History of the Calendar

 

We all know there are 365 days in a year and we all know that leap years occur every 4 years.  But have you ever wondered why?  Have you ever wondered about the history of our means of measuring history - the history of the calendar itself ?

Two major influences on our calendar system are the sun and the moon.  According to very precise modern measurements, we now know that it takes approximately 365.242 days for the Earth to orbit the sun.  And we also now know that it takes about 29.531 days to cycle through from full moon to the next full moon.  Our calendar became what it is today because of the fact that these numbers are not exact integers.

One of the early developers of our calendar system was Julius Cesar.  He is the one who devised the law that created a leap year.  This was done in what we now call the year 45 B.C.  The reason for the leap year was that at the time, astronomers and mathematicians thought that the Earth takes 365.25 days to orbit the sun.  They decided that if they added one day to the year, every four years, they could keep the calendar synchronized with the seasons. Over a period of 4 years, the average length of the year would then become 365.25 days. For religious reasons and convenience it was very important to have the same season occurring during the same month each year.  Without the leap year, it was realized that it wouldn't take very long before the seasons had drifted to different dates in the calendar.  This was a good solution and lasted for about 1500 years.  It was called the Julian calendar.

By the year 1582 the calendar had shifted out of sync with the seasons by about 10 days. This is because the length of Earth's orbit is not exactly 365.25 days but something slightly less.  The medieval poet Dante wrote that eventually January would no longer be part of winter.  For many reasons including religious ones - many Christian rituals are closely tied to the calendar - it was decided that dates from October 4th to October 15th of 1582 would be completely skipped to realign the calendar with the traditional dates for seasonal events (like the solstice and equinox which have bearing on religious and agricultural activities )  Because astronomers and mathematicians had calculated that the solar year was less than 365.25 it was decided that 3 leap years would be removed every 400 hundred years.  The rule used was this:  Leap years will occur every 4 years except during century years (years ending with 00) except if the century year is divisible by 400.  Below is an example of how this works:

1600 - this year was a leap year, it is divisible by 400, it marks the beginning of a 400 year cycle
leap years every four years until...
1700 - not a leap year
leap years every four years until...
1800 - not a leap year
leap years every four years until...
1900 - not a leap year
leap years every four years until...
2000 - this year is a leap year because it is divisible by 400, it marks the beginning and end of a 400 year cycle
leap years every four years until...
2100 - not a leap year
leap years every four years until...
2200 - not a leap year
leap years every four years until...
2300 - not a leap year
leap years every four years until...
2400 - this year is a leap year, its the beginning and end of a 400 year cycle

The scheme of dropping 3 leap years out of every 400 years was first adopted by predominately Catholic countries beginning in the year 1582 during the time of Pope Gregory XIII.  It was called the Gregorian calendar and it is the calendar that we now use in modern times.

It is interesting that the division because Catholic and Orthodox Christian and other faiths played a role here in the acceptance of the new calendar system.  The last country to accept the Gregorian calendar was Greece in 1923.  It is also the reason why historical records for the 16th and 17th century sometimes disagree by 10 days.  England and the American colonies accepted the new calendar in 1752.

There is also an interesting history to the names of our months and days of the week.

First of all, the word "month" originated with the word for "moon" because a month measure the period from one full moon to the next.  Also, the word for "week" is from a Tuetonic word (from northern Europe until about 100 BC) meaning change as it measured changes in the moon during one complete cycle.

Thousands of years before the birth of Christ, Babylonians worshipped the moon.  Months began and ended with a full moon.  At the full moon, at the half moon and the new moon, they would take a day off from work to rest and worship.  This meant that a holy day (holiday) would occur about every 7 days.  The Babylonians called this day "Sappatu".  The Babylonians had Jewish slaves who called this day the Sabbath. Eventually every week became 7 days because 7 became an important number: some considered it magic or mystical.  This is because astronomers had found 7 planets in the night sky (the word planet means "wanders the universe").  The planets were thought to be (or represent) the gods and each day of the week was named after the planets.  Our current names for the days derive from those original names in the following way:

Sunday = the Sun's day
Monday = the Moon's day
Tuesday = Tiw's day (a Norse name for Mars, the god of war)
Wednesday = Woden's day (Woden is the Norse name for Mercury, the messenger)
Thursday = Thor's day (Thor is the Norse name for Jupiter, the supreme Roman god)
Friday = Frigg's day (Frigg is the Norse name for Venus)
Saturday = Saturn's day (Roman god of agriculture)

Perhaps you are familiar with the children's rhyme about the days of the week:  Monday's child is fair of face, Tuesday's child is full of grace, Wednesday's child is full of woe, Thursday's child has far to go, Friday's child is loving and giving, Saturday's child works hard for a living, But the child that's born on the Sabbath day, Is bonny and blithe, and good and gay.

Early Christians were Jews and worshipped Christ on the Sabbath.  When the Roman empire converted to Christianity in the year 324, Sunday became the official first day of the week and the day for rest and worship.  After World War II, because of the holocaust, many people across the world adopted Saturday, the traditional Jewish Sabbath as a day of rest also out of respect for the Jewish people.  That is why in this country we have a tradition of a 5 day work week.

