The Mayans believed at at the conclusion of each pictun cycle of about 7,885 years the universe is destroyed and re-created. Those with apocalyptic inclinations will be relieved to observe that the present cycle will not end until Columbus Day, October 12, 4772 in the Gregorian calendar. Speaking of apocalyptic events, it's amusing to observe that the longest of the cycles in the Mayan calendar, alautun, about 63 million years, is comparable to the 65 million years since the impact which brought down the curtain on the dinosaurs--an impact which occurred near the Yucatan peninsula where, almost an alautun later, the Mayan civilisation flourished. If the universe is going to be destroyed and the end of the current pictun, there's no point in writing dates using the longer cycles, so we dispense with them here.
Dates in the Long Count calendar are written, by convention, as:
and thus resemble present-day Internet IP addresses!
For civil purposes the Mayans used the Haab calendar in which the year was divided into 18 named periods of 20 days each, followed by five Uayeb days not considered part of any period. Dates in this calendar are written as a day number (0 to 19 for regular periods and 0 to 4 for the days of Uayeb) followed by the name of the period. This calendar has no concept of year numbers; it simply repeats at the end of the complete 365 day cycle. Consequently, it is not possible, given a date in the Haab calendar, to determine the Long Count or year in other calendars. The 365 day cycle provides better alignment with the solar year than the 360 day tun of the Long Count but, lacking a leap year mechanism, the Haab calendar shifted one day with respect to the seasons about every four years.
The Mayan religion employed the Tzolkin calendar, composed of 20 named periods of 13 days. Unlike the Haab calendar, in which the day numbers increment until the end of the period, at which time the next period name is used and the day count reset to 0, the names and numbers in the Tzolkin calendar advance in parallel. On each successive day, the day number is incremented by 1, being reset to 0 upon reaching 13, and the next in the cycle of twenty names is affixed to it. Since 13 does not evenly divide 20, there are thus a total of 260 day number and period names before the calendar repeats. As with the Haab calendar, cycles are not counted and one cannot, therefore, convert a Tzolkin date into a unique date in other calendars. The 260 day cycle formed the basis for Mayan religious events and has no relation to the solar year or lunar month.
frequently specified dates using both the Haab and Tzolkin
calendars; dates of this form repeat only every 52 solar years.
Bahá'í calendarThe Bahá'í calendar is a solar calendar organised as a hierarchy of cycles, each of length 19, commemorating the 19 year period between the 1844 proclamation of the Báb in Shiraz and the revelation by Bahá'u'lláh in 1863. Days are named in a cycle of 19 names. Nineteen of these cycles of 19 days, usually called "months" even though they have nothing whatsoever to do with the Moon, make up a year, with a period between the 18th and 19th months referred to as Ayyám-i-Há not considered part of any month; this period is four days in normal years and five days in leap years. The rule for leap years is identical to that of the Gregorian calendar, so the Bahá'í calendar shares its accuracy and remains synchronised. The same cycle of 19 names is used for days and months.
begins at the equinox, March 21, the Feast of Naw-Rúz; days begin
at sunset. Years have their own cycle of 19 names, called the
Váhid. Successive cycles of 19 years are numbered, with
cycle 1 commencing on March 21, 1844, the year in which the Báb
announced his prophecy. Cycles, in turn, are assembled into Kull-I-Shay
super-cycles of 361 (19˛) years. The first Kull-I-Shay
will not end until Gregorian calendar year 2205. A week of seven
days is superimposed on the calendar, with the week considered
to begin on Saturday. Confusingly, three of the names of weekdays
are identical to names in the 19 name cycles for days and months.
Indian Civil calendarA bewildering variety of calendars have been and continue to be used in the Indian subcontinent. In 1957 the Indian government's Calendar Reform Committee adopted the National Calendar of India for civil purposes and, in addition, defined guidelines to standardise computation of the religious calendar, which is based on astronomical observations. The civil calendar is used throughout India today for administrative purposes, but a variety of religious calendars remain in use. We present the civil calendar here.
The National Calendar of India is composed of 12 months. The first month, Caitra, is 30 days in normal and 31 days in leap years. This is followed by five consecutive 31 day months, then six 30 day months. Leap years in the Indian calendar occur in the same years as as in the Gregorian calendar; the two calendars thus have identical accuracy and remain synchronised.
the Indian calendar are counted from the start of the Saka Era,
the equinox of March 22nd of year 79 in the Gregorian calendar,
designated day 1 of month Caitra of year 1 in the Saka Era. The
calendar was officially adopted on 1 Caitra, 1879 Saka Era, or
March 22nd, 1957 Gregorian. Since year 1 of the Indian calendar
differs from year 1 of the Gregorian, to determine whether a year
in the Indian calendar is a leap year, add 78 to the year of the
Saka era then apply the Gregorian calendar rule to the sum.
