# The year before the year 1

Markus Kuhn Markus.Kuhn at cl.cam.ac.uk
Wed Aug 11 17:09:17 UTC 2004

```"Olson, Arthur David (NIH/NCI)" wrote on 2004-08-11 16:18 UTC:
> One of Paul's documentation changes that I left out of the update was...
> 	+The year before the year 1 is the year 0, the year before that is
> 	+the year \-1, and so forth.
> If I recall correctly, there's no year zero: the sequence (going backward)
> is...
> ...or, for "Common Era" fans...
> 	3 CE, 2 CE, 1 CE, 1 BCE, 2 BCE, 3 BCE..
>
> Have our standard-making friends said anything on the matter?

Historical practice was that way simply because the "anno domini"
technology has allegedly been developped by some monk of the name
Dionysius Exiguus in the 6th century and was finally rolled-out by the
church around the year 1000 A.D.

But the technology of negative numbers and the number zero became only
widely known after decimal numbers became widely accepted and popular,
which was certainly not before Fibonacci's textbook "Liber Abacci", was
first published in 1202.

The idea of the year zero has been widely used in modern astronomical
tables. It was more recently also sanctioned by ISO 8601:2000 for the
international date notation, which uses the prolaptic Gregorian calendar
with year zero:

---------------------------------------------------------------------
4.3.2 Date and time reference systems

4.3.2.1 The Gregorian calendar

This International Standard uses the Gregorian calendar for the
identification of calendar days.

The Gregorian calendar provides a reference system consisting of a,
potentially infinite, series of contiguous calendar years. Consecutive
calendar years are identified by sequentially assigned year numbers. A
reference point is used which assigns the year number 1875 to the
calendar year in which the "Convention du mètre" was signed at Paris.

The Gregorian calendar distinguishes common years with a duration of 365
calendar days and leap years with a duration of 366 calendar days. A
leap year is a year whose year number is divisible by four an integral
number of times. However, centennial years are not leap years unless
they are divisible by four hundred an integral number of times.

This International Standard allows the identification of calendar years
by their year number for years both before and after the introduction of
the Gregorian calendar. For the determination of calendar years and year
numbers only the rules mentioned above are used. For the purposes of
this International Standard these rules are referred to as the Gregorian
calendar. The use of this calendar for dates preceding the introduction
of the Gregorian calendar (i.e. before 1582) should only be done by
agreement of the partners in information interchange.

NOTE 1 In the prolaptic Gregorian calendar the calendar year [0000] is a
leap year.

NOTE 2 No dates shall be inserted or deleted when determining dates in
the prolaptic Gregorian calendar (this may be necessary for the
calculation of dates in the Julian calendar before 1582). Also note that
the year numbers of years before the calendar year [0001] differ from
the year numbers in the  BC/AD calendar system, where the year 1 BC is
followed by the year 1 AD.

[...]

4.7 Expansion

By mutual agreement of the partners in information interchange it is
permitted to expand the component identifying the calendar year, which
is otherwise limited to at most four digits. This enables reference to
dates and times in calendar years outside the range supported by
complete representations, i.e. before the start of the year [0000] or
after the end of the year [9999].

When expanded representations are used, provisions should be made to
prevent confusion of the expanded representations, with other date and
time representations used by the application.
---------------------------------------------------------------------

ISO 8601 then also defines an extended year format, in which the year
can be longer than four digits and outside the range 0000 to 9999, but
it must then start with either + or -, e.g. today is

+002004-08-11

Markus

--
Markus Kuhn, Computer Lab, Univ of Cambridge, GB
http://www.cl.cam.ac.uk/~mgk25/ | __oo_O..O_oo__

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