The Millennium

For many thousands of years, people all over the world have invented elaborate calendar systems, originally for the purpose of agriculture. They tried to reconcile three astronomical cycles, the rotation of the Earth, the revolution of the Moon around the Earth, and the revolution of the Earth around the Sun. People could see the effects on these astronomical cycles as the day and night, the phases of the moon, and the passage of the seasons. Other astronomical cycles, such as the revolution of Titan around Saturn, or the rotation of the Milky Way, would have gone unnoticed by primitive people. Since these three periods are not integer multiples of each other, calendar systems incorporating all three have to be very complicated. Examples include the Mayan, Aztec, Babylonian, and Chinese calendars. The Babylonians had lunisolar calendar of 12 lunar months of 30 days each, and they added extra months when necessary to keep the calendar in line with the year. The Egyptians replaced the lunar calendar with a solar calendar. They measured the solar year as 365 days, divided into 12 months of 30 days each, with 5 extra days at the end.

There are different ways of measuring a month. First there is the Synodic month (synod = meeting, in astronomy it means conjunction or lining-up) being the time between successive new moons (29.53059 days mean value, min 29.26, max 29.80). This does fit well into years. The Babylonians tried 8 years = 99 months = 2922 days, then 27 years = 334 months but the best approximation was 19 years = 235 months = 6940 days. This last is attributed to Meton (432 BC Athenian Greek) but may have been Babylonian and is preserved today in the Jewish "Metonic Cycle". Each of these was used to create a sequence of years where roughly every third year has thirteen months.

Eclipses present manifold problems that the Babylonians chipped away at with observation. We can approach them from theory. The Moon's orbit is inclined at 5( to the Earth's so eclipses can only occur when the moon crosses the 'ecliptic' (apparent path of the Sun). Such points are called nodes, either ascending or descending. The Draconic month is the time between two ascending nodes (27.21222 days mean value) and since eclipses can only occur when the moon is also full or new we need some nice round numbers where the draconic and synodic month match up. A nice one is 6 synodic months for 61/2 draconic months but it tends to slip fairly quickly being useful for only seven or eight cycles.

A further problem is that the moon's orbit is elliptical and it will be traveling faster when closer to earth (nearest = perigee) and slower when further away (furthest = apogee). The Anomalistic month is the time between perigees (27.55455 days mean value). The Babylonians discovered that 223 synodic = 242 draconic = 239 anomalistic = 6585 days (accurate to a few hours) making eclipses fairly predictable. This is also only a couple of weeks more than 18 years. Halley mistakenly thought they referred to it as the Saros Cycle but the name has stuck. Just for completeness, there is one more month: the Sidereal month (sidereal = of the stars) when the moon returns to the same position relative to the background stars (27.32166 days mean value).

By the sixth century BC the Greeks had taken over everything and refined the convergences. Kallipos (370 BC) took four Metonic cycles and dropped one day to make 76 years = 940 months = 27759 days. Hipparchos did the same to Kallipos and got 304 years = 3760 months = 111035. Euktemon (5th century BC) noted that the times between solstices (longest, shortest days) and equinoxes (equal day and night) were different. The seasons vary from 89 to 94 days due to another orbital irregularity.

The common year is called the Tropical year meaning the time between spring equinoxes (365.24219 days mean value decreasing by 0.000 006 14 days per century). Because the Earth's orbit is elliptical it will travel faster at perihelion (closest, now early January) and slower at aphelion (furthest, now early July). This means that the season around perihelion will be shorter than the one around aphelion. Currently the gaps between equinoxes and solstices are, starting at the Northern Hemisphere Spring Equinox, 92.72, 93.66, 89.84, and 88.98 days. The southern hemisphere gets a few extra days of winter and the northern hemisphere gets a few extra days of summer.

The Anomalistic year is the time between perihelions (365.25964 days mean value). It is longer than the tropical so the date of perihelion will creep a little later each year, about a month in 200 years, so the hemispheres get to exchange the advantageous seasons eventually. The Sidereal year is the time for the Earth to return to the same position relative to the fixed stars (365.25636 days mean value increasing by 0.000 000 12 days per century). Because it is slightly longer than the tropical the equinoxes will gradually creep westward around the ecliptic by 1( in 71.71 years or 360( in 25800 years. This is the famous 'Precession of the Equinoxes' discovered by Hipparchos.