The history of the names of the months is also very interesting.  Originally, the ancient Romans had a 10 month calendar which ended with December (the tenth month.) Two months were eventually added and then Julius Cesar reformed the calendar which led to our current names:

January - from the month of Janus, the god of gates and doorways.
February - from Februa, a Roman festival of purification
March - from the god Mars, the beginning of the year for the Romans - it was the time to resume war
April - from the goddess Aphrodite, the goddess of love and beauty
May - from Maia, a goddess of spring
June - from Juno, wife to Jupiter.  She is the goddess of marriage
July - named after Julius Caesar - hey if you rewrite the calendar, you can name a month after yourself too!
August - named after Augustus Caesar, who made some changes after Julius
September - meaning seventh month
October - meaning eighth month
November - meaning ninth month
December - meaning tenth month

By the way, the word "Calendar" comes from the Greek meaning "to call" and evolved from the fact that the first day of the month was the day when accounts were due.

Another interesting peculiarity involving the calendar is the zodiac.  The zodiac is a collection of twelve constellations which lie in a band in the sky in which we see the apparent rotation of the sun.  Ancient astronomers had determined that the stars remained fixed in the night sky, but the sun seemed to move relative to these stars.  They were able to determine which stars the sun was blinding from their view throughout the year.  Each part of the year then was assigned a sign from the zodiac.  About 2000 years ago the astronomer Hipparchus determined the positions of the sun during the year.  This determination forms the basis of astrology:

Aries (the Ram)

March 21-April 19

Taurus (the Bull)

April 20-May 20

Gemini (the Twins)

May 21-June 20

Cancer (the Crab)

June 21-July 22

Leo (the Lion)

July 23-Aug. 22

Virgo (the Virgin)

Aug. 23-Sept. 22

Libra (the Scales)

Sept. 23-Oct. 22

Scorpius (the Scorpion)

Oct. 23-Nov. 21

Sagittarius (the Archer)

Nov. 22-Dec. 21

Capricornus (the Goat)

Dec. 22-Jan. 19

Aquarius (the Water Bearer)

Jan. 20-Feb. 18

Pisces (the Fishes)

Feb. 19-March 20

However, now, 2000 years later, because of a 10,000 year cycle in which the Earth wobbles slightly about its axis, the above original dates are no longer accurate!  In 1997, the correct dates were:

Jan.

1

-

Jan.

19

Sagittarius

Jan.

20

-

Feb.

15

Capricornus

Feb.

16

-

Mar.

11

Aquarius

Mar.

12

-

Apr.

18

Pisces

Apr.

19

-

May

13

Aries

May

14

-

June

20

Taurus

June

21

-

July

20

Gemini

July

21

-

Aug.

10

Cancer

Aug.

11

-

Sept.

16

Leo

Sept.

17

-

Oct.

30

Virgo

Oct.

31

-

Nov.

22

Libra

Nov.

23

-

Nov.

29

Scorpius

Nov.

30

-

Dec.

17

Ophiuchus

Dec.

18

-

Dec.

31

Sagittarius

In other words, astrology is based on observations from 2000 years ago which are no longer even correct!  Astrology, something we can still find in our daily newspapers, is actually of no value because it is based on incorrect data and incorrect assumptions and is completely unscientific - that is, it has nothing to do with actual reality.  Astrology, is called a pseudo-science because it pretends to be science when it definitely is not.  Astrology provides theories and predictions to explain what has happened and will happen but it is a bunch of nonsense because (1) it is based on incorrect observations (2) makes predictions which are not legitimately scientific because they are not falsifiable.

Another interesting fact about our calendar is that there is no year 0.  Since a century represents one hundred years, the first century is from the year 1 to (and including) the year 100. The second century from 101 to 200 (inclusive).  Thus the 20th century is from the year 1901 to 2000.  The year 2000 was part of the 20th century.  The year 2001 is the first year of the 21st century.

The date for Easter has an interesting history:  In the year 325, at the Council of Nicea, early church leaders decided that Easter would be the first Sunday after the first full moon occurring on, or after, the spring equinox.  The spring equinox is the date in March when day and night have equal length.  This is because the date of Christ's resurrection was determined to have been on a Sunday after the Jewish Sabbath during Passover. And the date of Passover is in part based on the date of the spring equinox.  The date of Easter was originally based on the Julian calendar and by 1582 the dates of seasons and the equinox had drifted about 10 days earlier in the calendar from their original dates.  When the change was made from the Julian calendar to the Gregorian, the church began to calculate the date of Easter based on where the moon was in its cycle at the beginning of each year and then using that in conjunction with the date of the spring equinox.  Because number of days in a lunar cycle is approximately 29.531 and the number of days in a solar year is 365.242 changes have to be made every so often in the formulas used in the calculation for Easter.  The last change was in 1900. Then next will be made in 2200. 

