What Is Today, Anyway?
by Gil Davis
Dates and elapsed time can be an obsession with some people. Man is the only animal that recognizes and marks the passage of time. Several civilizations created calendars to mark historic, religious, and astronomical events, and many of these calendars are still in use today.
My curiosity about date reckoning was aroused by an example program I read in a programming manual. The program contained two formulas, one for calculating a "serial number" for a particular date, and one for calculating the day of the week for that date. It was a rather odd formula, and I was intrigued by the constants it used. I began to investigate where these constants came from.
A day's serial number was defined as follows:
N = INT(1461 x (if month <= 2 then year - 1 else year) / 4) +
INT(153 x (if month <= 2 then month + 13 else month + 1) / 5) +
(if year <= 1900 and month <= 2 then 1) +
(if year <= 1800 and month <= 2 then 1) + day
Further, the day of the week was defined as follows:
D = (N - 621049) MOD 7
where D=0 through 6, representing Sunday through Saturday.
I plugged in a few dates that I knew what day of the week they were, and I got the right answer. But the example stated that these formulas were only good after March 1, 1700. In fact, the number 621049 in the second formula is the serial number for March 1, 1700 when using the first formula. The number 1461 is four times the approximate number of days in a solar year (365.25). The number 153 is five times the mean length of a month (30.6). These approximations and the other "fudge factors" bothered me, so I set out to learn about calendars. First stop - The Encyclopaedia Britannica. Here is some of what I learned.
The calendar we use today is referred to as the Gregorian Calendar, named after Pope Gregory XIII who established the rules in 1582. It is a corrected Julian Calendar, named after Roman Emperor Julius Caesar, who originated it in 46 B.C.E. (before the common era). Great Britain (and I assume the British colonies) used the Julian Calendar up until 1752, and then adopted the Gregorian Calendar.
The calendar in use prior to Julius Caesar was originated by Romulus around 800 B.C.E. This calendar was based on phases of the moon, combined with an attempt to rectify lunation with solar seasons. There were ten months in the year, starting with March and ending with December, followed by an uncounted winter gap to fill in the remaining year. Six of the months contained 30 days, and four contained 31. This made the year around 304 days long, far short of the 365.242199 days of a solar year.
Around 700 B.C.E. Numa Pompilis, the third King of Rome, split the winter gap into January and February, changed the length of the months with 30 days to 29 days, and the total length of the year became 355 days. Tarquinius Priscus, the fifth King of Rome, adjusted the months further. February contained 28 days; March, May, Quintilis, and October contained 31 days each; January, April, June, Sextilis, September, November, and December contained 29 days. The Encyclopaedia Britannica noted that the Romans had a dread of even numbers, and so most of the months were given an odd number of days. February was given over to the infernal gods, and it was deemed fitting that it contained an even number of days. In order to keep the calendar in step with the seasons, every two years a month called Intercalans was added between the 23rd and 24th of February while dropping the last 5 days of February. The length of Intercalans alternated between 27 days and 28 days on each occurrance. This in effect added 45 days every 4 years for an average of 366.25 days per year, actually a day too long.
The occurrance of the month Intercalans was abused regularly by the Pontifices of Rome, who had the duty of managing this calendar. For their own selfish political gain, they would either add or skip Intercalans to modify terms of office. Seasonal chaos resulted from their combination of greed, ignorance, and neglegence. The vernal equinox, which signifies a new solar year, was occurring further and further from its intended date of March 25.
Enter the hero, Julius Caesar, and the "last year of confusion" became 46 B.C.E.. Caesar enlisted the help of the astronomer Sisogenes to fix the calendar. Together thay established the year at 365 days and adjusted the lengths of the months. February contained 29 days; March, May, Quintilis, September, November, and January contained 31 days each; April, June, Sextilis, October, and December contained 30 days. A bissextile day would be added between February 23 and 24 (called a "point in time") every fourth year to correct the quarter day per year error. In order to correct all the past abuses and errors in applying Intercalans, Caesar added enough days to 46 B.C.E. making that year 445 days long.
When Caesar was assasinated in 44 B.C.E., his adopted son Gaius Octavius took the throne. To honor Caesar, the Senate renamed the month Quintilis, Caesar's month of birth, to Julius (July).
In 8 B.C.E., Octavius discovered that the Pontifices were up to their old tricks, misinterpreting the bissextile rule and adding the extra day every three years. Octavius repaired the errors by not observing the bissextile between 8 B.C.E. and 8 C.E. (common era). Around that same time, Octavius defeated Cleopatra and brought peace to Rome after almost a century of war. To honor their leader, the Senate named him Augustus (the venerable one) Caesar, and in his honor changed the month of Sextilis to Augustus (August). Sextilis was chosen because many fortunate events had occurred during that month. Since it was a 30 day month, and not wanting Augustus to seem inferior to Julius, the Senate made August a 31 day month by taking a day from February. However, this made three 31 day months in a row, so September and November were shortened to 30 days and December was lengthened to 31 days, thus establishing the months as we know them today.
After 8 C.E., the Julian Calendar was finally in full and correct use, but there was still an error in the lenght of the year. By the year 1545, this error amounted to 10 days, and was messing up the date calculated for celebrating Easter. The Council of Trent authorized Pope Paul III to correct the calendar, but he was unable to do so. Another 27 years passed before Pope Gregory XIII finally decided to fix the calendar. He enlisted Christopher Clavius to suggest a scheme to repair the calendar. Clavius found that the problem with the Julian Calendar was that it was 3.12 days too long over 400 years. Clavius proposed a centennial rule, whereby a century year would be a normal year rather than a leap year, unless the year was evenly divisible by 400. In other words, 3 out of 4 century years would be of normal length. This would shorten the error by 3 days over the 400 years. The Pope enacted a Bull to establish the Gegorian Calendar in 1582, ten years later. The calendar was adjusted that year by making October 15 occur after October 4. This rule was slowly adopted by other countries, with some not accepting the change until the 1900's.
When Great Britain adopted the Gegorian Calendar in 1752, the Julian Calendar had erred by a total of 11 days. These days were removed by making September 14 occur after September 2 in that year, which caused a riot over lost wages. Finally, the calendar was set as we observe it today.
By the way, the end of the 20th century is the year 2000, not 1999. When historians began numbering years according to the birth of Jesus, his birth year became 1 AD (Anno Dominus, in the year of our Lord), which followed the year 1 BC (before Christ). This makes year reckoning an ordinal method, meaning that there is no zero year. Therefore, the 20th century started in 1901, and ends in 2000.
Want to see a web page that will generate a calendar for you using JavaScript? Just click here!
More interesting information can be found at these sites:
References to B.C.E. (before the common era) and C.E. (common era) are made in this document to refer to the system of years. This nomenclature is accepted by most scholars. The change was made from BC and AD when historians discovered that Jesus was born several years earlier than previously thought. (Back)
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Copyright© 1988-2006, Gilbert A. Davis. All Rights Reserved.