Rome conquered Greece in 146 BC and had been developing their own calendar. All of our calendar names come from the Romans including the word calendar itself. The Roman month began when an official went into the streets and shouted out that a new moon had just happened (Indo-European root kel = shout, calends = start of month) and announce the ides (13th or 15th day) and the nones (9 days before ides).

Originally there were ten months making a year of 304 days: Martius (Mars, god of war), Aprilus (aperire = to open - buds of spring), Maius (Maia, goddess of fertility), Junius (Juno, goddess of the moon), Quintilis, Sextilis, September, October, November, December, the last being the Roman numbers five to ten. In the 8th century B. C., King Numa Pompilius added January (Janus, god of doorways) and February (februa, festival of purification) although the year still began on March 1 until 153 BC when it was set to January 1. In 44 B.C., Julius Caesar changed the name of the month of Quintilis to Julius, naming it after himself. Later Augustus changed the name of Sextilis to Augustus.

January - Janus's month
February - month of Februa
Intercalaris - inter-calendar month, abolished by Julius Caesar
March - Mars' month
April - Aphrodite's month
May - Maia's month
June - Juno's month
July - Julius Caesar's month, originally Quintilis, the fifth month
August - Augustus Caesar's month, originally Sextilis, the sixth month
September - the seventh month
October - the eighth month
November - the ninth month
December - the tenth month

The calendar system we use comes from the Greeks and Romans. The Greeks had a lunisolar calendar, with a year of 354 days. The original Roman calendar was introduced in the 7th Century B. C., and had 10 months with 304 days in a year. In 45 B. C., Julius Caesar, on the advise of the Greek astronomer Sosigenes, who he met in Egypt, switched to a purely solar calendar. This calendar became known as the Julian Calendar and had 365 days per year, except every fourth year, an extra day was added. The leap year is so named because the extra day causes any date after February in a leap year to leap over one day in the week and occur two days later in the week than it did the previous week, rather than just one day later.

Some very minor events in history have had a profound effect on our calendar. Normally the division between the years would fall in either spring or fall, which corresponds to when the Earth goes through dramatic changes, and is also when farmers either plant or harvest. The Celts celebrated New Year's on November 1. New Year's Eve was therefore October 31, which later became Halloween. Originally, the Roman calendar had New Year's Day on March 1. In warm climates, the agricultural season begins around March 1. In 153 B. C., they shifted New Year's back two months, so that the year began on January 1. Thus our calendar is the only calendar system in the world in which New Year's falls in the dead of winter. It's not clear why they did this. The reason usually given is that it gave the consuls more time to reach their provinces. At any rate, it would have seemed less significant a change to them than it would be to us for subtle psychological reasons. In the ancient world, with all societies revolving around agriculture, time was thought of as more cyclical whereas we think of it as more linear.

The Greeks named the days week after the sun, the moon and the five known planets, which were in turn named after the gods Ares, Hermes, Zeus, Aphrodite, and Cronus. The Greeks called the days of the week the Theon hemerai "days of the Gods". The Romans substituted their equivalent gods for the Greek gods, Mars, Mercury, Jove (Jupiter), Venus, and Saturn. The two pantheons are very similar. The Germanic peoples generally substituted roughly similar gods for the Roman gods, Tiu (Twia), Woden, Thor, Freya (Fria), but did not substitute Saturn. Tiu is an extremely obscure Germanic war god that hardly deserves a day of the week named after him.

