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calendar
& conversion
Gregorian
calendar
The Gregorian
calendar was proclaimed by Pope Gregory XIII and took effect in
most Catholic states in 1582, in which October 4, 1582 of the Julian
calendar was followed by October 15 in the new calendar, correcting
for the accumulated discrepancy between the Julian calendar and
the equinox as of that date. When comparing historical dates, it's
important to note that the Gregorian calendar, used universally
today in Western countries and in international commerce, was adopted
at different times by different countries. Britain and her colonies
(including what is now the United States), did not switch to the
Gregorian calendar until 1752, when Wednesday 2nd September in the
Julian calendar dawned as Thursday the 14th in the Gregorian.
The Gregorian
calendar is a minor correction to the Julian. In the Julian calendar
every fourth year is a leap year in which February has 29, not
28 days, but in the Gregorian, years divisible by 100 are not
leap years unless they are also divisible by 400. How prescient
was Pope Gregory! Whatever the problems of Y2K, they won't include
sloppy programming which assumes every year divisible by 4 is
a leap year since 2000, unlike the previous and subsequent years
divisible by 100, is a leap year. As in the Julian calendar,
days are considered to begin at midnight.
The average
length of a year in the Gregorian calendar is 365.2425 days compared
to the actual solar tropical year (time from equinox to equinox)
of 365.24219878 days, so the calendar accumulates one day of error
with respect to the solar year about every 3300 years. As a purely
solar calendar, no attempt is made to synchronise the start of
months to the phases of the Moon.
While one
can't properly speak of "Gregorian dates" prior to the adoption
of the calendar in 1582, the calendar can be extrapolated to prior
dates. In doing so, this implementation uses the convention that
the year prior to year 1 is year 0. This differs from the Julian
calendar in which there is no year 0the year before year 1 in
the Julian calendar is year 1. The date December 30th, 0 in the
Gregorian calendar corresponds to January 1st, 1 in the Julian
calendar.
A slight
modification of the Gregorian calendar would make it even more
precise. If you add the additional rule that years evenly divisible
by 4000 are not leap years, you obtain an average solar
year of 365.24225 days per year which, compared to the actual
mean year of 365.24219878, is equivalent to an error of one day
over a period of about 19,500 years; this is comparable to errors
due to tidal braking of the rotation of the Earth.
Julian
day
Astronomers,
unlike historians, frequently need to do arithmetic with dates.
For example: a double star goes into eclipse every 1583.6 days and
its last mideclipse was measured to be on October 17, 2003 at 21:17
UTC. When is the next? Well, you could get out your calendar and
count days, but it's far easier to convert all the quantities in
question to Julian day numbers and simply add or subtract. Julian
days simply enumerate the days and fraction which have elapsed since
the start of the Julian era, which is defined as beginning
at noon on Monday, 1st January of year 4713 B.C.E. in the Julian
calendar. This date is defined in terms of a cycle of years, but
has the additional advantage that all known historical astronomical
observations bear positive Julian day numbers, and periods can be
determined and events extrapolated by simple addition and subtraction.
Julian dates are a tad eccentric in starting at noon, but then so
are astronomers (and systems programmers!)when you've become accustomed
to rising after the "crack of noon" and doing most of your work
when the Sun is down, you appreciate recording your results in a
calendar where the date doesn't change in the middle of your workday.
But even the Julian day convention bears witness to the eurocentrism
of 19th century astronomynoon at Greenwich is midnight on the
other side of the world. But the Julian day notation is so deeply
embedded in astronomy that it is unlikely to be displaced at any
time in the foreseeable future. It is an ideal system for storing
dates in computer programs, free of cultural bias and discontinuities
at various dates, and can be readily transformed into other calendar
systems, as the source code for this page illustrates. Use Julian
days and fractions (stored in 64 bit or longer floating point numbers)
in your programs, and be ready for Y10K, Y100K, and Y1MM!
While any event
in recorded human history can be written as a positive Julian day
number, when working with contemporary events all those digits can
be cumbersome. A Modified Julian Day (MJD) is created by
subtracting 2400000.5 from a Julian day number, and thus represents
the number of days elapsed since midnight (00:00) Universal Time
on November 17, 1858. Modified Julian Days are widely used to specify
the epoch in tables of orbital elements of artificial Earth satellites.
Since no such objects existed prior to October 4, 1957, all satelliterelated
MJDs are positive.
Julian
calendar
The Julian calendar
was proclaimed by Julius Cćsar in 46 B.C. and underwent several
modifications before reaching its final form in 8 C.E. The Julian
calendar differs from the Gregorian only in the determination of
leap years, lacking the correction for years divisible by 100 and
400 in the Gregorian calendar. In the Julian calendar, any positive
year is a leap year if divisible by 4. (Negative years are leap
years if when divided by 4 a remainder of 3 results.) Days are considered
to begin at midnight.
In the Julian
calendar the average year has a length of 365.25 days. compared
to the actual solar tropical year of 365.24219878 days. The calendar
thus accumulates one day of error with respect to the solar year
every 128 years. Being a purely solar calendar, no attempt is
made to synchronise the start of months to the phases of the Moon.
