that it be in the Autumn and after (or perhaps on) "Summer's End," i.e. the equinox.

A follow up Sky & Telescope article, "What's a Blue Moon?" by Donald W. Olson, Richard Tresch Fienberg, and Roger W. Sinnott, in the May 1999 issue, seems to have cleared up the problems. After the questions raised by the original article, an examination of more than a century of copies of the Maine Farmers' Almanac revealed the rule they were using for Blue Moons. Rather than using the actual position of the sun, the mean position of the sun was used, March 21 was always used for the Vernal Equinox, and the principle that the third Full Moon out of four in a season was discerned. Thus, the Lenten Moon would always occur in Lent and the Egg Moon would always be the Paschal Moon. Using the mean longitude of the sun would make the seasons of equal length. The error that the second Full Moon in a calendar month was a Blue Moon was traced to a specific issue of Sky & Telescope magazine in March 1946. What does not seem to have been revealed is the source used by the Maine Farmers' Almanac for its method and information.

Reading the original article, my impression was that the rule for Blue Moons was probably the second Full Moon in a zodiacal period. This was unsatisfactory, since it would mean that the Full Moon in Lent might be a Blue Moon rather than the Lenten Moon. It is therefore satisfying to discover that the actual rule preserves the Lenten Moon for Lent. However, the new article lists me as one of the people who proposed that the Blue Moon was the second Full Moon under a "given astrological sign." I think this is a bit of a misrepresentation, since the longitude of the sun defining the zodiacal period does not necessarily have anything to do with astrology. The use of the mean position of the sun also means that different methods, and different results, could be obtained for assigning the Full Moon names. I have discussed a purely astronomical determination. It will be interesting to see when this will diverge from the results of the mean longitude of the sun.

The clear, or clarified, picture from the 1937 Farmer's Almanac has now become muddled. I noticed this when the Weather Channel referred to the Lunar Eclipse of October 2013 as the "Hunter's Moon" eclipse, when I would have expected it to be the Harvest Moon. I could not find that the Weather Channel website explained this, but soon enough I found the treatment of the Full Moon names at the 2014 Farmer's Almanac site.

Full Moons
1937 Farmer's Almanac2014 Farmer's Almanac2014 Alternates
Yule, Winter Solstice
0.Moon after YuleWolf MoonSnow Moon
1.Wolf MoonSnow MoonHunger Moon
2.Lenten MoonWorm MoonCrow/Crust/Sap Moon
First Day of Spring, Vernal Equinox
3.Egg/Paschal MoonPink MoonSprouting
Grass/Fish Moon
4.Milk MoonFlower MoonCorn Planting Moon
5.Flower MoonStrawberry MoonRose Moon
The Long Day, Summer Solstice
6.Hay MoonBuck MoonThunder Moon
7.Grain MoonSturgeon MoonGreen Corn/Red Moon
8.Fruit MoonCorn/Harvest Moon
Summer's End, Autumnal Equinox
9.Harvest MoonHunter's/Harvest MoonBlood Moon
10.Hunter's MoonBeaver MoonFrosty Moon
11.Moon before
Yule
Cold/Long Nights Moon
After a fashion, all hell has broken lose, and the presumably authoritative list that the Almanac gave in 1937 has now been thoroughly revised and complicated. Some of the names of 1937 are not even mentioned (e.g. the Fruit Moon), while most of the others are relegated to mention as alternatives, often at the end of the list, as afterthoughts (the second column in the table gives the names as they occur in the headings of the Almanac treatment). This is improper, if not dishonest, given the 1937 list. And while the older treatment was presented in terms of English tradition, with a key role for the Lenten Moon, the Farmer's Almanac has now shifting to prefering a narrative in which the names "date back to Native Americans." Since American Indians did not originally observe Easter, the Lenten Moon obviously would have had no meaning.

There is no mention on the 2014 Farmer's Almanac page about the Sky & Telescope discussion of the rule for Blue Moons. Indeed, the Full Moon names are identified by calendar month. The only reference to the astronomical benchmarks is the assertion that the Harvest Moon can occur in September or October because it is supposed to be the closest Full Moon to the Autumnal Equinox. If such a Moon occurs before the Equinox, of course, it is in the Summer rather than the Autumn, according to the Babylonian system used by Western astronomy. There is no reference cited for this rule, which would confuse the principle for Blue Moons as determined by Sky & Telescope, which names the Moons by the astronomical seasons. Indeed, the aspect of the rule that the Blue Moon is the third moon of the season, preserving the standard name of the third moon as the last moon of the season, only makes sense when we realize that the Lenten Moon should be immediately followed by the Full Moon associated with Easter. Again, this consideration would not arise if our frame of reference is pre-Christian American Indians. Much of the point of the Sky & Telescope discussion thus voided.