Sunday - Sun's day, Greek name: Heliou, Roman name: Solis
Monday - Moon's day, Greek name: Selenes, Roman name: Lunae
Tuesday - Tiu's day, Greek name: Areos, Roman name: Martis
Wednesday - Woden's day, Greek name: Hermu, Roman name: Mercurii
Thursday - Thor's day, Greek name: Dios (meaning Zeus), Roman name: Jovis
Friday - Freya's day, Greek name: Aphrodites, Roman name: Veneris
Saturday - Saturn's day, Greek name: Khronu, Roman name: Saturni

The number twelve has had numerological significance since Mesopotamia. Therefore twelve marks were put around the edge of the sundial. Thus the daylight hours were divided into twelve intervals, which were hours. The night is the same length, and so each day had 24 hours. The Babylonian number system was based on both 10 and 60. Therefore, a circle has 360 degrees. This is also the reason why an hour is divided into 60 minutes, and a minute is divided into 60 seconds.

Different people had different systems for numbering calendars. In the Egyptian system, the name of the year, was the name of the pharaoh and the numbers of years he had reigned. Often, people would count the number of years they imagined to have taken place since a mythological event. The Romans counted the number of years to have occurred since Romulus slay his brother Remus, and founded Rome. The fact that no such people ever existed was considered of no consequence. Later the Christians counted from the year they imagined that Jesus was born. The fact that no such person ever existed was considered of no consequence.

How did the Christians select this arbitrary date as the supposed year of birth for their fictional founder? There are 12 lunar months per solar year with roughly 10 days left over. In order to keep a lunar calendar in step with the solar calendar, it is necessary to add a 13th month every two or three years. Two millennia ago, to keep the Jewish calendar in line with the seasons, a committee of the Sanhedrin used to examine vegetation in the spring to determine if the extra month should be added. Because Easter is timed according to Passover, early Christians depended on the annual report from the Sanhedrin to know when to celebrate. As Christianity spread throughout the Roman Empire, it became increasingly inconvenient to wait for word from Jerusalem, so at the Council of Nicea in 325 A. D., the bishops agreed to regularize the calculation of Easter. This calculation could be done with reasonable accuracy because lunar months and solar years get back in step every 19 years if precisely seven months have been added beyond the usual 12 per year. This 19 year cycle, recognized by the Babylonians, is called the Metonic cycle, after a Greek astronomer who discovered it independently in the 5th Century B. C.

After the Council of Nicea, a bishop of Alexandria named Cyril provided a 95-year table for calculating the date of Easter. His table ended on the year we call 531 A. D., and the task of extending the table was assigned to a monk named Dionysius Exiguus. Dionysius realized that to get a repeatable cycle of the Easter dates he had to multiply three cycles: 19 for the Metonic cycle, 7 for the days of the week, and 4 for the leap-year cycle of the Julian calendar, yielding the number 532, the basis for the Dionysian cycle. Starting his cycle just where Cyril's table left off, Dionysius discovered that 532 years earlier the vernal equinox had coincided with a full moon. He thought this was so amazing, he decided that this marked the immaculate conception of Jesus Christ, who was then born about nine months later on December 25. The date December 25 had previously been selected for Jesus' birth because the pre-existing Mithric cult had long believed that their god Mithra had been born on December 25. The whole story of the Nativity was taken directly from the story of Mithra's birth.

At that time, it was customary to mark events by the reign of the emperor. The year in which the emperor came to power would not be counted. The following year would be year 1 of his reign. Dionysius decided to count "The Reign of the Lord" in the same way. The conception and birth of Jesus took place in the year in which the vernal equinox was on a new moon, which was the year we now call 1 B. C., and so the following year would be year 1. We have been counting years like this ever since.

There have been many changes in the calendar since then. The Julian year was 11 min and 14 sec longer than the solar year. This discrepancy accumulated until by 1582 the vernal equinox occurred 10 days early. To make the vernal equinox occur on March 21, as it had at the Council of Nicea in 325 A. D., Pope Gregory XIII ordered that 10 days be dropped from the calendar. To prevent further displacement, he instituted the Gregorian calendar that said that century years divisible evenly by 400 should be leap years, and that all other century years should be common years. It took centuries for it to be globally accepted. When Britain adopted the Gregorian calendar in 1752, the day after September 2, 1752 in Britain, became September 14, 1752. The Soviet Union adopted the Gregorian calendar in 1918. The October Revolution was actually in November according to our calendar. Greece adopted the Gregorian calendar in 1923. Eastern Orthodox people still use the Julian calendar for religious purposes.