In 1876, an anonymous American wrote an article in the journal Nature describing the first flawless procedure to calculate the date for Easter (as opposed to method used at the time, which had to be occasionally corrected.)  In 1965, Thomas O'Beirne of Glasgow University published the following algebraic procedure for finding the date of Easter.

Choose any year of the Gregorian calendar and call it x.

1. Divide x by 19 to get a quotient and a remainder A.

2. Divide x by 100 to get a quotient B and a remainder C.

3. Divide B by 4 to get a quotient D and a remainder E.

4. Divide (8B + 13) by 25 to get the quotient G.

5. Divide (19A + B - D - G + 15) by 30 and call the remainder H.

6. Divide (A + 11H)  by 319 to get a quotient M.

7. Divide C by 4 to get a quotient J and a remainder K.

8. Divide (2E + 2J - K - H + M + 32) by 7 and call the remainder L.

9. Divide (H - M + L + 90) by 25 to get a quotient N

10. Divide (H - M + L + N + 19) by 32 to take the remainder as P.

Easter Sunday will be the Pth day of the Nth month.  (N = 3 for March or 4 for April)

It is also interesting that we can use an algebraic formula to determine the day of the week for a given date.  That is, based on a mathematical analysis of the calendar, we can develop a method to determine the day of the week for any date in the calendar.  Because the analysis is long and complicated a deductive proof  is omitted!  What is provided below is the result only of a mathematical analysis of the calendar the yields an algebraic function to find the day of the week for a given date.

The procedure below is valid only for the Gregorian calendar.  Suppose we are given the date with year y, month m, and day d, then we can use the following procedure to determine the day of the week for that date.

1. If we are given a month m with any integer in the set (1,..,12), then calculate j(m) as a function of m as follows: 

j(1)=0, j(2)=3, j(3)=2, j(4)=5, j(5)=0, j(6)=3, j(7)=5, j(8)=1, j(9)=4, j(10)=6, j(11)=2, j(12)=4.

2. If we are given a month of January or February, then first, subtract 1 from the year.  Otherwise, given any year y, we calculate g(y) as a function of y as follows: g(y) = y + [y/4] - [y/100] + [y/400].   Note that [x] is the greatest integer in x.  

3.  Now calculate the number N for the day of the week as follows: N = (d + j(m) + g(y)) mod 7.  Here, "mod" means find the remainder after division.  In other words we find the remainder when (d + j(m)+g(y)) is divided by 7.

Now, N=0 means Sunday, N=1 means Monday, N=2 means Tuesday, N=3 means Wednesday, N=4 means Thursday, N=5 means Friday and N=6 means Saturday.

To summarize, we have developed a function of three variables.  We can call this function N and refer to it as N(d,m,y) to emphasize that the function N depends on three variables d, m and y.

To write this function explicitly, we have

     N(d,m,y) = (d + j(m) + g(y) ) mod 7. 

Note that N(d,m,y) is a composite of several other functions as discussed above.  N is a composition of functions because it is function that contains other functions.  In fact, N contains the function g(y) which contains the greatest integer function.  That is, N is composition of a composition. 

Note that the domain of N is based on the acceptable values of d, m and y.  That is, 0<d<31, 1<m<12 and because the function is valid only for the Gregorian calendar, y>1582.  The range of the function N is the set of integers from 0 through 6, inclusive.

Here is an example of how to use the above procedure for calculating the day of the week for a particular date.

Suppose we want to find the day of the week for July 19th, 1969.  Then we'll use d=19, m=7 and y=1969.

1.  First we determine, given the definitions above, that j(7)=5.

2. Now we calculate g(1969) which is 1969 + [1969/4] - [1969/100] + [1969/400].  Because we use [x] to indicate the greatest integer function, this gives us g(1969) = 1969 + 492 - 19 + 4  = 2446 (note how we rounded down in each calculation using the greatest integer function.)

3.  Finally, we determine N as follows:  N = (19 + 5 + 2446) mod 7.  This requires dividing 2470 by 7 and taking the remainder.  This division produces a remainder of 6.  In other words, N = (19+5+2446) mod 7  = 2470 mod 7 = 6.  Therefore, based on the rule stated above, N = 6 means July 19th, 1969 was a Saturday.  (Be careful when you do the division - if you use a calculator it will not tell you the actual remainder.)

Below are two Java programs using the algebraic formulas described above.

The first calculates the date for Easter for any year after 1582.
The second program calculates the day of the week for any date after 1582.

The reason the programs don't work for any date before 1582 is that they are based on the
current Gregorian calendar which was created in Rome in 1582.

So if you are interested in a date in Italian or Spanish history dating back to 1582, these programs will work.
However, because England and the American colonies were predominately protestant, they did not adopt this
calendar until 1752. Greece, an orthodox Christian country, did not adopt the current calendar until 1923. 

So, for example, for a date in American history, these programs are valid only back to 1752. 

EASTER DATE CALCULATOR:


DAY OF WEEK CALCULATOR: