C Becomes B Today

In that strange title above  my reference is to the year’s Dominical Letters. 2016 is a leap year, and all such years have two such letters. 2015, more modestly, was simply a D; 2016 is, more self-promotingly, CB.

A paragraph such as the one above would have been totally incomprehensible to me on February 1st, the day on which I wrote a post on the year 1932 to mark Brigitte’s 84th birthday. In that process I discovered that 1932 was also a CB year, like 2016; Wikipedia tells you such things. I discovered what a Dominical Letter was, where it fits into the scheme of things, and, furthermore, that 84 is meaningful because it is a multiple of 28, and every 28 years the days of the week in a year begin repeating. Therefore 1932, 1960, 1988, and 2016 are all CB years. If you were 0 years of age in 1932, you will be 84 in 2016, and you can prove it by calculating 3 x 28. Check.

In the medieval scheme of things it was important to know on which date in January the first Sunday of the year fell—or to predict on which day it will fall in future years in order to prepare future calendars for Easter and other Church festivals. The ecclesiastical Latin for Sunday was dies Dominica, or simply Dominica, hence “dominical,” the Sunday Letter.

Now it so happens that the Dominical Letter, once you know it, automatically tells you the date in January. In the following tabulation are all the letters (note that there are seven) with their actual number:

A	B	C	D	E	F	G
1	2	3	4	5	6	0 or 7

Thus if the first Sunday of the year falls on January 1, the DL is A. If on the 7th, DL is G. In mathematical algorithms devised to determine the Dominical Letter, the result for G will always be 0 but must be transformed into 7 before applying its results to an actual calendar. Incidentally, once you know the Dominical Letter, the weekday of January 1 can also be determined by a simple formula: If DL=1, the Day of Week (DW) is 1; in all other cases, DW is 9 minus DL. Taking a G year, the DL is 7; that means Sunday, January 7. January 1 will be 9-7=2, a Monday. The Days of the Week, are numbered thus:

Sun	Mon	Tue	Wed	Thu	Fri	Sat
1	2	3	4	5	6	7

In 2016, where DL is CB, we use the first letter for Sundays in January and February, the B for Sundays the rest of the year. Therefore Sunday is on January 3 (C in the first table) and January 1 will be a Friday; 9-3=6, that 6 being in the table immediately above.

The fact that Days of the Week have a fixed number whereas Dominical Letters have a variable number depending on the year illustrates the maddening confusions that can surround learning this subject.

Let’s next turn to the reason why leap years have two Dominical letters. Lets take as an example 2010 and 2016. 2010 was a C year, meaning that its first Sunday fell on January 3. All other Sundays in the year were therefore designated by C. 2010 is a common year, not divisible by 4. 2016 is a leap year, also a C year at the beginning. It has the same exact days in January and up to the 28th of February. In March, however, its Sunday designation shifts “back” by one.

February-March 2010 - a Common Year starting on a Sunday "C"
Sun	Mon	Tue	Wed	Thu	Fri	Sat
	1	2	3	4	5	6
7	8	9	10	11	12	13
14	15	16	17	18	19	20
21	22	23	24	25	26	27
28
	1	2	3	4	5	6
7	8	9	10	11	12	…
February-March 2016 - a Leap Year starting on a Sunday "CB"
	1	2	3	4	5	6
7	8	9	10	11	12	13
14	15	16	17	18	19	20
21	22	23	24	25	26	27
28	29
		1	2	3	4	5
6	5	6	7	8	9	…

Notice how in 2016 the first Sunday in March “falls back” by one—compared to 2010. The March pattern shown is that of a B-year (e.g. 2011), thus one starting on a Saturday, its first Sunday being January 2nd. Therefore the B is shown next to the C to indicate that in 2016 C only applies to January and February, not to the year as in and after March.

Quite wondrous algorithms have been devised to calculate the Dominical Letter for any year—in the Gregorian or the Julian calendars. The only input needed is the number of the year. The sleekest of these was devised by Karl Friedrich Gauss (1777-1855). The process, on the surface, is simple enough. One counts the total days in target year – 1, 2015 in our case, minding leap days. The total is then divided by 7; the remainder is the number of the Dominical Letter.

Here’s a threat. One of these days I will discuss how that is done. Meanwhile this rather rare February 29 must be lived more fully while the sunshine still lasts.

