Calendars exhibit

What years are leap years?

Leap years were introduced to keep New Year’s Day on autumnal equinox. But this turned out to be difficult to handle, because equinox is not completely simple to predict.

In fact, the first decree implementing the calendar (5 Oct 1793) contained two contradictory rules, as it stated that:

• the first day of each year would be that of the autmunal equinox
• every 4th year would be a leap year

In practice, the first calendars were based on the equinoxial condition.

To remove the confusion, a rule similar to the one used in the Gregorian Calendar (including a 4000 year rule) was proposed by the calendar’s author, Gilbert Romme, but his proposal ran into political problems.

In short, during the time when the French Revolutionary Calendar was in use, the the following years were leap years: 3, 7, and 11.

Is there a 4000-year rule?

It has been suggested (by the astronomer John Herschel (1792-1871) among others) that a better approximation to the length of the tropical year would be 365 969/4000 days = 365.24225 days. This would dictate 969 leap years every 4000 years, rather than the 970 leap years mandated by the Gregorian calendar. This could be achieved by dropping one leap year from the Gregorian calendar every 4000 years, which would make years divisible by 4000 non-leap years.

This rule has, however, not been officially adopted.

Do the Greeks do it differently?

When the Orthodox church in Greece finally decided to switch to the Gregorian calendar in the 1920s, they tried to improve on the Gregorian leap year rules, replacing the "divisible by 400" rule by the following:

Every year which when divided by 900 leaves a remainder of 200 or 600 is a leap year.

This makes 1900, 2100, 2200, 2300, 2500, 2600, 2700, 2800 non-leap years, whereas 2000, 2400, and 2900 are leap years. This will not create a conflict with the rest of the world until the year 2800.

This rule gives 218 leap years every 900 years, which gives us an average year of 365 218/900 days = 365.24222 days, which is certainly more accurate than the official Gregorian number of 365.2425 days.

However, this rule is not official in Greece.

What day is the leap day?

It is 24 February!

Weird? Yes! The explanation is related to the Roman calendar.

From a numerical point of view, of course 29 February is the extra day. But from the point of view of celebration of feast days, the following correspondence between days in leap years and non-leap years has traditionally been used:

What is the Solar Cycle?

In the Julian calendar the relationship between the days of the week and the dates of the year is repeated in cycles of 28 years. In the Gregorian calendar this is still true for periods that do not cross years that are divisible by 100 but not by 400.

A period of 28 years is called a Solar Cycle. The Solar Number of a year is found as:

Solar Number = (year + 8) mod 28 + 1

In the Julian calendar there is a one-to-one relationship between the Solar Number and the day on which a particular date falls.

(The leap year cycle of the Gregorian calendar is 400 years, which is 146,097 days, which curiously enough is a multiple of 7. So in the Gregorian calendar the equivalent of the "Solar Cycle" would be 400 years, not 7 x 400 = 2800 years as one might be tempted to believe.)

What is the Dominical Letter?

Each ordinary (non-leap) year is assigned a letter in the range A to G which describes what days of the year are Sundays. This letter is called the "Dominical Letter" ("Sunday Letter") of the year.

It works in this manner: Assign the letter A to 1 January, B to 2 Jan, C to 3 Jan, ... G to 7 Jan, A to 8 Jan, B to 9 Jan, and so on, using the letters A to G and omitting the leap day.

In a year with Dominical Letter A, all days marked A are Sundays. In a year with Dominical Letter B, all days marked B are Sundays. And so on.

Leap years have two Dominical Letters, one which is used from the start of January until the leap day, and another one which is used for the rest of the year.

The Dominical Letter of 2006 is A. The Dominical Letters of 2008 will be F and E.

When can I reuse my 1992 calendar?

Let us first assume that you are only interested in which dates fall on which days of the week; you are not interested in the dates for Easter and other irregular holidays.

Let us further confine ourselves to the years 1901-2099.

With these restrictions, the answer is as follows:

• If year X is a leap year, you can reuse its calendar in year X+28.
• If year X is the first year after a leap year, you can reuse its calendar in years X+6, X+17, and X+28.
• If year X is the second year after a leap year, you can reuse its calendar in years X+11, X+17, and X+28.
• If year X is the third year after a leap year, you can reuse its calendar in years X+11, X+22, and X+28.

Note that the expression X+28 occurs in all four items above. So you can always reuse your calendar every 28 years.