Dionysius Exiguus first used the expression "annus Domini" for the "year of the Lord". However it was the Venerable Bede, who lived in Britain in the 8th Century, who made it popular. Bede also invented the descending years for dates before 1 A. D., these became the B. C. dates. However this did not really catch on until the 16th Century. However Bede did succeed in making the phrase "annus Domini" popular. Thus years were listed as "A. D. 300". Later when the descending dates were invented, they were called "Before Christ", and thus a year would be given as "300 B.C." Since you always say "B. C." when referring to B. C. dates, but hardly ever say A. D., when referring to A. D. dates, people became used to seeing the letters, if any, behind the date. Therefore in the 19th Century, it became common to put the A. D. letters behind the year in the rare times when you use them. Thus the phrase" 1969 A. D." appears on the plaque left by the Apollo 11 astronauts on the Moon. Also, originally people would use the cardinal numbers plus the word "Century", such "the 15th Century" to refer to dates from 1401-1500. In the 19th Century, people shifted the phrase to include the lower but not upper round number, so "the 15th Century" would be the years 1400-1499. Thus, people used the phrase "the turn of the century" to mean the year 1900. This method of describing centuries was never intended to mean the "15th Century to have elapsed since a point in time". All it is, is that if you look at the centuries since 1 A. D., there appears to be a century of two digit years, which they called the first century, another group with a one in hundreds decimal place which they called the second century, etc.

One of the most baffling things to me is how some people believe that a calendar system that existed earlier is somehow superior to a calendar system that existed later. They claim that to say "A. D. 1969" is somehow more "correct" than saying "1969 A. D." because the former convention existed earlier. They claim that to say that the 20th Century spans 1901-2000 is more "correct" than saying it contains the years 1900-1999, simply because former was done in the remote past. Presumably, these people believe that the Julian calendar is more "correct" than the Gregorian calendar. They must believe that you should pretend that New Year's Day is on the day most of us call March 1. They presumably grow red in the face if someone does not count the years from when Romulus killed his brother Remus. They presumably believe the Egyptian calendar is even more correct. Better still, you should not use any calendar system since our most remote ancestors, stone-age tribes of hunter-gathers, did not have calendar system. Who are these strange people? Have you ever heard some baffoon, gloating in the self-confidence that only such extreme retardation can bring, claim that the "real Millennium" is in 2001? It's really a question for a psychiatrist as to what motivates these people to say this.

In the Roman Empire, an emperor would come to power in the middle of the year, and that year would not be counted as a year of his reign. The following year would be year 1 of his reign. It was not intended as a measure of the length of time the emperor had been in office. It was merely a designation attached to events that gave a vague sense as to when the event occurred in an emperor's reign. When Dionysius came up with his calendar system, the Roman Emperor was Diocletian who persecuted Christians mercilessly. It is not surprising that Dionysius would want to mark events by something else. He decided that he would rather use the year Christ was conceived, which he decided was when a new moon fell on the vernal equinox. The following year was designated 1. That's all there is to it. However, today many people seem to be under the impression that the numbers for the years, centuries, and millennia are supposed to be the number of the appropriate durations to have taken place since the birth of Christ. That was never what it was.

Let's determine what the numbers for the years, centuries, and millennia actually are the number of time units since. We have to do it separately for the two conventions: the old way in which the 20th Century would be considered to span 1901-2000, and the modern way in which the 20th Century is considered to span 1900-1999. I'm just using the labels "old way" and "modern way" for want of better names. Probably more people used the phrase "turn of the century" to mean 1901 than used the phrase "the millennium" to mean 2001. However, there were people using both the "old way" and "modern way" at all times throughout history up to the present day.

First the old way. Let's look at the following time line, and see at what times what numbers of full years have elapsed since Jan 1, 1 B. C.


      0              1             2              3
|----------|----------|----------|----------|
1 B.C.     1 A.D.     2 A.D.      3 A.D.     4 A.D.

Therefore, starting with 1 A. D., the number of the year at any point is the number of full years to have elapsed since Jan 1, 1 B. C.