A regularity we might notice in the revised names is that the 1937 names sometimes occur a month earlier in the 2014 version. This is the case with the Wolf Moon, the Flower Moon, the Harvest Moon, and the Hunter's Moon (as in the Weather Channel name for the October 2013 Full Moon). Of course, the 1937 names often do occur in the previous month, precisely because they are following the equinoxes and solstices rather than the (Gregorian) calendar months. Given the curious treatment of the Harvest Moon, perhaps a general confusion about this has crept into the Almanac account. In fact, I like some of the new names better. The "Moon before Yule" and the "Moon after Yule" tell us nothing about the nature of the season or the weather. "Cold Moon" and "Snow Moon" are much more evocative. However, the whole business is a mess when the whole basis of the treatment shifts from "English ancestors" to "Native Americans" without explanation, and even without coherence (e.g. over the Lenten Moon). In the tables below, the 1937 names are used because that is what I have been using since 1999.

1999
Full MoonZodiacal by Month
2 January 2h 49mMoon after YuleMoon after Yule
31 January 16h 6mWolf MoonBlue Moon
2 March 6h 58mLenten MoonLenten Moon
31 March 22h 49mEgg/Paschal MoonBlue Moon
30 April 14h 55mMilk MoonEgg Moon
30 May 6h 40mFlower MoonMilk Moon
28 June 21h 37mHay MoonFlower Moon
28 July 11h 25mGrain MoonHay Moon
26 August 23h 48mFruit MoonGrain Moon
25 September 10h 51mHarvest MoonFruit Moon
24 October 21h 2mHunter's MoonHarvest Moon
23 November 7h 4mMoon before YuleHunter's Moon
22 December 17h 31mMoon after YuleMoon before Yule
1999 is an unusual year for Full Moons. They are all listed in the table at left, with their exact occurrence in Universal Time (or "Terrestrial [Dynamical] Time," TDT or TT), as given in the The Astronomical Almanac for the Year 1999 [U.S. Government Printing Office, Washington, and Her Majesty's Stationery Office, London, 1999], which is what Greenwich Mean Time is now called. There are 13 Full Moons in the calendar year, but only 12 in the tropical year (solstice to solstice). Thus, there would be a Blue Moon when reckoning by months but not when reckoning by seasons. More unusal is that there is no Full Moon in the calendar month of February, the only month where that is possible, since it is only 28 days long (and the synodic month, from New Moon to New Moon, is 29.5 days). This means that the Full Moon that might have occurred in February, the Wolf Moon, must be in some other month instead, so that, with 13 months in the calendar year, two months will have two Full Moons. Those are January and March, which, with two Full Moons, both have a Blue Moon by the monthly reckoning. This will happen again in 2018.

2000
Full MoonZodiacal by Month
21 January 4h 40mWolf MoonMoon after Yule
19 February 16h 27mBlue MoonWolf Moon
20 March 4h 44mLenten MoonLenten Moon
18 April 17h 41mEgg/Paschal MoonEgg Moon
18 May 7h 34mMilk MoonMilk Moon
16 June 22h 27mFlower MoonFlower Moon
16 July 13h 55mHay MoonHay Moon
15 August 05h 13mGrain MoonGrain Moon
13 September 19h 37mFruit MoonFruit Moon
13 October 8h 53mHarvest MoonHarvest Moon
11 November 21h 15mHunter's MoonHunter's Moon
11 December 9h 3mMoon before YuleMoon before Yule
The Full Moons of 2000 are completely conventional if we reckon by month but are a nice illustration of the principle of the system if we reckon by seasons. There are only twelve Full Moons in the calendar year, but the Moon after Yule has already occurred late in 1999, so by seasons the year begins with the Wolf Moon -- which experienced a spectacular Total Eclipse conveniently visible from North America. The actual Paschal Moon occurs on April 18th (Gregorian Easter is April 23rd), so we end up with four Full Moons during the Winter of 1999-2000. The actual Full Moon during Lent is March 20th. This leaves the odd Full Moon as that of February 19. So it's a Blue Moon. The Blue Moon that actually didn't occur during the 13 Full Moons of the calendar year of 1999, we get at the beginning of 2000.
 