But if you also want your calendar’s indication of Easter and other Christian holidays to be correct, the rules are far too complex to be put to a simple formula. Sometimes calendars can be reused after just six years. For example, the calendars for the years 1981 and 1987 are identical, even when it comes to the date for Easter. But sometimes a very long time can pass before a calendar can be reused; if you happen to have a calendar from 1940, you won’t be able to reuse it until the year 5280!

What is the correct way to write dates?

The answer to this question depends on what you mean by "correct." Different countries have different customs.

In the U.S.A. a month-day-year format is common:

12/25/1998 or 12-25-1998 |

Most other countries use a day-month-year format, such as:

25.12.1998 or 25/12/1998 or 25/12-1998 or 25.XII.1998

International standard ISO-8601 mandates a year-month-day format, namely either

1998-12-25 or 19981225.

In all of these systems, the first two digits of the year are frequently omitted:

25.12.98 or 12/25/98 or 98-12-25

However, although the last form is frequently seen, it is not allowed by the ISO standard.

This confusion leads to misunderstandings. What is 02-03-04? To most people it is 2 Mar 2004; to an American it is 3 Feb 2004; and to a person using the international standard it could be 4 Mar 2002 (although a year specified with only two digits does not conform to the ISO standard).

If you want to be sure that people understand you, you should:

• write the month with letters instead of numbers, and
• write the years as 4-digit numbers.

How does one count years?

In about C.E. 523, the papal chancellor, Bonifatius, asked a monk by the name of Dionysius Exiguus to devise a way to implement the rules from the Nicean council (the so-called "Alexandrine Rules") for general use.

Dionysius Exiguus (in English known as Denis the Little) was a monk from Scythia, he was a canon in the Roman curia, and his assignment was to prepare calculations of the dates of Easter. At that time it was customary to count years since the reign of emperor Diocletian; but in his calculations Dionysius chose to number the years since the birth of Christ, rather than honour the persecutor Diocletian.

Dionysius (wrongly) fixed Jesus’ birth with respect to Diocletian’s reign in such a manner that it falls on 25 December 753 AUC (ab urbe condita, i.e., since the founding of Rome), thus making the current era start with C.E. 1 on 1 January 754 AUC.

How Dionysius established the year of Christ’s birth is not known (see History of our Calendar for a couple of theories). Jesus was born under the reign of king Herod the Great, who died in 750 AUC, which means that Jesus could have been born no later than that year. Dionysius’ calculations were disputed at a very early stage.

When people started dating years before 754 AUC using the term "Before Christ," they let the year 1 B.C.E. immediately precede C.E. 1 with no intervening year zero.

Note, however, that astronomers frequently use another way of numbering the years B.C.E. Instead of 1 B.C.E. they use 0, instead of 2 B.C.E. they use -1, instead of 3 B.C.E. they use -2, etc.

The earliest uses of BC dating are found in the works of the Venerable Bede (673-735).

In this section we have used C.E. 1 = 754 AUC. This is the most likely equivalence between the two systems. However, some authorities state that C.E. 1 = 753 AUC or 755 AUC. This confusion is not a modern one, it appears that even the Romans were in some doubt about how to count the years since the founding of Rome.

When did the 3rd millennium start?

The first millennium started in AD 1, so the millennia are counted in this manner:

1st millennium: 1-1000

2nd millennium: 1001-2000

3rd millennium: 2001-3000

Thus, the 3rd millennium and, similarly, the 21st century started on 1 Jan 2001.

This is the cause of some heated debate, especially since some dictionaries and encyclopedias say that a century starts in years that end in 00. Furthermore, the change 1999/2000 is obviously much more spectacular than the change 2000/2001.

Let us propose a few compromises:

Any 100-year period is a century. Therefore the period from 23 June 2004 to 22 June 2104 is a century. So please feel free to celebrate the start of a century any day you like!

Although the 20th century started in 1901, the 1900s started in 1900. Similarly, the 21st century started in 2001, but the 2000s started in 2000.

What do A.D., B.C., C.E., and B.C.E. stand for?

Years before the birth of Christ are in English traditionally identified using the abbreviation B.C. ("Before Christ").

Years after the birth of Christ are traditionally identified using the Latin abbreviation AD ("Anno Domini", that is, "In the Year of the Lord").

