Calendar FAQ v1.6 -- Part 3

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5. The Week
-----------

Both the Christian, the Hebrew, and the Islamic calendar have a 7-day
week.


5.1. What Is the Origin of the 7-Day Week?
------------------------------------------

Digging into the history of the 7-day week is a very complicated
matter. Authorities have very different opinions about the history of
the week, and they frequently present their speculations as if they
were indisputable facts. The only thing we seem to know for certain
about the origin of the 7-day week is that we know nothing for
certain.

The first pages of the Bible explain how God created the world in six
days and rested on the seventh. This seventh day became the Jewish
day of rest, the sabbath, Saturday.

Extra-biblical locations sometimes mentioned as the birthplace of the
7-day week include: Egypt, Babylon, Persia, and several others. The
week was known in Rome before the advent of Christianity.


5.2. What Do the Names of the Days of the Week Mean?
----------------------------------------------------

An answer to this question is necessarily closely linked to the
language in question. Whereas most languages use the same names for
the months (with a few Slavonic languages as notable exceptions),
there is great variety in names that various languages use for the
days of the week. A few examples will be given here.

Except for the sabbath, Jews simply number their week days.

A related method is partially used in Russian:

    English     Russian        Meaning of Russian name
    -------     -------        -----------------------
    Monday      ponedelnik     After do-nothing day
    Tuesday     vtornik        Second day
    Wednesday   sreda          Center
    Thursday    chetverg       Four
    Friday      pyatnitsa      Five
    Saturday    subbota        Sabbath
    Sunday      voskresenye    Resurrection

Most Latin-based languages connect each day of the week with one of
the seven "planets" of the ancient times: Sun, Moon, Mercury, Venus,
Mars, Jupiter, and Saturn. The reason for this may be that each
planet was thought to "rule" one day of the week. French, for
example, uses:

    English     French         "Planet"
    -------     ------         --------
    Monday      lundi          Moon
    Tuesday     mardi          Mars
    Wednesday   mercredi       Mercury
    Thursday    jeudi          Jupiter
    Friday      vendredi       Venus
    Saturday    samedi         Saturn
    Sunday      dimanche       (Sun)

The link with the sun has been broken in French, but Sunday was
called "dies solis" (day of the sun) in Latin.

It is interesting to note that also some Asiatic languages (Hindi, for
example) have a similar relationship between the week days and the
planets.

English has retained the original planets in the names for Saturday,
Sunday, and Monday. For the four other days, however, the names of
Anglo-Saxon or Nordic gods have replaced the Roman gods that gave
name to the planets. Thus, Tuesday is named after Tiw, Wednesday is
named after Woden, Thursday is named after Thor, and Friday is named
after Freya.


5.3. Has the 7-Day Week Cycle Ever Been Interrupted?
----------------------------------------------------

There is no record of the 7-day week cycle ever having been broken.
Calendar changes and reform have never interrupted the 7-day cycles.
It very likely that the week cycles have run uninterrupted at least
since the days of Moses (c. 1400 BC), possibly even longer.

Some sources claim that the ancient Jews used a calendar in which an
extra Sabbath was occasionally introduced. But this is probably not
true.


5.4. Which Day is the Day of Rest?
----------------------------------

For the Jews, the Sabbath (Saturday) is the day of rest and
worship. On this day God rested after creating the world.

Most Christians have made Sunday their day of rest and worship,
because Jesus rose from the dead on a Sunday.

Muslims use Friday as their day of rest and worship, because Muhammad
was born on a Friday.


5.5. What Is the First Day of the Week?
---------------------------------------

It is common Jewish and Christian practice to regard Sunday as the
first day of the week. However, the fact that, for example, Russian
uses the name "second day" for Tuesday, indicates that some nations
regard Monday as the first day.

In international standard IS-8601 the International Organization for
Standardization (ISO) has decreed that Monday shall be the first day
of the week.


5.6. What Is the Week Number?
-----------------------------

International standard IS-8601 (mentioned in section 5.5) assigns a
number to each week of the year. 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. This means that

        Week 1 of any year is the week that contains 4 January,

or equivalently

        Week 1 of any year is the week that contains the first
        Thursday in January.

