Monday, February 29, 2016

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.

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