2001
Full MoonZodiacal by Month
9 January 20h 24mMoon after YuleMoon after Yule
8 February 07h 12mWolf MoonWolf Moon
9 March 17h 23mLenten MoonLenten Moon
8 April 03h 22mEgg/Paschal MoonEgg Moon
7 May 13h 52mMilk MoonMilk Moon
6 June 01h 39mFlower MoonFlower Moon
5 July 15h 4mHay MoonHay Moon
4 August 05h 56mGrain MoonGrain Moon
2 September 21h 43mFruit MoonFruit Moon
2 October 13h 49mHarvest MoonHarvest Moon
1 November 05h 41mHunter's MoonHunter's Moon
30 November 20h 49mMoon before YuleBlue Moon
30 December 10h 40mMoon after YuleMoon before Yule
There are thirteen Full Moons in calendar 2001. None of these is, properly speaking, a Blue Moon. But two of them do occur in one month, November, which then would have a Blue Moon by the monthly reckoning.
 

2002
Full MoonZodiacal by Month
28 January 22h 50mWolf MoonMoon after Yule
27 February 9h 17mLenten MoonWolf Moon
28 March 18h 25mEgg/Paschal MoonLenten Moon
27 April 03h 00mMilk MoonEgg Moon
26 May 11h 51mFlower MoonMilk Moon
24 June 21h 42mHay MoonFlower Moon
24 July 09h 7mGrain MoonHay Moon
22 August 22h 29mBlue MoonGrain Moon
21 September 13h 59mFruit MoonFruit Moon
21 October 07h 20mHarvest MoonHarvest Moon
20 November 01h 34mHunter's MoonHunter's Moon
19 December 19h 10mMoon before YuleMoon before Yule
There are twelve Full Moons in calendar 2002. The "Moon after Yule," however, already occurred in 2001, leaving only eleven names. One of the Full Moons therefore, that of August 22nd, ends up as a proper Blue Moon -- there are four Full Moons between the Summer Solstice and the Autumnal Equinox. As they should be, the Lenten Moon is in Lent, which begins February 13th, and the Egg Moon is the Paschal Moon, with (Gregorian) Easter falling on March 31st.

This table, like the previous ones, is taken from The Astronomical Almanac, in this case for the year 2002 [published as for 1999 above].
 

2003
Full MoonZodiacal by Month
18 January 10h 48mMoon after YuleMoon after Yule
16 February 23h 51mWolf MoonWolf Moon
18 March 10h 35mLenten MoonLenten Moon
16 April 19h 36mEgg/Paschal MoonEgg Moon
16 May 03h 36mMilk MoonMilk Moon
14 June 11h 16mFlower MoonFlower Moon
13 July 19h 21mHay MoonHay Moon
12 August 04h 48mGrain MoonGrain Moon
10 September 16h 36mFruit MoonFruit Moon
10 October 07h 27mHarvest MoonHarvest Moon
09 November 01h 13mHunter's MoonHunter's Moon
08 December 20h 37mMoon before YuleMoon before Yule
There are twelve Full Moons in calendar 2003, matching up completely with the reckoning by month. As they should be, the Lenten Moon is in Lent, which begins March 5th, and the Egg Moon is the Paschal Moon, with (Gregorian, Western) Easter falling on April 20th (Julian, Eastern Easter on April 27th).

This table, like the previous ones, is taken from The Astronomical Almanac, in this case for the year 2003 [published as for 1999 above, 2001].
 

2004
Full MoonZodiacal by Month
7 January 15h 40mMoon after YuleMoon after Yule
6 February 08h 47mWolf MoonWolf Moon
6 March 23h 14mLenten MoonLenten Moon
5 April 11h 03mEgg/Paschal MoonEgg Moon
4 May 20h 33mMilk MoonMilk Moon
3 June 04h 20mFlower MoonFlower Moon
2 July 11h 09mHay MoonHay Moon
31 July 18h 05mGrain MoonBlue Moon
30 August 02h 22mFruit MoonGrain Moon
28 September 13h 09mHarvest MoonFruit Moon
28 October 03h 07mHunter's MoonHarvest Moon
26 November 20h 07mMoon before YuleHunter's Moon
26 December 15h 06mMoon after YuleMoon before Yule
There are thirteen Full Moons in calendar 2004, but no true Blue Moon, since the Full Moon of December occurs after the Winter Solstice and so is the Moon after Yule, adding a thirteenth name for the thirteenth moon. Reckoning by month, there are two Full Moons in July.