I have never heard of a cardinal number being attached to the decades. Today, we simply refer to the decades of the 20th Century as "the 60's", "the 80's", etc. If you were to refer to earlier decades, you'd say "the 1470's, etc. However, let's determine cardinal numbers for the decades anyway. The number of the decade would be defined as the number of full decades to have occurred since Jan 1, 10 B. C.


|<-----0----->|<-----1----->|<-----2----->|
0 1234 5678 9012 3456 789 01234 56789
|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|
| 9876 543 21 | 2345 6789 |          15        |                      |
10 B.C.       1 A.D.            10 A.D.           20 A.D.          30 A.D.

Jan 1 , 1 A. D. is when one full decade has elapsed since Jan 1, 10 B. C. On Jan 1, 10 A.D., you still have only one full decade elapsed since Jan 1, 10 B. C. You have to wait until Jan 1. 11 A. D. in order to have two full decade elapsed since Jan 1, 10 B. C. On Jan 1, 20 A. D., you still have only two full decades elapsed since Jan 1, 10 B. C. You have to wait until Jan 1, 21 A. D., in order to have three full decades elapsed since Jan 1, 10 B. C. Therefore, the "1st Decade" spans 1-10 A. D., the "2nd Decade" spans 11-20 A. D., etc.

The number of the century is defined as the number of complete full centuries to have elapsed since Jan 1, 100 B. C. This is done the exact same way as the decades above. In this case, the vertical slashes represent the decades, 10 B. C., 10 A. D., 20 A. D., etc. Remember that only nine years elapse between Jan 1, 1 A. D. and Jan 1, 10 A. D.


|<-----0---->|<------1---->|<-----2----->|
|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|
|                    |                     |                      |                      |
100 B.C.      1 A.D.           100 A.D.         200 A.D.        300 A.D.

In this case, the 1st Century spans 1-100 A. D., the 2nd Century spans 101-200 A. D., etc. This is consistent with the old fashioned convention of saying that the 20th Century spans 1901-2000.

You would do the millennia the same way. The number of the millennium is defined as the number of complete full millennia to have elapsed since Jan 1, 1000 B. C.


|<-----0----->|<----1----->|<-----2----->|
|--------------|--------------|--------------|--------------|
1000 B.C      1 A.D.           1000 A.D.     2000 A.D.      3000 A.D.

The First Millennium would span 1-1000 A. D., the Second Millennium would span 1001- 2000 A. D., and the Third Millennium would span 2001-3000 A. D. This is consistent with the claim you sometimes here that the "real millennium" begins in 2001. These people are evidently measuring the number of complete full millennia to have elapsed since Jan 1, 1000 B. C.

The modern way of considering the 20th Century to span 1900-1999, and saying the Third Millennium begins on Jan 1, 2000, is the following way. The years are done in the exact same way as the old version. The number of the year is the number of complete years to have elapsed since Jan 1, 1 B. C.


      0              1             2              3
|----------|----------|----------|----------|
1 B.C.     1 A.D.     2 A.D.      3 A.D.     4 A.D.

The number of the decade, although no one ever refers to such a thing, is the number of complete decades to have elapsed since Jan 1, 11 B. C. instead of Jan 1, 10 B. C.


|<-----0----->|<-----1----->|<-----2----->|
0 123 456789 01 23456 7890 123 456789
|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|
|10987654 321 | 2345 6789 |          15        |                      |
11 B.C.       1 A.D.            10 A.D.           20 A.D.          30 A.D.

In this system, the "1st Decade" spans from 1 B.C. to 9 A. D., the "2nd Decade" spans from 10 A. D. to 19 A. D., etc.

The centuries are done the same way. The number of the century is defined as the number of full centuries to have elapsed since Jan 1, 101 B. C.


|<-----0---->|<------1---->|<-----2----->|
|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|
|                    |                     |                      |                      |
101 B.C.      1 A.D.           100 A.D.         200 A.D.        300 A.D.

The 1st Century is from 1 B.C. to 99 A.D. The 2nd Century is from 100 A.D. to 199 A.D. This is consistent with the modern view that the 20th Century spans 1900-1999.

