What Time Is It?

by

John T Lockwood

Whilst struggling through yet another pathetic, meaningless day in my so-called career, I made a modern-style office error. I was working with a computer spreadsheet and inadvertently typed a large integer into a field formatted for dates. I typed in "885643" and the spreadsheet cell returned 10/21/24. This looked like October 21, 1924 but it was, in fact, returning October 21, 4324. "Gosh" , I thought, "I'll be retired by then" . The spreadsheet program was using a date scheme which simply counted days from some fixed point and calculated the date corresponding to that day using a mathematical function. The program I was using sets day zero at January Nothing, 1900. This makes day one January 1, 1900. Day 366 is December 31, 1900.

Calculating dates from sequential numbers is not as easy as it sounds. Leap years raise problems. In a leap year, of course, an extra day is inserted into the calendar -- a process known as intercalating. The first leap year in the 1900's was 1904. Under the computer number scheme it was day 1,521 of the century. Each subsequent leap day fell on the 1 + [365 x 4] day or 1,461st day following its predecessor. The sixty day difference between 1,521 and 1,461 arose from starting day one on 1/1/1900, after the first four years one must count 31 days in January and 28 days in February, 1904 until the initial February 29th was encountered. These 59 days, added to 4 x 365 for the years 1900,01,02,03 made 59 + 1,460 = 1,519. The next day should be February 29, 1904. Problem: that means that the first leap day should be day 1,520 by this scheme but it is day 1,521 instead. What's wrong? Well, the program is cheating so that the current century will appear to have 36,525 days in it. It counts day 60 as February 29, 1900. There was no such date. Leap years occur every four years, but skip those century years not evenly divisible by 400. The year 1900 was therefor, not a leap year.

The scheme used by the computer program creates 25 leap years in the 100 years encompassing 1900 through 1999 inclusive. This makes day 36,525 equal December 31, 1999. The century is therefor exactly 365.25 days x 100 years long. In the real world, of course, there were only 24 leap years in that span of time, meaning the century lasted 36,524 days. If the 20th century were taken to begin on 1/1/1901 and end on 12/31/2000, then we would have a century that lasted 36,525 days with 25 leap years, as the year 2000 is evenly divisible by 400 and is perforce a leap year.

Three out of every four centuries last 36,524 days, with the fourth lasting 36,525. Whether the century just ended was a "short" century or a "long" century depends on when you believe the century began. The 19th century posed no such dilemma, it was 36,524 days in length no matter how one looked at it, as both 1800 and 1900 contained no February 29th. The above signifies that an " average" century lasts 36,524.25 days, or 365.2425 days in a year -- just in case somebody asks. This works out to a total of 146,097 days in a four hundred year cycle. This cycle is the basis for the Gregorian Calendar, which is the civil calendar commonly in use throughout the world.

146,097 is evenly divisible by 7 and yields 20,871 weeks in four hundred years, and 20,871/4 = 5,217.75 weeks in an average century or 52.1775 weeks in year. 1,775/10,000 of a week is 1.2425 days - an important number. A common year contains 52 weeks and 1 day, a leap year has 52 weeks and 2 days. If leap years occurred every four years the leap year cycle would work out to exactly 1,461 days in length (365+365+365+366 = 1,461) which , you remember, was the apparent cycle used for day-numbering in the computer program. This would engender a four hundred year cycle of 146,100 days - 3 days longer than the Gregorian calendar we use. This would cause an average year length of exactly 365.25 days. In the 2,000 years of the common era, the calendar would drift 15 days out of phase. By requiring three " short" centuries for every " long" century, we get an average year length of 365.2425 days. That is 364 (which is 7 x 52) plus 1,775/10,000 (which equals 1.2425) days long. This is, as I said, important -- but why?

Well...........

There once was a monk named Dionysius Exiguus ("Dennis Short") who had a passion for Easter. A good Christian, he was compiling a list of dates on which Easter would fall. His was not an easy task as the calendar for which he was trying to predict future Easter dates was not one designed for the Christian world at all. Working in what we now call the sixth century, a generation or two after the fall of the western Roman Empire (which occurred in the year 476) Dionysius was using a calendar which started with the first year of the reign of the emperor Gaius Aurelius Valerius Diocletianus -- Diocletian to you. Diocletian's reign was a landmark event in Roman history as it closed out the period known as the Principate and ushered in the culminating period of the western empire known as the Autocracy.