Albert the 1st

In a day and age in which science can even transplant a uterus, one can permit oneself to dream! My dream is that our next NASA venture will be to move the Planet Earth just enough closer to the Sun so that a year will be exactly 364 days—to the minute, nay, to the second and the nanosecond. With that we shall have made the year to last precisely 52 weeks (rather than a pesky 52.14285714). Leap years will have been abolished. The difficult we should do immediately; the impossible—getting rid of Friday the 13th—will take a little longer—unless we hit upon a genuinely creative fix and simply banish Sunday ever falling on the first of any month! No Sunday the 1st—no Friday the 13th. Logical, isn’t it. When Sunday would, under the old dispensation, falls on the 1st of the month, we would substitute Albert for it and simply shove Sunday to the 2nd of the month. Albert is for you-know-who.

The neat solution above has a little problem. It comes from the fact that when a common year (one with 365 days in our benighted times) begins on a Sunday, it also ends on a Sunday. And, surprising people like me, whom calendars generally baffle, a year beginning on Monday also ends on a Monday, and so on for all the days of the week. But if January 1 falls on Albert, what do we do with the last day of the year? Problems. Problems.

In the case of leap years, of course, a January 1st falling on Sunday, the year ends on a Monday what with that pesky February 29th pushing everything out by one. Similarly with all the other possible leap year starting days. 2015 started on a Thursday. Therefore 2016, which also happens to be is a leap year, will start on Friday.

Every common year starting on Thursday has three Fridays the 13th—in February, March, and November. Because, of course, those months start on Sunday. They ought to start on Albert. To help others carry on the future labors of getting rid of Friday the 13th, I herewith present a table for starters. We’ve got to get this whole business simplified. I think you’ll all agree.

Note please that in common years no Friday the 13th falls into July. The Leap year is also finicky: it features no Fridays the 13th in August. And also note, lest my entry title be forgotten, that in all the months shown for Friday the 13th, the first day of the month would be an Albert in my new calendar.

Minding the Nones of July

We’re frequently reminded that an exercised mind retards the onset of senility. Minds aged eighty or thereabouts and higher tend to notice stories like that; the ballpoint marks the article for closer reading. Keeping the mind sharp is our excuse, hereabouts, for working crossword puzzles, as in “you learn something new every day,” e.g. that OREO is an almost indispensably useful word in crossword puzzles. Well, the other day, we had the following clue: July 7, e.g. Brigitte and I always do puzzles together; and what with our respective backgrounds, we fill in our respective gaps of knowledge and never fail to solve a puzzle. This time, again, we found the answer to that clue—but only by finding the other words that intersected with it. The answer was NONES. But what does that mean?

Nones, of course, vaguely hinted at the ninth canonical hour, but the clue was July 7. So how do we get from 9 to 7. To get an answer to that illustrates what might be called the useful activity of “extended crossword puzzle solving.” One has to research the subject. Well, Brigitte and I are both quite familiar with the Ides of March; assassinations of important people have a way of lingering in racial memory. We also knew that it was the 15th of the month. Oddly enough, as we discovered, counting backward from 15, with 15 being 1, the 9th day turns out to be the 7th. So if you count back from the Ides of July by nine, including that day in your count, the ninth (nonae in Latin) day will be the 7th.  Nones is always the 9th day of the month in the Julian calendar—but it falls on the 7th of the month only in March, May, July, and October—because the Ides falls on the 15th. In all other months, the Ides fall on the 13th and hence Nones is on the 5th of the month!

Having discovered this, we learned that Roman naming of the days was rather awkward. The Romans only had three “named” days, Kalends (the first day of the month), Nones (5th or 7th depending on the month), and Ides (15th or 13th, again depending on the months). All other days were defined with reference to these three. The following table shows the naming conventions, which seem very hard to remember for us, for the month of July:

1st	Kalends (of July)	17th	Day 15 before Kalends
2nd	Day 5 before Nones	18th	Day 14 before Kalends
3rd	Day 4 before Nones	19th	Day 13 before Kalends
4th	Day 3 before Nones	20th	Day 12 before Kalends
5th	Day 2 before Nones	21st	Day 11 before Kalends
6th	Day before Nones	22nd	Day 10 before Kalends
7th	Nones	23rd	Day 9 before Kalends
8th	Day 7 before Ides	24th	Day 8 before Kalends
9th	Day 6 before Ides	25th	Day 7 before Kalends
10th	Day 5 before Ides	26th	Day 6 before Kalends
11th	Day 4 before Ides	27th	Day 5 before Kalends
12th	Day 3 before Ides	28th	Day 4 before Kalends
13th	Day 2 before Ides	29th	Day 3 before Kalends
14th	Day before Ides	30th	Day 2 before Kalends
15th	Ides	31st	Day before Kalends
16th	Day 16 before Kalends	1st	Kalends (of August)