Lent begins on February 25th, and the Lenten Moon is on March 6th. Both Gregorian and Julian Easter in 2004 fall on April 11th, after the Egg or Paschal Moon on April 5th.

This table, with universal times for the Full Moons, is taken from The Astronomical Almanac for the year 2004 [Washington, U.S. Government Printing office; London, The Stationery Office, 2002].
 

2005
Full MoonZodiacal by Month
25 January 10h 32mWolf MoonMoon after Yule
24 February 04h 54mLenten MoonWolf Moon
25 March 20h 58mEgg/Paschal MoonLenten Moon
24 April 10h 06mMilk MoonEgg Moon
23 May 20h 18mFlower MoonMilk Moon
22 June 04h 14mHay MoonFlower Moon
21 July 11h 00mGrain MoonHay Moon
19 August 17h 53mBlue MoonGrain Moon
18 September 02h 01mFruit MoonFruit Moon
17 October 12h 14mHarvest MoonHarvest Moon
16 November 00h 57mHunter's MoonHunter's Moon
15 December 16h 15mMoon before YuleMoon before Yule
There are twelve Full Moons in calendar 2005, but like 2002 the "Moon after Yule" already occurred (in 2004), leaving only eleven names. One of the Full Moons therefore, that of August 19th, ends up as a proper Blue Moon -- there are four Full Moons between the Summer Solstice and the Autumnal Equinox. As they should be, the Lenten Moon is in Lent, which begins February 9th, and the Egg Moon is the Paschal Moon, with (Gregorian) Easter falling on March 27th. While this Gregorian (Western) Easter occurs relatively early this year, Easter by the Julian (Eastern) reckoning occurs very late, on May 1st, five weeks later.

The Full Moons on this table, in Universal Time (GMT), like the previous ones, are taken from The Astronomical Almanac, in this case for the year 2005 [U.S. Government Printing Office, Washington, and Her Majesty's Stationery Office, London, 2003].
 

2006
Full MoonZodiacal by Month
14 January 9h 48mMoon after YuleMoon after Yule
13 February 04h 44mWolf MoonWolf Moon
14 March 23h 35mLenten MoonLenten Moon
13 April 16h 40mEgg/Paschal MoonEgg Moon
13 May 6h 51mMilk MoonMilk Moon
11 June 18h 03mFlower MoonFlower Moon
11 July 03h 02mHay MoonHay Moon
9 August 10h 54mGrain MoonGrain Moon
7 September 18h 42mFruit MoonFruit Moon
7 October 03h 13mHarvest MoonHarvest Moon
5 November 12h 58mHunter's MoonHunter's Moon
5 December 00h 25mMoon before YuleMoon before Yule
There are twelve Full Moons in calendar 2006, each matching up to their expected month. As they should be, the Lenten Moon is in Lent, which begins March 1st, and the Egg Moon is the Paschal Moon, with (Gregorian) Easter falling on April 16th.

The Full Moons on this table, in Universal Time (GMT), like the previous ones, are taken from The Astronomical Almanac, in this case for the year 2006 [U.S. Government Printing Office, Washington, and Her Majesty's Stationery Office, London, 2004].
 

2007
Full MoonZodiacal by Month
3 January 13h 57mMoon after YuleMoon after Yule
2 February 05h 45mWolf MoonWolf Moon
3 March 23h 17mLenten MoonLenten Moon
2 April 17h 15mEgg/Paschal MoonEgg Moon
2 May 10h 09mMilk MoonMilk Moon
1 June 01h 04mFlower MoonFlower Moon
30 June 13h 49mHay MoonBlue Moon
30 July 00h 48mGrain MoonHay Moon
28 August 10h 35mFruit MoonGrain Moon
26 September 19h 45mHarvest MoonFruit Moon
26 October 04h 52mHunter's MoonHarvest Moon
24 November 14h 30mMoon before YuleHunter's Moon
24 December 01h 16mMoon after YuleMoon before Yule
There are thirteen Full Moons in calendar 2007, but no true Blue Moon, since the Full Moon of December occurs after the Winter Solstice and so is the Moon after Yule, adding a thirteenth name for the thirteenth moon. Reckoning by month, there are two Full Moons in June, giving us a Blue Moon by monthly reckoning.

As they should be, the Lenten Moon is in Lent, which begins February 21st, and the Egg Moon is the Paschal Moon, with (Gregorian) Easter falling on April 8th.

The Full Moons on this table, in Universal Time (GMT), like the previous ones, are taken from The Astronomical Almanac, in this case for the year 2007 [U.S. Government Printing Office, Washington, and Her Majesty's Stationery Office, London, 2005].
 

2008
Full MoonZodiacal by Month
22 January 13h 35mWolf MoonMoon after Yule
21 February 03h 30mLenten MoonWolf Moon
21 March 18h 40mEgg/Paschal MoonLenten Moon
20 April 10h 25mMilk MoonEgg Moon
20 May 02h 11mBlue MoonMilk Moon
18 June 17h 30mFlower MoonFlower Moon
18 July 07h 59mHay MoonHay Moon
16 August 21h 16mGrain MoonGrain Moon
15 September 09h 13mFruit MoonFruit Moon
14 October 20h 02mHarvest MoonHarvest Moon
13 November 06h 17mHunter's MoonHunter's Moon
12 December 16h 37mMoon before YuleMoon before Yule
There are twelve Full Moons in calendar 2008, but like 2005 the "Moon after Yule" already occurred (in 2007), leaving only eleven names. One of the Full Moons therefore, that of May 20th, ends up as a proper Blue Moon -- there are four Full Moons between the Vernal Equinoz and the Summer Solstice. As they should be, the Lenten Moon is in Lent, which begins February 6th, and the Egg Moon is the Paschal Moon, with (Gregorian) Easter falling on March 23rd. While this Gregorian (Western) Easter occurs relatively early this year, Easter by the Julian (Eastern) reckoning occurs late, on April 27th, five weeks later.

The Full Moons on this table, in Universal Time (GMT), like the previous ones, are taken from The Astronomical Almanac, in this case for the year 2008 [U.S. Government Printing Office, Washington, and Her Majesty's Stationery Office, London, 2006].
 

2009
Full MoonZodiacalby Month
11 January 03h 27mMoon after YuleMoon after Yule
09 February 14h 49mWolf MoonWolf Moon
11 March 02h 38mLenten MoonLenten Moon
09 April 14h 56mEgg/Paschal MoonEgg Moon
09 May 04h 01mMilk MoonMilk Moon
07 June 18h 12mFlower MoonFlower Moon
07 July 09h 21mHay MoonHay Moon
06 August 00h 55mGrain MoonGrain Moon
04 September 16h 03mFruit MoonFruit Moon
04 October 06h 10mHarvest MoonHarvest Moon
02 November 19h 14mHunter's MoonHunter's Moon
02 December 07h 30mMoon before YuleMoon before Yule
31 December 19h 13mMoon after YuleBlue Moon
There are thirteen Full Moons in calendar 2009, but like 2007, there is no true Blue Moon. This is the first time in the years covered that two Full Moons occur in December. So the names of the Moons all match until the last Full Moon.

Despite the good work of Sky & Telescope in clearing up the issues of Blue Moons, I notice in December, 2009, that the Weather Channel is still uncritically touting the Full Moon of 31 December as being a "Blue Moon," according to the principle that it is the second Full Moon in the calendar month. Someone did not do their homework.

The Full Moons on this table, in Universal Time (GMT) are taken from The Astronomical Almanac, in this case for the year 2009 [U.S. Government Printing Office, Washington, and Her Majesty's Stationery Office, London, 2007].
 

2010
Full MoonZodiacalby Month
30 January 06h 18mWolf MoonMoon after Yule
28 February 16h 38mLenten MoonWolf Moon
30 March 02h 25mEgg/Paschal MoonLenten Moon
28 April 12h 18mMilk MoonEgg Moon
27 May 23h 07mFlower MoonMilk Moon
26 June 11h 30mHay MoonFlower Moon
26 July 01h 37mGrain MoonHay Moon
24 August 17h 05mFruit MoonGrain Moon
23 September 09h 17mHarvest MoonFruit Moon
23 October 01h 37mHunter's MoonHarvest Moon
21 November 17h 27mBlue MoonHunter's Moon
21 December 08h 13mMoon before YuleMoon before Yule
There are twelve Full Moons in calendar 2010; but there is a true Blue Moon, since the Moon after Yule occurred in the previous calendar year. Easter falls on April 4th this year by both Julian and Gregorian reckoning. Lent began on February 17th.

The Full Moons on this table, in Universal Time (GMT) are taken from The Astronomical Almanac, in this case for the year 2010 [U.S. Government Printing Office, Washington, and Her Majesty's Stationery Office, London, 2008].
 

2011
Full MoonZodiacal by Month
19 January 21h 21mMoon after YuleMoon after Yule
18 February 08h 36mWolf MoonWolf Moon
19 March 18h 10mLenten MoonLenten Moon
18 April 02h 44mEgg/Paschal MoonEgg Moon
17 May 11h 09mMilk MoonMilk Moon
15 June 20h 14mFlower MoonFlower Moon
15 July 06h 40mHay MoonHay Moon
13 August 18h 57mGrain MoonGrain Moon
12 September 09h 27mFruit MoonFruit Moon
12 October 02h 06mHarvest MoonHarvest Moon
10 November 20h 16mHunter's MoonHunter's Moon
10 December 14h 36mMoon before YuleMoon before Yule
There are twelve Full Moons in calendar 2011, and no true Blue Moon. The months and the moon all match up for the first time since 2006.

The Full Moons on this table, in Universal Time (GMT) are taken from The Astronomical Almanac, in this case for the year 2011 [U.S. Government Printing Office, Washington, and Her Majesty's Stationery Office, London, 2010].
 

2012
Full MoonZodiacalby Month
09 January 07h 30mMoon after YuleMoon after Yule
07 February 21h 54mWolf MoonWolf Moon
08 March 09h 39mLenten MoonLenten Moon
06 April 19h 19mEgg/Paschal MoonEgg Moon
06 May 03h 35mMilk MoonMilk Moon
04 June 11h 12mFlower MoonFlower Moon
03 July 18h 52mHay MoonHay Moon
02 August 03h 27mGrain MoonGrain Moon
31 August 13h 58mFruit MoonBlue Moon
30 September 03h 19mHarvest MoonFruit Moon
29 October 19h 49mHunter's MoonHarvest Moon
28 November 14h 46mMoon before YuleHunter's Moon
28 December 10h 21mMoon after YuleMoon before Yule
There are thirteen Full Moons in calendar 2012, but like 2009, there is no true Blue Moon. There are two proper Moons after Yule. Since two Full Moons do occur in calendar August, the monthly reckoning shows a Blue Moon there.

The Full Moons on this table, in Universal Time (GMT) are taken from The Astronomical Almanac, in this case for the year 2012 [U.S. Government Printing Office, Washington, and Her Majesty's Stationery Office, London, 2011].
 

2013
Full MoonZodiacal by Month
27 January 04h 38mWolf MoonMoon after Yule
25 February 20h 26mLenten MoonWolf Moon
27 March 09h 27mEgg/Paschal MoonLenten Moon
25 April 19h 57mMilk MoonEgg Moon
25 May 04h 25mFlower MoonMilk Moon
23 June 11h 32mHay MoonFlower Moon
22 July 18h 16mGrain MoonHay Moon
21 August 01h 45mBlue MoonGrain Moon
19 September 11h 13mFruit MoonFruit Moon
18 October 23h 38mHarvest MoonHarvest Moon
17 November 15h 16mHunter's MoonHunter's Moon
17 December 09h 28mMoon before YuleMoon before Yule
There are twelve Full Moons in calendar 2013; but there is a true Blue Moon, since the Moon after Yule occurred in the previous calendar year and there are four Full Moons in the Summer. Gregorian Easter falls on March 31st this year. Lent began on February 13th.

The Full Moons on this table, in Universal Time (GMT) are taken from The Astronomical Almanac, in this case for the year 2013 [U.S. Government Printing Office, Washington, and the United Kingdom Hydrographic Office, London, 2012].

Note that the Weather Channel called the October 2013 Full Moon the "Hunter's Moon" rather than the Harvest Moon. This has happened because of shifting ideas about the proper names of the Full Moons, as I have discussed above.
 