Some people, who want to avoid the reference to Christ that is implied in these terms, prefer the abbreviations BCE ("Before the Common Era" or "Before the Christian Era") and CE ("Common Era" or "Christian Era").

Historical eras & chronology

The calendars described in this exhibit, except for the Chinese calendar, have counts of years from initial epochs. In the case of the Chinese calendar and some calendars not included here, years are counted in cycles, with no particular cycle specified as the first cycle. Some cultures eschew year counts altogether but name each year after an event that characterized the year. However, a count of years from an initial epoch is the most successful way of maintaining a consistent chronology. Whether this epoch is associated with an historical or legendary event, it must be tied to a sequence of recorded historical events.

This is illustrated by the adoption of the birth of Christ as the initial epoch of the Christian calendar. This epoch was established by the sixth-century scholar Dionysius Exiguus, who was compiling a table of dates of Easter. An existing table covered the nineteen-year period denoted 228-247, where years were counted from the beginning of the reign of the Roman emperor Diocletian. Dionysius continued the table for a nineteen-year period, which he designated Anni Domini Nostri Jesu Christi 532-550. Thus, Dionysius’ Anno Domini 532 is equivalent to Anno Diocletian 248. In this way a correspondence was established between the new Christian Era and an existing system associated with historical records. What Dionysius did not do is establish an accurate date for the birth of Christ. Although scholars generally believe that Christ was born some years before A.D. 1, the historical evidence is too sketchy to allow a definitive dating.

Given an initial epoch, one must consider how to record preceding dates. Bede, the eighth-century English historian, began the practice of counting years backward from A.D. 1 (see Colgrave and Mynors, 1969). In this system, the year A.D. 1 is preceded by the year 1 B.C.E., without an intervening year 0. Because of the numerical discontinuity, this "historical" system is cumbersome for comparing ancient and modern dates. Today, astronomers use +1 to designate A.D. 1. Then +1 is naturally preceded by year 0, which is preceded by year -1. Since the use of negative numbers developed slowly in Europe, this "astronomical" system of dating was delayed until the eighteenth century, when it was introduced by the astronomer Jacques Cassini (Cassini, 1740).

Even as use of Dionysius’ Christian Era became common in ecclesiastical writings of the Middle Ages, traditional dating from regnal years continued in civil use. In the sixteenth century, Joseph Justus Scaliger tried to resolve the patchwork of historical eras by placing everything on a single system (Scaliger, 1583). Instead of introducing negative year counts, he sought an initial epoch in advance of any historical record. His numerological approach utilized three calendrical cycles: the 28-year solar cycle, the nineteen-year cycle of Golden Numbers, and the fifteen-year indiction cycle. The solar cycle is the period after which weekdays and calendar dates repeat in the Julian calendar. The cycle of Golden Numbers is the period after which moon phases repeat (approximately) on the same calendar dates. The indiction cycle was a Roman tax cycle. Scaliger could therefore characterize a year by the combination of numbers (S,G,I), where S runs from 1 through 28, G from 1 through 19, and I from 1 through 15. Scaliger noted that a given combination would recur after 7980 (= 28*19*15) years. He called this a Julian Period, because it was based on the Julian calendar year. For his initial epoch Scaliger chose the year in which S, G, and I were all equal to 1. He knew that the year 1 B.C.E. was characterized by the number 9 of the colar cycle, by the Golden Number 1, and by the number 3 of the indiction cycle, i.e., (9,1,3). He found that the combination (1,1,1) occurred in 4713 B.C.E. or, as astronomers now say, -4712. This serves as year 1 of Scaliger’s Julian Period. It was later adopted as the initial epoch for the Julian day numbers.

ISO 8601

What date format does the Standard mandate?

There are three basic formats: Calendar date, ordinal date, and week date.

A calendar date should be written as a 4-digit year number, followed by a 2-digit month number, followed by a 2-digit day number. Thus, for example, 2 August 1953 may be written:

19530802 or 1953-08-02

An ordinal date should be written as a 4-digit year number, followed by a 3-digit number indicating the number of the day within the year. Thus, for example, 2 August 1953 may be written:

1953214 or 1953-214

2 August is the 214th day of a non-leap year.

A week date should be written as a 4-digit year number, followed by a W, followed by a 2-digit week number followed by a 1-digit week day number (1=Monday, 2=Tuesday, ..., 7=Sunday). The week number is defined in section 7.7. Thus, for example, 2 August 1953 may be written:

1953W317 or 1953-W31-7

2 August was the Sunday of week 31 of 1953.

In all the examples above, the hyphens are optional.