Hebrew
calendar
The Hebrew (or
Jewish) calendar attempts to simultaneously maintain alignment between
the months and the seasons and synchronise months with the Moonit
is thus deemed a "lunisolar calendar". In addition, there
are constraints on which days of the week on which a year can begin
and to shift otherwise required extra days to prior years to keep
the length of the year within the prescribed bounds. This isn't
easy, and the computations required are correspondingly intricate.
Years are
classified as common (normal) or embolismic
(leap) years which occur in a 19 year cycle in years 3, 6, 8,
11, 14, 17, and 19. In an embolismic (leap) year, an extra month
of 29 days, "Veadar" or "Adar II", is added to the end of the
year after the month "Adar", which is designated "Adar I" in such
years. Further, years may be deficient, regular,
or complete, having respectively 353, 354, or 355 days
in a common year and 383, 384, or 385 days in embolismic years.
Days are defined as beginning at sunset, and the calendar begins
at sunset the night before Monday, October 7, 3761 B.C.E. in the
Julian calendar, or Julian day 347995.5. Days are numbered with
Sunday as day 1, through Saturday: day 7.
The average
length of a month is 29.530594 days, extremely close to the mean
synodic month (time from new Moon to next new Moon) of
29.530588 days. Such is the accuracy that more than 13,800 years
elapse before a single day discrepancy between the calendar's
average reckoning of the start of months and the mean time of
the new Moon. Alignment with the solar year is better than the
Julian calendar, but inferior to the Gregorian. The average length
of a year is 365.2468 days compared to the actual solar tropical
year (time from equinox to equinox) of 365.24219 days, so the
calendar accumulates one day of error with respect to the solar
year every 216 years.
Islamic
calendar
The Islamic calendar
is purely lunar and consists of twelve alternating months of 30
and 29 days, with the final 29 day month extended to 30 days during
leap years. Leap years follow a 30 year cycle and occur in years
1, 5, 7, 10, 13, 16, 18, 21, 24, 26, and 29. Days are considered
to begin at sunset. The calendar begins on Friday, July 16th, 622
C.E. in the Julian calendar, Julian day 1948439.5, the day of Muhammad's
flight from Mecca to Medina, with sunset on the preceding day reckoned
as the first day of the first month of year 1 A.H."Anno Hegirć"the
Arabic word for "separate" or "go away". Weeks begin on Sunday,
and the names for the days are just their numbers: Sunday is the
first day and Saturday the seventh.
Each cycle
of 30 years thus contains 19 normal years of 354 days and 11 leap
years of 355, so the average length of a year is therefore ((19
× 354) + (11 × 355)) / 30 = 354.365... days, with a mean length
of month of 1/12 this figure, or 29.53055... days, which closely
approximates the mean synodic month (time from new Moon
to next new Moon) of 29.530588 days, with the calendar only slipping
one day with respect to the Moon every 2525 years. Since the calendar
is fixed to the Moon, not the solar year, the months shift with
respect to the seasons, with each month beginning about 11 days
earlier in each successive solar year.
The calendar
presented here is the most commonly used civil calendar in the
Islamic world; for religious purposes months are defined to start
with the first observation of the crescent of the new Moon.
Persian
Calendar
The modern Persian
calendar was adopted in 1925, supplanting (while retaining the month
names of) a traditional calendar dating from the eleventh century.
The calendar consists of 12 months, the first six of which are 31
days, the next five 30 days, and the final month 29 days in a normal
year and 30 days in a leap year.
As one of
the few calendars designed in the era of accurate positional astronomy,
the Persian calendar uses a very complex leap year structure which
makes it the most accurate solar calendar in use today. Years
are grouped into cycles which begin with four normal
years after which every fourth subsequent year in the cycle is
a leap year. Cycles are grouped into grand cycles of
either 128 years (composed of cycles of 29, 33, 33, and 33 years)
or 132 years, containing cycles of of 29, 33, 33, and 37 years.
A great grand cycle is composed of 21 consecutive 128
year grand cycles and a final 132 grand cycle, for a total of
2820 years. The pattern of normal and leap years which began in
1925 will not repeat until the year 4745!
Each 2820
year great grand cycle contains 2137 normal years of 365 days
and 683 leap years of 366 days, with the average year length over
the great grand cycle of 365.24219852. So close is this to the
actual solar tropical year of 365.24219878 days that the Persian
calendar accumulates an error of one day only every 3.8 million
years. As a purely solar calendar, months are not synchronised
with the phases of the Moon.
Mayan
calendars
The Mayans employed
three calendars, all organised as hierarchies of cycles of days
of various lengths. The Long Count was the principal calendar
for historical purposes, the Haab was used as the civil
calendar, while the Tzolkin was the religious calendar.
All of the Mayan calendars are based on serial counting of days
without means for synchronising the calendar to the Sun or Moon,
although the Long Count and Haab calendars contain cycles of 360
and 365 days, respectively, which are roughly comparable to the
solar year. Based purely on counting days, the Long Count more closely
resembles the Julian Day system and contemporary computer representations
of date and time than other calendars devised in antiquity. Also
distinctly modern in appearance is that days and cycles count from
zero, not one as in most other calendars, which simplifies the computation
of dates, and that numbers as opposed to names were used for all
of the cycles.
Cycle
 Composed of
 Total
Days
 Years
(approx.)

