Lunar calendars and "Qualifications"

Over at Multiple Musings I left a comment in response to the post on Easter. The blogger had written

Because first century Jews used a lunar calendar, every month was twenty-eight days long, beginning with the new moon and having the full moon on the 14th of the month.

I wrote in response

Not quite. A month of the moon's phases is twenty-nine and a half days long, so a lunar calendar--such as the Hebrew Calendar--that tracks the moon's phases will have 30-day and 29-day months, not 28-day months. If the first day is defined by the visibility of the new waxing crescent, as the ancient Babylonian (and probably the 1st century Jewish) calendar defined it, then the full moon will, as you say, occur around the 14th day. The Gregorian lunar calendar, used to determine Easter, attempts to approximate this scheme at the present day, though it is based on averages, not on the actual visibility of the new crescent.

In a calendar that begins its lunar months on the day of the lunar conjunction, however, as the present-day Chinese lunar calendar does, and, with some qualifications, the present-day Hebrew calendar does, the full moon will tend to be closer to the 15th of the month. So, for example, today, Thursday, April 9th, 2009, was the 13th day of the moon by the Gregorian lunar calendar, but the 15th day of Nisan (the 1st day of Unleavened Bread, popularly called "Passover") by the modern Hebrew calendar. This situation often occurs, when the Gregorian lunar calendar is a day or two behind the Hebrew calendar.

In this post, I thought I might elaborate on the "qualifications" mentioned there, and the agreement between the Hebrew and Gregorian lunar calendars.

The Gregorian lunar calendar, that is, the cycle used to compute Easter, was indeed devised (or, at least, Christoph Clavius claimed it was so devised) in such a way that its new moons would fall no earlier than the day after the mean lunar conjunction. This was deliberately done (Clavius wrote) in order to keep the full moon close to the 14th day of the lunar month, which Christian tradition associated with the full moon.

The present-day Hebrew calendar, to a first approximation, sets the first day of its lunar months to the day of the molad, an event which recurs at intervals of 29 days, 12 hours, and 793 "divisions", where a division is the 1080th part of an hour, or three and one-third seconds. In other words, the molad recurs at intervals of a synodic lunar month, a month of the moon's phases. Hence the molad can be, and sometimes is, identified with the mean lunar conjunction at some reference meridian. In the first part of the computation of when the first day of the Jewish numbered year, Tishri 1, should fall, the day is tentatively assigned to the day of the molad.

But now we come to the "qualifications". The year's starting day is moved to the day after the molad if the molad occurs at noon or later. So the start of the day is not permitted to occur 18 hours or more prior to the molad. If the molad is interpreted as a mean conjunction at some longitude in central Asia, then the rule that the start of the year must not precede the molad by 18 hours or more will have the effect of sometimes moving the start of the year to the day after the molad.

Furthermore, the year is not permitted to start on Sunday, Wednesday, or Friday. (This is equivalent to a rule that Nisan 15, the first Day of Unleavened Bread, can never fall on Monday, Wednesday, or Friday.) If the molad falls on one of these days, the 1st of Tishri is pushed back by a day. If the molad fell at noon or later on a Saturday, Tuesday, or Thursday, then it was pushed back onto Sunday, Wednesday, or Friday because of the late molad. But since the year cannot begin on one of these days, the start of the year is pushed back a second day in these cases. This will create a further tendency for the Hebrew Calendar's lunar months to begin later than otherwise. Hence we should expect to see the Hebrew Calendar to agree with the Gregorian lunar calendar some of the time due to these postponements, even though the Hebrew calendar initially fixes the year's start to the day of the molad, which can be interpreted as a mean conjunction, while the Gregorian lunar calendar was devised so that the new moons would always follow "the mean new moon of the astronomers." That this in fact occurs is shown by the following table, which compares Hebrew calendar and Gregorian calendar new moons to the true lunar conjunction at zero degrees longitude. The conjunction times are referred to a day starting at midnight.

Conjunction                                 Tishri 1                  Gregorian new moon

1995 Sept 24 16:55   Sept 25         Sept 25
1996 Sept 12 23:07   Sept 14         Sept 14
1997 Oct   1 16:51   Oct   2         Oct   2
1998 Sept 20 17:01   Sept 21         Sept 22
1999 Sept  9 22:02   Sept 11         Sept 11
2000 Sept 27 19:53   Sept 30         Sept 29
2001 Sept 17 10:27   Sept 18         Sept 19
2002 Sept  7 03:10   Sept  7         Sept  8
2003 Sept 26 03:09   Sept 27         Sept 27
2004 Sept 14 14:29   Sept 16         Sept 16
2005 Oct   3 10:28   Oct   4         Oct   4
2006 Sept 22 11:45   Sept 23         Sept 24
2007 Sept 11 12:44   Sept 13         Sept 13
2008 Sept 29  8:12   Sept 30         Oct   1
2009 Sept 18 18:44   Sept 19         Sept 21
2010 Sept  8 10:30   Sept  9         Sept 10
2011 Sept 27 11:09   Sept 29         Sept 28
2012 Sept 16 02:11   Sept 17         Sept 18
2013 Sept  5 11:36   Sept  5         Sept  7

2014 Sept 24 06:14   Sept 25         Sept 25
2015 Sept 13 06:41   Sept 14         Sept 14
2016 Oct   1 00:11   Oct   3         Oct   2
2017 Sept 20 05:30   Sept 21         Sept 22
2018 Sept  9 18:01   Sept 10         Sept 11
2019 Sept 28 18:26   Sept 30         Sept 29
2020 Sept 17 11:00   Sept 19         Sept 19
2021 Sept  7 00:52   Sept  7         Sept  8
2022 Sept 25 21:54   Sept 26         Sept 27
2023 Sept 15 01:40   Sept 16         Sept 16
2024 Oct   2 18:49   Oct   3         Oct   4
2025 Sept 21 19:54   Sept 23         Sept 24
2026 Sept 11 03:27   Sept 12         Sept 13
2027 Sept 30 02:36   Oct   2         Oct   1
2028 Sept 18 18:24   Sept 21         Sept 21
2029 Sept  8 10:44   Sept 10         Sept 10
2030 Sept 27 09:54   Sept 28         Sept 28
2031 Sept 16 18:47   Sept 18         Sept 18
2032 Sept  4 20:56   Sept  6         Sept  7

It can be seen that for the Hebrew month of Tishri to begin earlier than the corresponding Gregorian lunar month is fairly common in this sample, occurring seventeen times in thirty-eight years. For Tishri to begin on the same day as the corresponding Gregorian month is almost as common, occuring sixteen times. In the remaining five of the thirty-eight years, the Gregorian lunar month begins a day earlier than Tishri. It is possible for the Gregorian month to begin two days prior to Tishri 1, though no cases occur in the years listed here.

This is not quite the whole story, though. Under the rules currently in force for the Gregorian lunar calendar, a lunar month beginning in September, on September 27th or earlier, has 29 days. The Hebrew month of Tishri always has 30 days. This means that at the beginning of the next lunar month, the Hebrew calendar will be one day behind the Gregorian lunar calendar in every year in which the month of Tishri begins on the same day as the Gregorian new moon, if this day is September 27th or earlier. If the table showed a comparison for the month of Heshvan instead of for the month of Tishri, it would show the Hebrew month starting on the same day as the Gregorian month in sixteen years out of thirty-eight, starting a day later than the Gregorian in eighteen years out of thirty-eight, and starting earlier than the Gregorian in four years of the thirty-eight. So occasions when a Hebrew month begins earlier than the corresponding Gregorian lunar month are sometimes balanced by occasions in other years when some other Hebrew month begins later than the corresponding Gregorian lunar month.

In both lunar calendars, the day starts at 18:00 on the day prior to the one listed in the table. Comparison of the new moon dates to the times of the true conjunctions listed in the first column shows that the Hebrew month begins before the conjunction in seven years out of the thirty-eight (2002, 2009, 2013, 2018, 2021, 2022, and 2024), while the Gregorian lunar month begins before the true conjunction only once, in 2019. In the month following that shown in the table, the Hebrew month begins before the true conjunction in two years out of the thirty-eight , while the Gregorian begins before the true conjunction in four years. This may indicate that the Hebrew month begins before the true conjunction at 0 degrees longitude slightly more often than the Gregorian month does. But if so, the effect is slight.

Clearly the "postponements" in the Hebrew calendar are working to push the new moon past the conjunction. Hence my comment over at Multiple Musings exaggerated somewhat the tendency of the Hebrew new moon to occur closer to the lunar conjunction than the Gregorian new moon. This tendency is there, but it is often overridden by the Hebrew calendar's "postponements", as scholars from Maimonides on have noted. In particular, the two-day difference in the current month--Saturday, April 11th, 2009 is the 15th day of the moon by the Gregorian lunar calendar but the 17th of Nisan by the Jewish calendar--is probably due more to the vicissitudes of these postponements, and the different scheduling of 30-day and 29-day months in the two calendars, than to any underlying bias of the Jewish calendar toward the day of the mean conjunction.