French Republican calendarThe French Republican calendar was adopted by a decree of La Convention Nationale on Gregorian date October 5, 1793 and went into effect the following November 24th, on which day Fabre d'Églantine proposed to the Convention the names for the months. It incarnates the revolutionary spirit of "Out with the old! In with the relentlessly rational!" which later gave rise in 1795 to the metric system of weights and measures which has proven more durable than the Republican calendar.
The calendar consists of 12 months of 30 days each, followed by a five- or six-day holiday period, the jours complémentaires or sans-culottides. Months are grouped into four seasons; the three months of each season end with the same letters and rhyme with one another. The calendar begins on Gregorian date September 22nd, 1792, the September equinox and date of the founding of the First Republic. This day is designated the first day of the month of Vendémiaire in year 1 of the Republic. Subsequent years begin on the day in which the September equinox occurs as reckoned at the Paris meridian. Days begin at true solar midnight. Whether the sans-culottides period contains five or six days depends on the actual date of the equinox. Consequently, there is no leap year rule per se: 366 day years do not recur in a regular pattern but instead follow the dictates of astronomy. The calendar therefore stays perfectly aligned with the seasons. No attempt is made to synchronise months with the phases of the Moon.
The Republican calendar is rare in that it has no concept of a seven day week. Each thirty day month is divided into three décades of ten days each, the last of which, décadi, was the day of rest. (The word "décade" may confuse English speakers; the French noun denoting ten years is "décennie".) The names of days in the décade are derived from their number in the ten day sequence. The five or six days of the sans-culottides do not bear the names of the décade. Instead, each of these holidays commemorates an aspect of the republican spirit. The last, jour de la Révolution, occurs only in years of 366 days.
Napoléon abolished the Republican calendar in favour of the Gregorian on January 1st, 1806. Thus France, one of the first countries to adopt the Gregorian calendar (in December 1582), became the only country to subsequently abandon and then re-adopt it. During the period of the Paris Commune uprising in 1871 the Republican calendar was again briefly used.
decree which established the Republican calendar contained a contradiction:
it defined the year as starting on the day of the true autumnal
equinox in Paris, but further prescribed a four year cycle called
la Franciade, the fourth year of which would end with
le jour de la Révolution and hence contain 366 days.
These two specifications are incompatible, as 366 day years defined
by the equinox do not recur on a regular four year schedule. This
problem was recognised shortly after the calendar was proclaimed,
but the calendar was abandoned five years before the first conflict
would have occurred and the issue was never formally resolved.
Here we assume the equinox rule prevails, as a rigid four year
cycle would be no more accurate than the Julian calendar, which
couldn't possibly be the intent of its enlightened Republican
ISO-8601 Week and Day, and Day of YearThe International Standards Organisation (ISO) issued Standard ISO 8601, "Representation of Dates" in 1988, superseding the earlier ISO 2015. The bulk of the standard consists of standards for representing dates in the Gregorian calendar including the highly recommended "YYYY-MM-DD" form which is unambiguous, free of cultural bias, can be sorted into order without rearrangement, and is Y9K compliant. In addition, ISO 8601 formally defines the "calendar week" often encountered in commercial transactions in Europe. The first calendar week of a year: week 1, is that week which contains the first Thursday of the year (or, equivalently, the week which includes January 4th of the year; the first day of that week is the previous Monday). The last week: week 52 or 53 depending on the date of Monday in the first week, is that which contains December 31 of the year. The first ISO calendar week of a given year starts with a Monday which can be as early as December 29th of the previous year or as late as January 4th of the present; the last calendar week can end as late as Sunday, January 3rd of the subsequent year. ISO 8601 dates in year, week, and day form are written with a "W" preceding the week number, which bears a leading zero if less than 10, for example February 29th, 2000 is written as 2000-02-29 in year, month, day format and 2000-W09-2 in year, week, day form; since the day number can never exceed 7, only a single digit is required. The hyphens may be elided for brevity and the day number omitted if not required. You will frequently see date of manufacture codes such as "00W09" stamped on products; this is an abbreviation of 2000-W09, the ninth week of year 2000.
In solar calendars such as the Gregorian, only days and years have physical significance: days are defined by the rotation of the Earth, and years by its orbit about the Sun. Months, decoupled from the phases of the Moon, are but a memory of forgotten lunar calendars, while weeks of seven days are entirely a social construct--while most calendars in use today adopt a cycle of seven day names or numbers, calendars with name cycles ranging from four to sixty days have been used by other cultures in history.
ISO 8601 permits us to jettison the historical and cultural baggage of weeks and months and express a date simply by the year and day number within that year, ranging from 001 for January 1st through 365 (366 in a leap year) for December 31st. This format makes it easy to do arithmetic with dates within a year, and only slightly more complicated for periods which span year boundaries. You'll see this representation used in project planning and for specifying delivery dates. ISO dates in this form are written as "YYYY-DDD", for example 2000-060 for February 29th, 2000; leading zeroes are always written in the day number, but the hyphen may be omitted for brevity.
All ISO 8601
date formats have the advantages of being fixed length (at least
until the Y10K crisis rolls around) and, when stored in a computer,
of being sorted in date order by an alphanumeric sort of their
textual representations. The ISO week and day and day of year
calendars are derivative of the Gregorian calendar and share its
Unix time() valueDevelopment of the Unix operating system began at Bell Laboratories in 1969 by Dennis Ritchie and Ken Thompson, with the first PDP-11 version becoming operational in February 1971. Unix wisely adopted the convention that all internal dates and times (for example, the time of creation and last modification of files) were kept in Universal Time, and converted to local time based on a per-user time zone specification. This far-sighted choice has made it vastly easier to integrate Unix systems into far-flung networks without a chaos of conflicting time settings.
The machines on which Unix was developed and initially deployed could not support arithmetic on integers longer than 32 bits without costly multiple-precision computation in software. The internal representation of time was therefore chosen to be the number of seconds elapsed since 00:00 Universal time on January 1, 1970 in the Gregorian calendar (Julian day 2440587.5), with time stored as a 32 bit signed integer (long in the original C implementation).
of Unix time representation has spread well beyond Unix since
most C and C++ libraries on other systems provide Unix-compatible
time and date functions. The major drawback of Unix time representation
is that, if kept as a 32 bit signed quantity, on January 19, 2038
it will go negative, resulting in chaos in programs unprepared
for this. Modern Unix and C implementations define the result
of the time() function as type time_t, which
leaves the door open for remediation (by changing the definition
to a 64 bit integer, for example) before the clock ticks the dreaded
Excel Serial Day NumberSpreadsheet calculations frequently need to do arithmetic with date and time quantities--for example, calculating the interest on a loan with a given term. When Microsoft Excel was introduced for the PC Windows platform, it defined dates and times as "serial values", which express dates and times as the number of days elapsed since midnight on January 1, 1900 with time given as a fraction of a day. Midnight on January 1, 1900 is day 1.0 in this scheme. Time zone is unspecified in Excel dates, with the NOW() function returning whatever the computer's clock is set to--in most cases local time, so when combining data from machines in different time zones you usually need to add or subtract the bias, which can differ over the year due to observance of summer time. Here we assume Excel dates represent Universal (Greenwich Mean) time, since there isn't any other rational choice. But don't assume you can always get away with this.
You'd be entitled to think, therefore, that conversion back and forth between PC Excel serial values and Julian day numbers would simply be a matter of adding or subtracting the Julian day number of December 31, 1899 (since the PC Excel days are numbered from 1). But this is a Microsoft calendar, remember, so one must first look to make sure it doesn't contain one of those bonehead blunders characteristic of Microsoft. As is usually the case, one doesn't have to look very far. If you have a copy of PC Excel, fire it up, format a cell as containing a date, and type 60 into it: out pops "February 29, 1900". News apparently travels very slowly from Rome to Redmond--ever since Pope Gregory revised the calendar in 1582, years divisible by 100 have not been leap years, and consequently the year 1900 contained no February 29th. Due to this morsel of information having been lost somewhere between the Holy See and the Infernal Seattle monopoly, all Excel day numbers for days subsequent to February 28th, 1900 are one day greater than the actual day count from January 1, 1900. Further, note that any computation of the number of days in a period which begins in January or February 1900 and ends in a subsequent month will be off by one--the day count will be one greater than the actual number of days elapsed.
By the time the 1900 blunder was discovered, Excel users had created millions of spreadsheets containing incorrect day numbers, so Microsoft decided to leave the error in place rather than force users to convert their spreadsheets, and the error remains to this day. Note, however, that only 1900 is affected; while the first release of Excel probably also screwed up all years divisible by 100 and hence implemented a purely Julian calendar, contemporary versions do correctly count days in 2000 (which is a leap year, being divisible by 400), 2100, and subsequent end of century years.
day numbers are valid only between 1 (January 1, 1900) and 2958465
(December 31, 9999). Although a serial day counting scheme has
no difficulty coping with arbitrary date ranges or days before
the start of the epoch (given sufficient precision in the representation
of numbers), Excel doesn't do so. Day 0 is deemed the idiotic
January 0, 1900 (at least in Excel 97), and negative days and
those in Y10K and beyond are not handled at all. Further, old
versions of Excel did date arithmetic using 16 bit quantities
and did not support day numbers greater than 65380 (December 31,
2078); I do not know in which release of Excel this limitation
Excel day numbers are valid only between 0 (January 1, 1904) and
2957003 (December 31, 9999). Although a serial day counting scheme
has no difficulty coping with arbitrary date ranges or days before
the start of the epoch (given sufficient precision in the representation
of numbers), Excel doesn't do so. Negative days and those in Y10K
and beyond are not handled at all. Further, old versions of Excel
did date arithmetic using 16 bit quantities and did not support
day numbers greater than 63918 (December 31, 2078); I do not know
in which release of Excel this limitation was remedied.
abstract calendar converter, maker John Walker