Dionysius was interested in calculating the date for Easter but felt it scandalous to record so sacred an event from the reign of a pagan emperor. He therefor attempted to calculate a date for the incarnation of Christ. Unfortunately, it was clear that Christ's life preceded the reign of Diocletian by some centuries. It did not occur to Dionysius to count negative years by the Diocletian calendar and he was therefor forced to use an older Roman calendar which took as year 1 the year of the founding of Rome -- a calendar known as the AUC calendar [AUC = Ad Urbe Condita -- " at the City's founding" ]. This would give him a method of tying a new Christian ecclesiastical calendar to an historical calendar already in use. He tried to place the life of Christ properly, based on what was known as handed down in the gospels and through tradition. Mainly, it had to take place within a time period encompassing some 33 years, he thought, begining sometime in the reign of Herod the Great in Judea. Herod is mentioned as the reigning monarch in Matthew 2:1 at the time of the Nativity and was the king who ordered the Slaughter of the Innocents (Matthew 2:16). Further, based on other new testament references, the public ministry and crucifixion of Jesus had to fall within the reign of Tiberius Caesar, that is, sometime between 767 and 791 AUC.

At Dionysius' time the period of Herod's reign was imperfectly known. Dionysius therefor used references in Luke to Jesus' baptism and beginning of the three-year period of his ministry as taking place in the fifteenth year of the reign of Tiberius Caesar -- a date which corresponded to 783/784 AUC. In Luke 3:23 the age of Jesus at this time is given as " ...Jesus himself began to be about thirty years of age..." . Dionysius took this for exactly thirty years of age and placed the incarnation of Christ at point zero in his calendar thirty years prior to 783/784 AUC and counted it as 1 Anno Domini Nostri -- " Year of Our Lord" or 1 AD. Dionysius established the start of the Christian era at March 25 (9 months prior to Chritsmas) in the year corresponding to 754 AUC. His calendar was called the Era of the Incarnation. Later scholarship established that by Dionysius's calendar, Herod reigned from 37 BC to 4 BC. If the evangelists were right in their chronologies, it meant that Christ must have been born no later than 4 BC and was crucified in about 32/33 AD.

Dionysius was interested in establishing pious dates for Christian feast days which would more or less correspond to historical references in the Bible and elsewhere and with events catlogued in other calendars. In particular, Easter should occur in Spring roughly at the time of the Jewish Passover. He was not much concerned with the astronomical consistency of his calendar. In any case, it is doubtful that Dionysius thought that his calendar would ever be used in the civil world. Indeed, for many centuries thereafter throughout Europe there were numerous local calendars some of which were traditional and based on old pagan calendars, but most of which were regnal. Regnal calendars count years as occurring in the reign of this or that local king or other nobleman. A man from Westphalia might say that he was born in the third year of the Margrave Ekkehardt of Blesséd Memory and was married in the tenth year and his firstborn son arrived in the twelfth year of the Regency of Ludwig the Short and so forth. For legal purposes, such as determining when that firstborn attained majority to receive an inheritance, this was acceptable -- at least for contemporary locals -- but it meant nothing to French guys across the Rhine and became increasing obscure over time as memory of long dead princes and their affairs became dim. It was also imprecise and difficult to square with the other local dating systems used throughout Europe.

This situation appalled a Frenchman who had the most un-French sounding name of Joseph Justus Scaliger. In 1583 Scaliger decided it was high time to sort out all this regnal blather and arrive at a succint method for calculating any historical date. He felt it made sense to simply number all the days of our lives sequentially. But where to start? He did not choose the birth of Christ, a date which he felt could not be accurately determined. Being a Frenchman, he had an inordinate fondness for number-jumbo and complicated mathematical schemes. He chose to coordinate three separate calendrical cycles and choose a starting year based on that. The cycles he chose were the 28 year Solar Cycle (the period after which the days of the week correspondence to the Julian calendar dates repeat), a lunar calendrical cycle known as the Golden Numbers (which shows on which dates the various phases of the moon will occur and which repeats every 19 years), and an obscure Roman fiscal cycle relating to taxation in the Empire that lasted 15 years and was known as the Indiction. The year zero by the Dionysian calendar, which corresponds to 1 BC was year 1 of the Golden Numbers, 9 of the Solar Cycle and 3 of the Indiction. The three cycles would be congruent every 7,980 (19 x 28 x 15) years and Scaliger was able to show that they would all be equal to 1 in the year 4713 BC. Therefor, he started counting the days from January 1, 4713 BC.