Most years have 52 weeks, but years that start on a Thursday and leap
years that start on a Wednesday have 53 weeks.


5.7. Do Weeks of Different Lengths Exist?
-----------------------------------------

If you define a "week" as a 7-day period, obviously the answer is
no. But if you define a "week" as a named interval that is greater
than a day and smaller than a month, the answer is yes.

The French Revolutionary calendar used a 10-day "week" (see section
6.1).

The Maya calendar uses a 13 and a 20-day "week" (see section 7.2).

The Soviet Union has used both a 5-day and a 6-day week. In 1929-30
the USSR gradually introduced a 5-day week. Every worker had one day
off every week, but there was no fixed day of rest. On 1 September
1931 this was replaced by a 6-day week with a fixed day of rest,
falling on the 6th, 12th, 18th, 24th, and 30th day of each month (1
March was used instead of the 30th day of February, and the last day
of months with 31 days was considered an extra working day outside
the normal 6-day week cycle). A return to the normal 7-day week was
decreed on 26 June 1940.


6. The French Revolutionary Calendar
------------------------------------

The French Revolutionary Calendar (or Republican Calendar) was
introduced in France on 24 November 1793 and abolished on 1 January
1806. It was used again briefly during under the Paris Commune in
1871.


6.1. What does a Republican year look like?
-------------------------------------------

A year consists of 365 or 366 days, divided into 12 months of 30 days
each, followed by 5 or 6 additional days. The months were:

1. Vendemiaire           7. Germinal
2. Brumaire              8. Floreal
3. Frimaire              9. Prairial
4. Nivose               10. Messidor
5. Pluviose             11. Thermidor
6. Ventose              12. Fructidor

(The second e in Vendemiaire and the e in Floreal carry an acute
accent. The o's in Nivose, Pluviose, and Ventose carry a circumflex
accent.)

The year was not divided into weeks, instead each month was divided
into three "decades" of 10 days, of which the final day was a day of
rest. This was an attempt to de-Christianize the calendar, but it was
an unpopular move, because now there were 9 work days between each day
of rest, whereas the Gregorian Calendar had only 6 work days between
each Sunday.

The ten days of each decade were called, respectively, Primidi, Duodi,
Tridi, Quartidi, Quintidi, Sextidi, Septidi, Octidi, Nonidi, Decadi.

The 5 or 6 additional days followed the last day of Fructidor and were
called:
        1. Jour de la vertu (Virtue Day)
        2. Jour du genie (Genius Day)
        3. Jour du travail (Labour Day)
        4. Jour de l'opinion (Reason Day)
        5. Jour des recompenses (Rewards Day)
        6. Jour de la revolution (Revolution Day)  (the leap day)

Each year was supposed to start on autumnal equinox (around 22
September), but this created problems as will be seen in section 6.3.


6.2. How does one count years?
------------------------------

Years are counted since the establishment of the first French Republic
on 22 September 1792. That day became 1 Vendemiaire of the year 1 of
the Republic. (However, the Revolutionary Calendar was not introduced
until 24 November 1793.)


6.3. 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. Therefore a rule similar
to the one used in the Gregorian Calendar (including a 4000 year rule
as descibed in section 2.2.2) was to take effect in the year 20. 
However, the Revolutionary Calendar was abolished in the year 14,
making this new rule irrelevant.

The following years were leap years: 3, 7, and 11. The years 15 and 20
should have been leap years, after which every 4th year (except every
100th year etc. etc.) should have been a leap year.

[The historicity of these leap year rules has been disputed. One
source mentions that the calendar used a rule which would give 31 leap
years in every 128 year period. I may have to update this section.]


6.4. How does one convert a Republican date to a Gregorian one?
---------------------------------------------------------------

The following table lists the Gregorian date on which each year of the
Republic started:

Year  1: 22 Sep 1792            Year  8: 23 Sep 1799
Year  2: 22 Sep 1793            Year  9: 23 Sep 1800
Year  3: 22 Sep 1794            Year 10: 23 Sep 1801
Year  4: 23 Sep 1795            Year 11: 23 Sep 1802
Year  5: 22 Sep 1796            Year 12: 24 Sep 1803
Year  6: 22 Sep 1797            Year 13: 23 Sep 1804
Year  7: 22 Sep 1798            Year 14: 23 Sep 1805


7. The Maya Calendar
--------------------

(I am very grateful to Chris Carrier (72157.3334@CompuServe.COM) for
providing most of the information about the Maya calendar.)