Reconstructing the Last Supper

Here are my speculations about the Last Supper:

The meal would have been preceded by a blessing over the bread and followed by a grace-after-meal. The first I assert on the basis of Acts 27.35 and 1 Corinthians 11.24, the second on the basis of 1 Corinthians 11.25 ("after supper") Sirach 33.13, and Jubilees 22.6. These two elements would have been present whether the Last Supper was a Passover meal or not. The precise words of these prayers are not known, though one can make guesses about the subject-matter based on the texts just cited and later witnesses, such as the Didache.

If one accepts that the Last Supper was a Passover meal, then it is possible that there were two additional elements: First, the Egyptian Hallel, Psalms 113-118. Philo (Special Laws 2.148) tells us that the Passover meal included "prayers and hymns". The grace provides the prayers. The psalms are good candidates for the hymns. Another element that might have been present is the blessing over the wine before the meal, in later times called kiddush. This is suggested by Luke 22.17, which also suggests one kiddush by the symposiarchos, rather than each banqueter saying his own blessing.

It is not certain where the Hallel would have been in relation to the other elements. Matthew 26.30 suggest the hymn came after the grace-after-meal, and the standard procedures of a hellenistic symposium, as I understand them, would suggest the same.

My hunch is that the matzoth eaten at a Passover meal in those days were not the stiff, dry crackers now used, but flexible, like a flour tortilla. The Passover lamb would have been roasted on a spit (Exodus 12.8, reflecting early posexilic practice). The banqueters would hold out the unleavened bread with one hand and would cut off chunks of lamb into it using a knife held in the other, at some point adding the bitter herbs--I would guess green onions or leeks for these--wrapping the whole, and eating it in the manner of a Greek gyro. The notion of eating no cheese with meat was (so I understand) just beginning to get traction in those days, and there is no evidence that Jesus followed it, so cheese could be available also.

Rich people, of course, would get their slaves to prepare the food for them. This could have been seen as technically against the law of the festival, (Leviticus 23.7), but was this law so interpreted, and if so, was it effectively enforced?

Whether the Last Supper was a Passover meal or not, the procedure might have been for the banqueters to begin in a lower room or courtyard (atrium) with bread and wine, then when everyone had arrived, move to another, possibly upper room (triclinium) where they would recline on couches for the main meal.

In Praise of Creative Freedom 4: "He took a straight walk up to Washington city"

This humorous popular song by The Corrigan Brothers discusses President Barack Obama's Irish ancestry. (The genealogical facts are discussed in some detail here.) One important aspect of the song is the melody, which is clearly derived from (though not identical to) a traditional tune, Sweet Betsy from Pike (also known as Villikins and his Dinah). The traditional air can be heard here at the Digital Tradition.

The Corrigan Brothers are not the first to re-use this traditional tune. Many popular songs were sung to it in the 19th century. One such song, found in the 1896 book Lincoln's Campaign was a political song from 1860 about then President-elect Abraham Lincoln:

One Abr'am there was who lived out in the West,
Esteemed by his neighbors the wisest and best;
And you'll see, on a time, if you follow my ditty,
How he took a straight walk up to Washington city.

Others are available on-line at the Library of Congress's American Memory web site. The song titled "A new song for Sherman & Sheriden", begins

To SHERIDAN and SHERMAN, great merit is due,
They routed the Rebels each place they went to.
In the Shenandoah Valley they struck a home blow,
Where SHERIDAN whipped EARLY, who was a great foe.

Writing words "to the tune of" a popular air is always possible, even if the air is under copyright. But performing the air publicly is an exclusive right of the holder of copyright in the air. It is because the air Sweet Betsy from Pike is publici juris that The Corrigan Brothers were able not only to write words for it, but to perform it publicly as well, and post a recording of it to You-tube, all without being impeded by the frictional force of copyright clearance. Had Sweet Betsy from Pike been under copyright, The Corrigan Brothers might have been compelled to use a different tune, possibly with less success, since it is at partly due to its catchy melody that their song has become popular.

So here is another example of what Professor Lessig calls "Remix culture." The creative freedom allowed by the public domain has led to "progress of Science", in this case, the sciences of music and political humor.

Video: How copyright extension in sound recordings actually works

This video from the Open Rights Group does a quick survey of the issues involved in the European proposal to extend the term of exclusive rights in phonograms by 45 years.


