A day here, a day there - pretty soon it adds up

kw: calendars, analysis

In the wake of the holidays, I was thinking about the origin of "Twelve Days of Christmas." It got me to thinking about the changes to the calendar that led to the 12 days, and the manipulations of the year that led to that. In the Science Q&A section of eNotes.com I find the following, posted by fact-finder:

The longest year on record was 46 B.C., when Julius Caesar (100-44 B.C.) introduced his Julian calendar. In order to make up for the difference between the calendar date and the season (determined by the position of the Earth in its yearly journey around the sun), Caesar inserted 2 extra months and added 23 extra days to February. Thus, 46 B.C. was 455 days long.

The shortest year on record was 1582, when Pope Gregory XIII (1502-1585) introduced his calendar, the Gregorian calendar. He decreed that October 5 would be October 15, eliminating 10 days, to make up for the accumulated error in the Julian calendar.

The world only gradually changed over to the Gregorian calendar. Catholic Europe adopted it by the year 1584. Many Protestant continental countries did so between 1699 and 1700; England imposed it on its colonies in 1752 and Sweden adopted it in 1753. Many non-European countries adopted it in the nineteenth century, with China doing so in 1912, Turkey in 1917, and Russia in 1918.

Sources: Famighetti, Robert, ed. The World Almanac and Book of Facts 1995, p. 288; Trefil, James. 1001 Things Everyone Should Know About Science, p. 138.

Based on the entire Gregorian correction, the year 1600 was a leap year, while 1700, 1800 and 1900 were not. In the late 1700s, there were some in England who went along with the calendar change and some who did not. The former practiced Christmas Day on December 25, according to the Gregorian Calendar. Those who stuck with the Julian calendar used their December 25, which fell on January 5. Over time, neighbors accommodated neighbors, and many began to celebrate the whole twelve days as the Christmas Season. Sometime thereafter, the familiar song was written (or perhaps it accumulated).

Since that time, the loss of two leap days in 1800 and 1900, followed by 2000 having a leap day, has shifted "Old Christmas Day" to January 7. It would be humorous to coin a new song of the fourteen days of Christmas!

All this takes care of making the average calendar year work out to a length of 365.2425 days, by mixing 365- and 366-day years. Since 1582, all the years have been of one of these two lengths. But there is more. The actual Tropical Year has a length of 365.2422 days (in 2000: 365.242189). This difference of 0.000311 days yearly means an extra leap year needs to be skipped about every 3,215 years. 3215+1582=4797. That is long enough that the gradual change in the length of the tropical year must be taken into account; the date we need to skip a leap year will be a year or two later, like in about the year 4799 or maybe 4800. 4800 has a nice ring to it. Let's use that.

Our fractured time sense

kw: observations, time perspective, calendars

I have been researching the 2012 craze. While I know it is largely a scam, I want solid data behind what I say when the subject comes up. At the 2012Science Blog I found the statement that we, as the Maya did, use multiple calendars. I hadn't thought such a thing before, so I contacted the blogger. Our discussion led me to some interesting insights. Firstly, While we do have different calendars in use by different cultures ("Civil" in the West, which is a Catholic calendar; then Chinese, Jewish and Islamic calendars used ceremonially by their various diasporas), just within the Western Civil calendar we have several ways of counting calendar time:

• Day names in a 7-day, or weekly, cycle (Sunday, Monday, etc. in English).
• Day numbers from 1-7 in the weekly cycle, but seldom used.
  
• Day numbers from 1-365 (or 366) in a yearly cycle. This "day count" is mainly used by merchants to calculate "shopping days until Christmas".
• Day numbers from 1-31 (or 30, 29, 28) used within a month; an irregular cycle.
  
• Week numbers from 1-52 in a yearly cycle, also rarely used but found in calendar/mail programs such as Lotus Notes.
• Month names in a 12-month, yearly cycle.
• Month numbers from 1-12 in a yearly cycle, mainly used for writing dates compactly.
• Season names in the yearly cycle. These are interesting, because we have at least three ways to determine a season boundary: Astronomical, Signs, and Business. Astronomically, Spring starts with the Vernal Equinox on March 21 or 22. The signs of Spring could be sighting the first robin or daffodil, or ice break-up on a river. Spring season for business purposes starts whenever garment salespeople decide to put winter coats on sale and begin filling the racks with lighter wares and seasonal items such as umbrellas.
• Business quarters, which are usually 91 or 92 days in length; Q1 begins when a business (or civil entity) begins its Fiscal Year; a cycle of four per year.
  
• Year numbers in a linear sequence. We have agreed-upon meanings for year numbers covering all of history since the Big Bang more than 13,000,000,000 years ago, but usually confine the writing of dates to periods beginning about 400BC with the Golden Age of Greece. Note that there is no "year zero" when using BC and AD (or BCE and CE), so 400BC equals year -399 in an undesignated count.
• Century numbers in a linear sequence. This is the twenty-first century.
• Millennium numbers in a linear sequence. This is the third millennium since 1AD began the first millennium. This convention is seldom used.

I had not thought before that our time systems are all cyclical for periods shorter than a year, and linear for years, centuries and millennia. We don't think of centuries and millennia as cycles, though we could. The current interest in December 21 (or 23), 2012 is because it (probably) is the last day in the Mayan "long count", which is not actually the longest period the Mayans wrote about, but was the longest cycle used for official inscriptions commemorating dates such as the coronations of kings.

We do have a "long count" of sorts to care for. The Gregorian calendar uses a 400-year cycle to determine which leap years to skip to keep the vernal equinox in the right place. The Gregorian Year is 365.2425 days in length. However, there is still a small fraction of a day left out. There are two definitions of an Astronomical Year, the Mean Tropical Year of 365.24219 days and the Equinoctial Year of 365.24237 days. If we want to keep our calendar lined up with the former year, we'll have to make a correction by about 4810AD; for correcting to the latter year, we can wait until about 9300AD, depending on how much the day and year length have changed by then.

So sometime before 4800AD we have to decide which astronomical year to adhere to. Ultimately, we keep our calendar in sync with the sky, so that the precessing equinoxes happen on the same day (within a day or two) year after year. And the Mayan long count? It has similar significance to December 31, 1999 (or 12/31/2000 for those of us who start counting with "one"!): the last day of a significant era, but with no prophetic meaning.