Among their other accomplishments, the ancient Maya invented a
calendar of remarkable accuracy and complexity. The Maya calendar was
adopted by the other Mesoamerican nations, such as the Aztecs and the
Toltec, which adopted the mechanics of the calendar unaltered but
changed the names of the days of the week and the months.

The Maya calendar uses three different dating systems in parallel, the
"Long Count", the "Tzolkin" (divine calendar), and the "Haab" (civil
calendar).  Of these, only the Haab has a direct relationship to the
length of the year.

A typical Mayan date looks like this: 12.18.16.2.6, 3 Cimi 4 Zotz.

12.18.16.2.6 is the Long Count date.
3 Cimi is the Tzolkin date.
4 Zotz is the Haab date.


7.1. What is the Long Count?
----------------------------

The Long Count is really a mixed base-20/base-18 representation of a
number, representing the number of days since the start of the Mayan
era. It is thus akin to the Julian Day Number (see section 2.12).

The basic unit is the "kin" (day), which is the last component of the
Long Count. Going from right to left the remaining components are:

   unial  (1 unial = 20 kin = 20 days)
   tun    (1 tun = 18 unial = 360 days = approx. 1 year)
   katun  (1 katun = 20 tun = 7,200 days = approx. 20 years)
   baktun (1 baktun = 20 katun = 144,000 days = approx. 394 years)

The kin, tun, and katun are numbered from 0 to 19.
The unial are numbered from 0 to 17.
The baktun are numbered from 1 to 13.

Although they are not part of the Long Count, the Maya had names for
larger time spans:

   1 pictun = 20 baktun = 2,880,000 days = approx. 7885 years
   1 calabtun = 20 pictun = 57,600,000 days = approx. 158,000 years
   1 kinchiltun = 20 calabtun = 1,152,000,000 days = approx. 3 million years
   1 alautun = 20 kinchiltun = 23,040,000,000 days = approx. 63 million years

The alautun is probably the longest named period in any calendar.


7.1.1. When did the Long Count Start?
-------------------------------------

Logically, the first date in the Long Count should be 0.0.0.0.0, but
as the baktun (the first component) are numbered from 1 to 13 rather
than 0 to 12, this first date is actually written 13.0.0.0.0.

The authorities disagree on what 13.0.0.0.0 actually means. I have
come across three possible equivalences:

13.0.0.0.0 =  8 Sep 3114 BC (Julian) = 13 Aug 3114 BC (Gregorian)
13.0.0.0.0 =  6 Sep 3114 BC (Julian) = 11 Aug 3114 BC (Gregorian)
13.0.0.0.0 = 11 Nov 3374 BC (Julian) = 15 Oct 3374 BC (Gregorian)

Assuming one of the first two equivalences, the Long Count will again
reach 13.0.0.0.0 on 21 or 23 December AD 2012 - a not too distant future.

The Long Count was not, however, put in motion on 13.0.0.0.0, but
rather on 7.13.0.0.0. The date 13.0.0.0.0 may have been the Maya's
idea of the date of the creation of the world.


7.2. What is the Tzolkin?
-------------------------

The Tzolkin date is a combination of two "week" lengths.

While our calendar uses a single week of seven days, the Mayan
calendar used two different lengths of week:
   - a numbered week of 13 days, in which the days were numbered from
     1 to 13
   - a named week of 20 days, in which the names of the days were:

        0. Ahau         5. Chicchan     10. Oc          15. Men
        1. Imix         6. Cimi         11. Chuen       16. Cib
        2. Ik           7. Manik        12. Eb          17. Caban
        3. Akbal        8. Lamat        13. Ben         18. Etznab
        4. Kan          9. Muluc        14. Ix          19. Caunac

As the named week is 20 days and the smallest Long Count digit is 20
days, there is synchrony between the two; if the last digit of today's
Long Count is 0, for example, today must be Ahau; if it is 6, it must
be Cimi. Since the numbered and the named week were both "weeks", each
of their name/number change daily; therefore, the day after 3 Cimi is
not 4 Cimi, but 4 Manik, and the day after that, 5 Lamat. The next
time Cimi rolls around, 20 days later, it will be 10 Cimi instead of 3
Cimi. The next 3 Cimi will not occur until 260 (or 13*20) days have
passed. This 260-day cycle also had good-luck or bad-luck associations
connected with each day, and for this reason, it became known as the
"divinatory year."

The "years" of the Tzolkin calendar are not counted.


7.2.1. When did the Tzolkin Start?
----------------------------------

Long Count 13.0.0.0.0 corresponds to 4 Ahau. The authorities agree on
this.


7.3. What is the Haab?
----------------------

The Haab was the civil calendar of the Maya. It consisted of 18
"months" of 20 days each, followed by 5 extra days, known as
"Uayeb". This gives a year length of 365 days.

The names of the month were:
        1. Pop           7. Yaxkin      13. Mac
        2. Uo            8. Mol         14. Kankin
        3. Zip           9. Chen        15. Muan
        4. Zotz         10. Yax         16. Pax
        5. Tzec         11. Zac         17. Kayab
        6. Xul          12. Ceh         18. Cumku
        
Since each month was 20 days long, monthnames changed only every 20
days instead of daily; so the day after 4 Zotz would be 5 Zotz,
followed by 6 Zotz ... up to 19 Zotz, which is followed by 0 Tzec.

The days of the month were numbered from 0 to 19. This use of a 0th
day of the month in a civil calendar is unique to the Maya system; it
is believed that the Maya discovered the number zero, and the uses to
which it could be put, centuries before it was discovered in Europe or
Asia.

The Uayeb days acquired a very derogatory reputation for bad luck;
known as "days without names" or "days without souls," and were
observed as days of prayer and mourning. Fires were extinguished and
the population refrained from eating hot food. Anyone born on those
days was "doomed to a miserable life."

The years of the Haab calendar are not counted.

The length of the Tzolkin year was 260 days and the length of the Haab
year was 365 days. The smallest number that can be divided evenly into
260 and 365 is 18,980, or 365*52; this was known as the Calendar
Round. If a day is, for example, "4 Ahau 8 Cumku," the next day
falling on "4 Ahau 8 Cumku" would be 18,980 days or about 52 years
later.  Among the Aztec, the end of a Calendar Round was a time of
public panic as it was thought the world might be coming to an
end. When the Pleaides crossed the horizon on 4 Ahau 8 Cumku, they
knew the world had been granted another 52-year extension.


7.3.1. When did the Haab Start?
-------------------------------

Long Count 13.0.0.0.0 corresponds to 8 Cumku. The authorities agree on
this.


7.4. Did the Maya Think a Year Was 365 Days?
--------------------------------------------

Although there were only 365 days in the Haab year, the Maya were
aware that a year is slightly longer than 365 days, and in fact, many
of the month-names are associated with the seasons; Yaxkin, for
example, means "new or strong sun" and, at the beginning of the Long
Count, 1 Yaxkin was the day after the winter solstice, when the sun
starts to shine for a longer period of time and higher in the
sky. When the Long Count was put into motion, it was started at
7.13.0.0.0, and 0 Yaxkin corresponded with Midwinter Day, as it did at
13.0.0.0.0 back in 3114 B.C. The available evidence indicates that the
Maya estimated that a 365-day year precessed through all the seasons
twice in 7.13.0.0.0 or 1,101,600 days.

We can therefore derive a value for the Mayan estimate of the year by
dividing 1,101,600 by 365, subtracting 2, and taking that number and
dividing 1,101,600 by the result, which gives us an answer of
365.242036 days, which is slightly more accurate than the 365.2425
days of the Gregorian calendar.



8. Date
-------

This version 1.6 of this document was finished on

        Thursday, the second day of Christmas, the 26th of
        December, anno ab Incarnatione Domini MCMXCVI, indict. IV,
        epacta X, luna XVI, anno post Margaretam Reginam Daniae natam
        LVI, on the feast of Saint Stephen.

        The 16th day of Tevet, Anno Mundi 5757.

        The 15th day of Sha'ban, Anno Hegirae 1417.

        Julian Day 2,450,444.

--- End of part 3 ---

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