Note that you must always write all the digits. Thus the year 47 must be written as 0047.

What time format does the Standard mandate?

A 24-hour clock must be used. A time is written as a 2-digit hour, followed by a 2-digit minute, followed by a 2-digit second, followed by a comma, followed by a number of digits indicating a fraction of a second. For example, thus:

140812,35 or 14:08:12,35

The fraction, the seconds, and the minutes may be omitted if less accuracy is required:

140812 or 14:08:12

1408 or 14:08

14

In all the examples above, the colons are optional. The comma may be replaced by a period (.), but this is not recommended.

The time may optionally be followed by a time zone indication. For UTC, the time zone indication is the letter Z. For other time zones, the indication is a plus or minus followed by the time difference to UTC (plus for times east of Greenwich, minus for times west of Greenwich). For example:

1130Z (11:30 UTC)

1130+0430 (11:30, at a location 4 and a half hours ahead of UTC)

1130-05 (11:30, at a location 5 hours behind of UTC)

What if I want to specify both a date and a time?

Date and time indications can be strung together by putting the letter T between them. For example, ten minutes to 7 p.m. on 2 August 1953 may be written as:

19530802T185000 or 1953-08-02T18:50:00

What format does the Standard mandate for a time interval?

There are several to choose from. A time interval can be specified as a starting time and an ending time or as a duration together with either a starting time and an ending time.

There are too many details to cover, so here are a few examples:

Using starting time and ending time:

1998-12-01T12:03/2004-04-02T14:12

Using starting time and duration:

1927-03-12T08:04/P1Y4M12DT6H30M9S

This last example should be read as the time interval starting on 12 March 1927 at 08:04 and lasting for 1 year, 4 months, 12 days, 6 hours, 30 minutes, and 9 seconds. The letter P following the slash indicates that a duration follows.

Can I write BC dates and dates after the year 9999 using ISO 8601?

Yes, you can.

The year 1 BC must be written as 0000. The year 2 BC must be written as -0001, the year 3 BC must be written as -0002 etc.

Years of more than 4 digits must be written with an initial plus sign. Thus the year AD 10000 must be written as +10000.

Can I write dates in the Julian calendar using ISO 8601?

No. The Standard requires that the Gregorian calendar be used for all dates. Dates before the introduction of the Gregorian calendar are written using the proleptic Gregorian calendar. This is one of the few places where the proleptic Gregorian calendar is used.

Thus the Julian date 12 March 826 must be written as 0826-03-16, because its equivalent date in the Gregorian calendar is 16 March.

Does the Standard define the Gregorian calendar?

Yes, ISO 8601 specifies how the Gregorian calendar works. The specification is completely compatible with the calendar specified by Pope Gregory XIII in 1582, except that ISO 8601 does not concern itself with the calculation of Easter.

However, the calendar reference point used by the Standard is not Christ’s birth but the date on which the metric convention ("Convention du Metre") was signed in Paris. The Standard defines that date to be 20 May 1875.

Similarly, the reference point of the week cycles is 1 January 2000, which is defined to be a Saturday.

Of course, these reference points are also completely compatible with common usage.

What does the Standard say about the week?

According to ISO 8601, Monday is the first day of the week.

Each week has a number. A week that lies partly in one year and partly in another is assigned a number in the year in which most of its days lie. The Standard specifies this by saying that week 1 of any year is the week that includes the first Thursday of that year.

Why are ISO 8601 dates not used in this Calendar FAQ?

The Standard specifies how to write dates using only numbers. The Standard explicitly does not cover the cases where dates are written using words (such as January, February, etc.). In fact, the Standard itself makes frequent use of dates such as "20 May 1875" and "15 October 1582".

In other words, ISO 8601 helps people with data communication where it is natural to use all-number dates. In everyday language (spoken and written) we are free to use the terms we like best.

Where can I get the Standard?

If you are looking for a free copy somewhere on the internet, forget it! ISO makes money from selling copies of their standards.

ISO 8601:2004 can be bought from ISO at http://www.iso.ch. It is very expensive. The last time we checked, the price was 126 Swiss Francs (about U.S. $103) for a 33 page document.

Your local library may be able to find a copy for you.