This batch of articles in the Independent implies that the two just-released box sets of Buddy Holly recordings only became possible this year due to expiration of the exclusive rights in Europe over phonograms made in 1958.

Are online used-book sales killing the publishing industry?

In an article in the "Week in Review" section of the Sunday, 28 December 2008 New York Times, David Streitfeld examines the question of whether on-line resale of used books is hurting the publishing industry. Streitfeld seems certain that "traditional bookstores will continue to fade" in this new environment.

I prefer to think that publishers and traditional bookstores will continue to adapt to this new environment. Mr. Streitfeld seems only peripherally aware of an important part of this equation: if a copy of a recently-published book is available used on-line, then that copy was already bought from its publisher. If a book is in high demand, the used copies available on-line will disappear from the market quickly. Those who wish to have a copy immediately will purchase new copies. Mr. Streitfeld seems to think (I say "seems to" because he doesn't work this out explicitly) that a small number of copies will flow from reader to reader through on-line channels; that most people will be willing to wait their turn for one of these few circulating copies. I think that for many books there will be readers who don't want to wait, or who want a new copy. If the publisher can issue a moderate initial print run and then, if demand proves to be strong, bring new copies to market quickly, it may still have a window in which to make a profit before the market for used copies saturates. Surely this calculus is little different from the hardback/paperback computation that publishers already do? Libraries and some readers will want a more durable hardback copy. Some readers will be willing to borrow the book from the library while waiting six months to a year to buy the paperback edition. The publishing industry has been pleading incompetence since the late 17th century. Yet it adapted to the existence of libraries and paperbacks. It will adapt to the existence of an on-line market for used books.

"The natural place of creative expression is in the public domain"

The Canadian Broadcasting Corporation's "Who Owns Ideas" is available at

http://www.cbc.ca/ideas/features/who-owns-ideas/index.html

The MP3 is narrated by Paul Kennedy, and includes interviews with James Boyle, science-fiction author Eric Flint, (author of 1632, Mother of Demons, and other works,) Cory Doctorow, and Michael Geist. The article devotes considerable time to discussing U.S. copyright law. Why the interest in U.S. law from Canadians? A bill has been proposed in the Canadian Parilament, bill C-61, which would introduce provisions into Canadian law similar to some provisions of the DMCA. And Canada has so far resisted extending the duration of Canadian copyright from life+50 to life+70. But the content industry will surely want to change that.

"Everything has to fall into the public domain sometime"

An article by Los Angeles Times staff writer Joseph Menn

Disney's rights to young Mickey Mouse may be wrong

contains little fresh information, but it draws useful connecting lines along the history of the development of the theory that the copyright in the early versions of Mickey Mouse is possibly defective. It begins with Gregory S. Brown, a former Disney researcher who first discovered that the copyright notice on the 1928 cartoon Steamboat Willie might have been defective. It then moves to Dennis Karjala, who, Menn says, was an acquaintance of Brown's, and whose student, Lauren Vanpelt, wrote a paper titled "Mickey Mouse--A Truly Public Character," which developed the idea of flaws in early representations of the mouse. The theory was further developed by Georgetown Law student Douglas A. Hedenkamp, who in 2003 published a paper in the Virginia Sports and Entertainment Law Journal titled "Free Mickey Mouse: Copyright Notice, Derivative Works, and the Copyright Act of 1909." But when Hedenkamp wrote to Disney's lawyers asking for more information, the response from Disney General Counsel Louis Meisinger was "please be advised that slander of title remains actionable under California law for both compensatory and punitive damages."  Hedenkamp wasn't intimidated, and published the article.  

Another article, also by Menn,

Mickey's Many Roles

mentions, but does not name, the case of Eldred v. Ashcroft, which challenged the 1998 Copyright Term Extension Act (CTEA) on constitutional grounds. In the summer of 1998, when the CTEA seemed to be stalled in the Senate, Disney Chairman Michael Eisner was seen at Mississippi Senator Trent Lott's office.  Lott signed on as a co-sponsor of the CTEA a week later.  The Senate passed the bill in October of that year, and President Bill Clinton signed it, without any comment or announcement, on the last day before it would have died in a pocket veto.

Menn quotes Louis Meisinger, the former Disney lawyer, who is now a California judge, as stating that "everything has to fall into the public domain sometime."  The question is, however, would he have been able to say so if he still worked for Disney?   Would he have been capable even of thinking such a thought?  

Don't count on it.