2014
Full MoonZodiacal by MonthAlmanac
16 January 04h 52mMoon after YuleMoon after YuleWolf Moon
14 February 23h 53mWolf MoonWolf MoonSnow Moon
16 March 17h 08mLenten MoonLenten MoonWorm Moon
15 April 07h 42mEgg/Paschal MoonEgg MoonPink Moon
14 May 19h 16mMilk MoonMilk MoonFlower Moon
13 June 04h 11mFlower MoonFlower MoonStrawberry Moon
12 July 11h 25mHay MoonHay MoonBuck Moon
10 August 18h 09mGrain MoonGrain MoonSturgeon Moon
09 September 01h 38mFruit MoonFruit MoonHarvest Moon
8 October 10h 51mHarvest MoonHarvest MoonHunter's Moon
06 November 22h 23mHunter's MoonHunter's MoonBeaver Moon
06 December 12h 27mMoon before YuleMoon before YuleCold Moon
There are twelve Full Moons in calendar 2014 and no Blue Moon by any reckoning.

The basic names that are now in the Farmer's Almanac have been added here for comparison. In these names, the relation of the series to Easter has obviously been purged, apparently on the principle that these are "Native American" names, where of course Christianity was not originally a factor. At the same, time there are no astronomical or scientific records present, let alone common, to all Native Americans. So the Farmer's Almanac names are in part a fantasy exercise, perhaps even part of the current cultural and political attack on Christianity in the United States -- ironically coupled with a complacent or apologetic attitude towards the terrors and horrors of radical Islâm. The Full Moon of September 9th was reported as the Weather Channel as the "Harvest Moon." See discussion above for more details.

The Full Moons on this table, in Universal Time (GMT) are taken from The Astronomical Almanac, in this case for the year 2014 [U.S. Government Printing Office, Washington, and Her Majesty's Stationery Office, London, 2013].

2015
Full MoonZodiacal by MonthFarmer's
Almanac
05 January 04h 53mMoon after
Yule
Moon after YuleWolf Moon
03 February 23h 09mWolf MoonWolf MoonSnow Moon
05 March 18h 05mLenten MoonLenten MoonWorm Moon
04 April 12h 06mEgg/Paschal MoonEgg MoonPink Moon
04 May 03h 42mMilk MoonMilk MoonFlower Moon
02 June 16h 19mFlower MoonFlower MoonStrawberry
Moon
02 July 02h 20mHay MoonHay MoonBuck Moon
31 July 10h 43mGrain MoonBlue MoonBlue Moon
29 August 18h 35mFruit MoonGrain MoonSturgeon
Moon
28 September 02h 50mHarvest MoonFruit MoonHarvest Moon
27 October 12h 05mHunter's MoonHarvest MoonHunter's Moon
25 November 22h 44mMoon before YuleHunter's MoonBeaver Moon
25 December 11h 11mMoon after YuleMoon before YuleCold Moon
There are thirteen Full Moons in calendar 2015. However, there is no true Blue Moon. The thirteenth Full Moon occurs after the Winter Solstice and so belongs to the following season. A Blue Moon by monthly reckoning occurs in July.

The Almanac names for 2015 have been supplied directly from the Old Farmer's Almanac [Yankee Publishing Inc., Dublin, New Hampshire, 2014, p.274]. This repeats the information discussed above. The Moon names, with variations, are given in terms of months, with the proviso that "The Harvest Moon is always the full Moon closest to the autumnal equinox. If the Harvest Moon occurs in October, the September full Moon is usually called the Corn Moon" [ibid.]. We also get the account here that the Moon names are due to "Native Americans" of the northeastern United States and that a name applied "to the entire month in which it occurred," which would seem to mean that the Native Americans used the Julian or Gregorian Calendars, which seems unlikely. The specific names in the Almanac, however, are now said to be those "used by the Algonquin tribes from New England to Lake Superior" [p.275], with no source for this information cited, nor any account of how the Algonquin would have reckoned the months. This increases one's curiosity about the rule for the "closest" Moon the the autumnal equinox, since this would bespeak an astronomical and calendrical tradition, and an awareness of the equinoxes and solstices, about which we otherwise hear nothing. The ability of a people like the Algonquin to determine the equinoxes and solstices, let alone be aware of them, is something, given their technology and environment (i.e. forests), is something about which some skepticism may be in order.