kin

 1


uinal
 20 kin
 20


tun
 18 uinal
 360
 0.986

katun
 20 tun
 7200
 19.7

baktun
 20 katun
 144,000
 394.3

pictun
 20 baktun
 2,880,000
 7,885

calabtun
 20 piktun
 57,600,000
 157,704

kinchiltun
 20 calabtun
 1,152,000,000
 3,154,071

alautun
 20 kinchiltun
 23,040,000,000
 63,081,429

The Long Count
calendar is organised into the hierarchy of cycles shown at the
right. Each of the cycles is composed of 20 of the next shorter
cycle with the exception of the tun, which consists of
18 uinal of 20 days each. This results in a tun
of 360 days, which maintains approximate alignment with the solar
year over modest intervalsthe calendar comes undone from the Sun
5 days every tun.
The Mayans
believed at at the conclusion of each pictun cycle of
about 7,885 years the universe is destroyed and recreated. 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 dinosaursan 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:
baktun . katun . tun . uinal . kin
and thus
resemble presentday 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.
The Mayans
frequently specified dates using both the Haab and Tzolkin
calendars; dates of this form repeat only every 52 solar years.
Bahá'í
calendar
The 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 AyyámiHá 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.
The year
begins at the equinox, March 21, the Feast of NawRúz; 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 KullIShay
supercycles of 361 (19˛) years. The first KullIShay
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 calendar
A 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.
Years in
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 calendar
The 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
sixday holiday period, the jours complémentaires or
sansculottides. 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 sansculottides 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 sansculottides
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 readopt it. During the
period of the Paris Commune uprising in 1871 the Republican calendar
was again briefly used.
The original
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
designers.
ISO8601
Week and Day, and Day of Year
The 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 "YYYYMMDD"
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 20000229 in year, month,
day format and 2000W092 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
2000W09, 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 constructwhile 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 "YYYYDDD",
for example 2000060 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
accuracy.
Unix
time() value
Development of
the Unix operating system began at Bell Laboratories in 1969 by
Dennis Ritchie and Ken Thompson, with the first PDP11 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 peruser time zone specification.
This farsighted choice has made it vastly easier to integrate Unix
systems into farflung 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 multipleprecision
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).
The influence
of Unix time representation has spread well beyond Unix since
most C and C++ libraries on other systems provide Unixcompatible
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
doomsday second.
Excel
Serial Day Number
Spreadsheet calculations
frequently need to do arithmetic with date and time quantitiesfor
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 toin 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 Redmondever 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 onethe 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.
PC Excel
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
was remedied.
Having saddled
every PC Excel user with a defective date numbering scheme wasn't
enough for Microsoftnothing ever is. Next, they proceeded to come
out with a Macintosh version of Excel which uses an entirely
different day numbering system based on the MacOS native time
format which counts seconds elapsed since January 1, 1904. To further
obfuscate matters, on the Macintosh they chose to number days from
zero rather than 1, so midnight on January 1, 1904 has serial value
0.0. By starting in 1904, they avoided screwing up 1900 as they
did on the PC. So now Excel users who interchange data have to cope
with two incompatible schemes for counting days, one of which thinks
1900 was a leap year and the other which doesn't go back that far.
To compound the fun, you can now select either date system on either
platform, so you can't be certain dates are compatible even when
receiving data from another user with same kind of machine you're
using. I'm sure this was all done in the interest of the "efficiency"
of which Microsoft is so fond. As we all know, it would take a computer
almost forever to add or subtract four in order to make
everything seamlessly interchangeable.
Macintosh
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.
Fourmilab's
abstract calendar converter, maker John Walker

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