Scaliger's scheme is known as Julian Days and for years I thought that it was named after Julius Caesar, though I did not know why. I have since discovered that Scaliger named the sequence after his father -- Julius Caesar Scaliger. His system was accurate but emotionally bleak. The Declaration of Independence does not fall on July 4, 1776 but on Julian Day two million something-or-other and Pearl Harbor was not bombed on December 7, 1941, but on Julian Day two million such-and-such -- a number that would live in infamy, if anyone could remember it.

Fortunately, the Dionysius calendar was widely in use for ecclesiastical purposes and available for adoption throughout Europe to arrange civil matters. It was gradually adopted to these purposes. The problem with it was that it was getting out of whack with the seasons for some reason. The Church was unhappy with this as the method used to calculate Easter (Dionysius's old passion, again) was yielding dates further and further removed from both the true Spring Equinox and from the Jewish Passover (itself determined by yet another calendar which intercalates leap months, no less) during which time, according to the Bible, it should take place. Easter is to fall on the first Sunday after the first ecclesiastical full moon after March 21. The "full moon" used to determine the date of Easter was and is determined by use of lunation tables which were and still are innacurate. These "full moons" are known as "ecclesiastical full moons" as opposed to "true full moons" and can differ from reality to varying degrees. Ecclesiatical full moons are regularly the 14^th day of a luntion and are the basis for the Golden Numbers tables. [see note 1 below]. By the sixteenth century, the Spring equinox, fixed in the calendar at March 21, trailed the true equinox by ten full days. This had to be addressed and fixed and was.

Pope Gregory XIII convoked a commission to reform the old calendar and came up with a solution which was issued in the form of the papal bull Inter gravissimus in 1582. It decreed that 10 days be dropped from the calendar in October of that year: the day after October 4, 1582 became October 15, 1582. It also instituted the system of leap years described above, setting the average year at the 365.2425 days we all use today. That had been the problem with most of the old Roman calendars -- they used a year of 365.25 days.

Yet the Gregorian calendar was not immediately accepted everywhere. It was the middle of the Reformation and Protestant areas such as England, Scandinavia and the northern German principalities rejected the Pope's commission out of hand, although it was accepted in Catholic countries such as Spain, Portugal, France, southern Germany including Austria, and the Italian states. But it was not long before the Protestant lands began to notice that something was indeed wrong with their calendars. It took England a mere 169 years to figure this out and adopt the Gregorian Calendar by a Proclamation of His Majesty's Government in1751. The United States, by the way, uses this calendar as an English hand-me-down from colonial days. Congress has never decreed an official calendar for the USA. Eastern Europe eventually accepted the Gregorian Calendar, but only for civil use. The Russian and Greek Orthodox churches still use the older model for calculating moveable Christian holidays. That is why the Greeks, Russians, Albainians, Serbs and others in Eastern Europe usually observe Easter a week or more later than the rest of Europe.

The great virtue of Pope Gregory's calendar scheme is that it keeps the civil calendar aligned with the " real" length of the year as measured by the time it takes the planet Earth to complete a circle of the sun once. How long is that? The following formula, based on orbital calculations, will yield the approximate length of the tropical year:

Never mind, I'll do the arithmetic for you. We can round the answer to about 365.2421 days (all the gobbledygook after the first number causes a small fraction to be subtracted from the first number and the amount will vary with the Julian day anyway). Notice that the Gregorian cycle year of 365.2425 differs from the " real" year by only about 0.0004 days or 4/10,000 of a day. This is much more accurate than the older calendars in use in the bad old days.

Yet......

I hate to be an alarmist but 4/10,000 of a day may be a small error but it is not nothing. It works out to 8.64 seconds per year. This means a full minute is lost every 6 years 344 days, 22 hours, 49 minutes, 461/4 seconds! After 10,000 years we will be out of phase by four days! By golly, in a measly 2,500 years we will have to skip a leap day just to keep the calendar in harmony with Universe. First the killer bee invasion and now this! And , of course, all of the foregoing is based on a civil day that lasts precisely 24 hours in length. But how long is a day? Is it exactly 86,400 seconds? And what kind of seconds? How are they measured? Are we talking Terrestrial Dynamical Time seconds or International Atomic Time seconds? Or what?

WHAT TIME IS IT ANYWAY?

NOTE 1: Explaining all this completely would require another and even more stupefying essay.

FIN

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