The number of the millennium is defined as the number of complete full millennia to have elapsed since Jan 1, 1001 B. C.


|<-----0----->|<----1----->|<-----2----->|
|--------------|--------------|--------------|--------------|
1000 B.C      1 A.D.           1000 A.D.     2000 A.D.      3000 A.D.

According to this, the First Millennium was from 1 B.C. to 999 A. D. The Second Millennium was from 1000 A. D. to 1999 A. D. The Third Millennium would be from 2000 A. D. to 2999 A. D. This is consistent with the modern view that the New Millennium will begin on Jan 1, 2000.

Some people believe, erroneously, that the cardinal numbers of various units of time were intended measure lengths of time since points in time. Therefore, I determined what they would refer to if you were to force these numbers to mean such a thing. However, this has nothing to do with the B. C. dates. By definition, the numbers attached to intervals of time occurring before 1 A.D. can not be thought of as measuring lengths of time since points in time. Therefore, how might you modify the above systems to also include the cardinal numbers attached to time intervals before 1 A. D.? You could draw a vertical line, and place it through the timeline at Jan 1, 1 A. D. Then you use this line as a axis of symmetry to create bilateral symmetry. Imagine the right hand side being rotated around to the left hand side, so both sides become mirror images of each other. All of the cardinal numbers for all the time intervals on the right hand side are then reproduced in reverse order on the left hand side. In the old system, the 2nd Century B.C. would span 200 B. C. - 101 B. C. The 1st Century B. C. would span 100 B. C. - 1 B. C. The 1st Century A. D. would span 1 A.D. - 100 A.D. The 2nd Century A.D. would span 101 A.D. - 200 A.D. In the modern system, the 2nd Century A. D. would span from 199 B. C. - 100 B. C. The 1st Century B. C. would span from 99 B. C. - 1 B. C., which is only 99 years. The 1st Century A. D. would span 1 A. D. - 99 A. D., which is also only 99 years. The 2nd Century A. D. would span 100 A. D. - 199 A. D.

This is all very silly of course, since these cardinal numbers were never intended to mean the such and such time unit to have elapsed since a point in time. This method of describing centuries was never intended to mean the "15th Century to have elapsed since a point in time". All it is, is that if you look at the centuries since 1 A. D., there appears to be a century of two digit years, which they called the first century, another group with a one in hundreds decimal place which they called the second century, etc. If you were to retroactively try to come up with a way in which these cardinal numbers could be viewed as the number of time units to have elapsed since a point in time, you have to come up with the irrational cumbersome system I just devised. Obviously, nothing like this crossed the mind of the people who invented the calendar system. In fact, Dionysius never even intended for the number of the year to be the number of years to have elapsed since the time he imagined Christ was born since otherwise he would have shifted New Year's to Dec 25. Actually, what he was concerned with was the conception not the birth of Christ anyway. It's just so ridiculous at so many levels.

1) Jesus is a completely fictional character that never existed. Talking about when this imaginary character was "born" is like arguing about when Sherlock Holmes was born.

2) Most scholars of this issue have long since put the imaginary birth of this fictional character at 5 B. C., not 1 B. C. The real reason 5 B. C. was selected as the new date of the imaginary birth of the fictional character was because Herod, a real person, died in 4 B. C. Since he's alive in the fictional story of the Nativity, this became embarrassing.

3) Dionysius was concerned, not with the birth but the conception of Christ, which he assumed must have occurred when there was a new moon on the vernal solstice. Hey, why not?

4) He assumed that this imaginary immaculate event took place on 1 B. C., not 1 A. D., as is often stated. Some particularly stupid people are actually under the impression that he put it on the year 0, which interesting since there was no year 0. This would have been particularly neat trick for Dionysius considering that the number 0 had not yet been invented. You would also be shocked by the number of people I've met who assumed that "A. D." stands for "after death".

5) The cardinal ordering of the centuries was never intended to mean "the such and such century to have elapsed since a specific point in time". It was merely that you see a block of centuries with no hundreds digit, so you call that first, a block with a one for the hundreds digit, you call that second, etc.

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