The Romans used a standard annotation to name a day. Lets take the 13th of July here. They would write that as “a.d. II Id. Iul.” Spelled out: “ante diem II, Ides, Iulius.” Ante diem  stands for “day before”; it amuses me, however, that A.D. was used in calendars once—and still is, but with a different meaning. Iulius, is, of course, our July. The phrasing on the day immediately before the named days (e.g. July 14) was “prid. Id. Iul.”; the prid. is pridie and means “the day before.”

Keeping track of the days, particularly in the second half of each month, was rather a chore, it seems, best left to scribes who had desks with appropriate writing instruments on which to record time's passage.

Now, knowing that it takes such exercises to ward off the onrush of senility makes you kind of wonder just how bad senility really might be…

Starting Anew

A notable aspect of New Year’s Day is that it has no anchorage in anything traditional—or seasonal. Going by western history, an early Roman calendar was that of Romulus (circa 771 BC). In that calendar the year began on March 1—and the calendar did not even have a January or a February; there were only ten months to a year. January and February make their first appearance under King Numa Pompilius (r. 715-673 BC), with the first day of January starting the year.

Under the calendar reforms of Julius Caesar, carried out in 46 BC, January retained its leading position—and does so to this day. Caesar’s year had 365.25 days; the earlier calendar had between 377 and 378 days, thus causing each month, each year, to “drift” from season to season. Under Pope Gregory XIII, the Gregorian calendar, introduced in 1582, further conformed the year to the actual movements of the sun just a tad more, to 365.2425 days. That has been good enough to last until today. Under the Gregorian calendar, however, Caesar’s January 1 became January 17—as the Gregorian made its correction.

Thus New Year’s Day, as we now find it, came about for (call it) scientific reasons—or the desire to have the months of the year conform to the seasons more or less perfectly, with one extra leap day added to every year divisible by 4. Years divisible by 100 are not leap years, however, unless they are also divisible by 400. Thus the year 2000 was a leap year but 1700, 1800, and 1900 were not.

For more detail on these numbers, see this post here (link).

While no tradition clings to New Year’s day, nonetheless it offers something all of us need at least once a year: a formal occasion for starting anew. Yes, for starting anew—with nothing else distracting from that resolution and, for those who overindulged on New Year’s eve, a strong motivation to clear the decks for the new and perfect life which every new year thus offers.

So, happy New Year! May your resolutions bloom!

Captain’s Log, Stardate 11312.31

Well, let’s see now. If Star Trek is any kind of guide on how we shall measure time in the distant future, thus  roughly from the next century onward, it appears that a kind of chaos of dates will dominate and every household will have to accumulate, at the beginning of each year, a quite diverse set of calendars. A quite amazing welter of mostly opaque information on Star Trek dating awaits the avid fan. I’m something even less than a rank amateur. Therefore, to mark this last day of 2013, I will stick to the dating convention that began with Star Trek, The Next Generation—a phrase that experts abbreviate as TNG.

The dating in that series was based on a five-digit number and a single-digit decimal. Suppose the stardate was 42437.5. In that case the digits have this meaning:

4          [Twenty]-fourth century

2          Star Trek TNG Season 2

4          { A three-digit number ranging from

3          { 000 to 999, advancing in

7          { uneven intervals through the season.

.

5          Time of day expressed as a decimal fraction. 0.5 is noon, thus half of a day.

The first stardate used in this format was 41153.7 for the first two episodes of TNG. The last was 47988—without a decimal point, therefore suggesting midnight of the release day. The stardate I’ve parsed out above is the date of the sixth episode of Season 2, “The Schizoid Man,” which so happens to feature Darnay’s disease (link).

Needless to say, there is no way to march from a stardate to an actual year except by searching the dialogue in each episode. In some of them actual dates using our own calendar—and presumably still in use then—are mentioned. And for the avid fan, this produces hours, days, even years of useful occupation.

The Powers that Be behind Star Trek’s creation, not least Gene Roddenberry, wished to avoid repeating actual years some 200-plus years in the future. People might then be tempted to speculate if such and such a technology could or could not as yet have been invented.

My own rationalizing attempt in that title is to bow respectfully in the direction of obfuscation. Therefore I use 1 for the [twenty]-first century, two digits for year, two for the month, and two digits beyond the decimal to indicate a day. That’s good enough for dates up to the twenty-ninths century into the future until a new convention must be introduced. And no pesky annotations like Anno Domini or Current Era need clutter up the pristine screen.

Happy New Year!

Full Worm Moon

One of our new calendars for 2013 is The Old Farmer’s Almanac Gardening Calendar, courtesy of the Paralyzed Veterans of America. We noted that it features the names of full moons as they were known to Native American tribes in what is now the Eastern and Northern United States.  March features Full Worm Moon (scheduled to appear March 27) so named because the ground will soften and worms will appear. More northerly tribes knew this as the Full Crow Moon; crows got active; around here, alas, even seeing crows, which were quite numerous a few years ago, is always an event! Another Nordic name was Full Crust Moon, a name derived from the behavior of snow, which melts and then freezes again, leaving a hard crust; we’ve just seen that sort of crusty snow quite recently around here. For a look at all moon names, try this link.

What the Old Farmer’s Almanac does not say is how the Indians measured the lunar month. Different cultures have different start and stop dates. They either measure from new to new or from full to full. If from new to new, today is still Full Snow Moon (or Full Hunger Moon—conditions being terrible for hunting); that month began February 10. If from full to full, this lunar month began February 27.

Leaving the tent late at night for a last look at the calendar in the sky. Sigh. Quite a while yet until Full Pink Moon in April comes—signaled by herb moss pink (Phlox subulata) the earliest plant to flower in the Spring.

The End of a Mayan Age

The Mayans believed in “world eons” each lasting, using the Gregorian calendar, 5125 years. The Mayans had three calendars. The civil calendar (the Haab’) had 365 days, the religious 260, and the Long Count Calendar 144,000 days. A “world” or eon was 13 of these long count years, called b’ak’tuns.  The length of each such age, therefore, is 1,872,000 days.

The beginning of the last world—the fourth such in the Long Count Calendar—was on August 11, 3114 BC. Adding 1.872 million days to that brings us to today, December 21, 2012. Now is it just a coincidence—or did the Mayans know that the end of this age would end on the day of the Winter Solstice? I think that they did.

As pointed out in the last post on this series (link), they well knew exactly how long the actual tropical (also called solar) year was (365.2422 days). Their own civil calendar, according to the scholar, Victoria Bricker (“The Origin of the Maya Solar Calendar,” in Current Anthropology,  February 1982) had its beginnings on the winter solstice around 550 BC. The Mayans therefore clearly associated that date with the completion of a period. My guess is that they calculated their long calendar looking both backward and forward—and picked the starting day of this Fourth Age so that it would coincide with today’s solar event at its end.

To bring this counting down to earth, lets trace it. Between 3114 BC and 2012 AD, we have the passage of 5,126 years. But the first year was partial, starting on August 11; so was the last year, ending on December 21, today. Now August 11, 3114 (not a leap year) was day 223; therefore we count only 143 days of that year. This leap year’s December 21 is day number 356. So let’s do the additions using years of 365.2422 days as the multiplier for full years:

	Days
5,124 full years	1,871,501
Days in the first year to be counted	143
Days in the last year to be counted	356
Total Days	1,872,000

The exact time of the Winter Solstice took place in the northern hemisphere at 11:12 Greenwich Mean Time, which was 6:12 am here in Detroit; the scare-mongers prefer 11:11—perhaps because it looks more ominous. If you are reading this, it means that the world, as a physical phenomenon, hasn’t ended. Nor did the Mayans ever suggest that it would. It’s just another fancy calendar running out—so that a new one must be purchased.

So what happens now to folks who have been earning advertising dollars by publicizing Doomsday? Well, there is still hope for them. The Mayan Long Count Calendar is truly long. The next important date comes when instead of 13 b’ak’tuns 20 will have passed. At that point we reach a Piktun. And that day will come October 12, 4772. That would seem to leave a fair amount of time yet to come up with the new websites proclaiming that calamity.

But, not to err in my own projections, one of these eons one of the catastrophists, surely, will turn out to be right! Not this time. And in the meantime, the Mayans have had their season in the spotlight. And their astronomy serves us as a reminder not ever to discount the cleverness of vanished cultures.