Since there are thirteen Full Moons in the year, some provision will need to be made for an intercalation or a Blue Moon. The Old Farmer's Almanac, although noting two Full Moons in July, makes no mention of Blue Moons and does not identify the extra Moon by name. This grave oversight seems characteristic of the carelessness and fantasy of the whole treatment. Meanwhile, a rival 2015 Farmer's Almanac, published by the "Almanac Publishing Company" of Lewiston, Maine [2014 -- this one says it has been published since 1818 -- is it the "Maine Farmer's Almanac"? -- while the Old Farmer's Almanac claims an origin in 1792] repeats the names given by other other Almanac but does identity the second Full Moon of July as a "Blue Moon" [p.107]. Both Almanacs, having constructed their own fantasy system of Moon names, without bothering to consider how "Native Americans" reckoned the months, recognized the equinoxes and solstices, or constructed their own calendars, thus have tossed and ignored the history of these questions from the Sky & Telescope examinations, let alone the history and system evident in the 1937 Maine Farmer's Almanac. That the reckoning of Lent and Easter has been purged from the matter is only part of its carelessness and shamefulness.

The Full Moons on this table, in Universal Time (GMT) are taken from The Astronomical Almanac, in this case for the year 2015 [U.S. Government Printing Office, Washington, and Her Majesty's Stationery Office, London, 2014].

The Occurrence of the Solar Terms in 1995-2013

The Solar Terms and the Chinese Calendar

Philosophy of Science, Calendars

Philosophy of Science

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Philosophy of History

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Copyright (c) 1999, 2000, 2001, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2012, 2013, 2014 Kelley L. Ross, Ph.D. All Rights Reserved

The French Revolutionary Calendar

The French Revolutionary Era, which was reckoned to begin on 22 September 1792 (roughly the Autumnal Equinox), was based on a year of 12 months of 30 days each, with five or six intercalary days at the end of the year. This was identical in form and position to the Coptic version of the ancient Egyptian Calendar, though with the year starting about ten days later. The months were poetically named for the seasons (in the northern hemisphere), which immediately inspired an English parody. I have added some Chinese characters, with Chinese proununciation (below) and
NametranslationParodyRoman MonthCoptic Month
1. VendémiairevintageWheezeySeptemberThout
2. Brumairemist SneezyOctoberPaape
3. Frimairefrost FreezyNovemberHator
4. Nivôsesnow SlippyDecemberKiahk
5. Pluviôserain DrippyJanuaryTobe
6. Ventôsewind NippyFebruaryMshir
7. GerminalseedShoweryMarchParmhat
8. FloréalblossomFloweryAprilParmute
9. PrairialmeadowBoweryMayPashons
10, MessidorharvestHoppyJunePaone
11. Thermidorheat CroppyJulyEpep
12. FructidorfruitsPoppyAugustMesore
Japanese (above), since the notion here (meteorological and agricultural referents) is comparable to what we see with the Chinese Solar Terms.

The French calendar, like the original Egyptian calendar again, included a ten day week. This was all supposed to be more natural and rational than the Roman/Gregorian calendar. Once Napoleon became reconciled with the Pope and the Catholic Church, however, it was doomed. Today revolutionary calendar dates are only heard because various events of the French Revolution came to be known by their Revolutionary dates, e.g. the arrest of Robespierre on 9 Thermidor (27 July 1794). Thus, those who ended the Reign of Terror became known as "Thermidoreans."

More recent attempts to rationalize the Western calendar have turned on the problem that the seven day week does not divide evenly into the 365 (or 366) day year. A day or two is left over. The simplest idea is simply to leave the extra day (days) out of the week. This sort of thing was never likely to be accepted because the seven day week is observed for religious reasons by Jews, Christians, and Muslims. Laid down by God, the succession of days is not going to be modified for calendrical convenience. On the other hand, calendar reforms in the early Soviet Union were directed at abolishing the traditional week altogether, precisely because of its religious basis. At one point, a six day week was used, with Sunday pointedly excluded. Eventually all this was abandoned (too many people had been keeping traditional observance anyway and missing work -- presumably too many people to just execute) and the traditional calendar and week restored.

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Copyright (c) 1999, 2007, 2009 Kelley L. Ross, Ph.D. All Rights Reserved