# RE: Internal inconsistency wrt year 0000

From: James Clark <jjc@jclark.com>
Date: Wed, 24 Apr 2002 09:37:00 +0700
Message-ID: <780953221.1019641020@[192.168.0.65]>
```
> Our current thinking is that ISO 8601 is in error and we want to request
> a change disallowing the year 0000.
>
> You said:
>> Now the year 1BC in the proleptic Gregorian calendar is a leap year.
>
> Where can I confirm this information?  We've been worrying about a
> related change in the comparison of durations that is affected by this
> information.

If you start from first principles, I think this has to be the case.  The
purpose of leap years in a calendar is to ensure that the mean length of a
year in the calendar is as close as possible to the length of the solar
tropical year.  This requires that the calendar have a regular cycle. The
cycle of the Gregorian calendar is 400 years.  The year 400AD is a leap
year. The year 1BC immediately precedes 1AD and so is 400 years before
400AD. Therefore 1BC must also be a leap year.  In other words, if 1BC was
not a leap year, there would be a discontinuity in the proleptic Gregorian
calendar for which there is no justification.  I did a bit of googling and
found the following:

http://www.bluewaterarts.com/calendar/InterGravissimas.htm  (translation of
Papal Bull establishing the Gregorian calendar)
http://www.wikipedia.com/wiki/Proleptic+Gregorian+Calendar
http://serendipity.magnet.ch/hermetic/cal_stud/cal_art.htm#Astronomical
http://astro.nmsu.edu/~lhuber/leaphist.html

As regards the the year 0000 issue, everything I have found on the Web
suggests that ISO 8601 is correct, and that the year -1 corresponds to 2 BC
not 1 BC.  There are two ways to number years:

-2, -1, 0, 1, 2

but never

-2, -1, 1, 2

In addition to the above see:

http://webexhibits.org/calendars/year-definitions.html
http://www.znaturforsch.com/df/gc.htm
http://www.maa.mhn.de/Scholar/calendar.html
http://webexhibits.org/calendars/calendar-christian.html

I have never found anything that suggests that the year -1 corresponds to 1
BC in the Gregorian calendar.

James

> All the best, Ashok
> ===========================================================
>
>
> -----Original Message-----
> From: James Clark [mailto:jjc@jclark.com]
> Sent: Tuesday, April 23, 2002 6:30 AM
> Subject: Internal inconsistency wrt year 0000
>
> The inconsistency between XML Schema Part 2 and ISO 8601:2000 wrt year
> 0000
> has already been commented on, but there is also a minor internal
> inconsistency.  XML Schema Part 2 disallows year 0000, which means that
> year -0001 corresponds to 1BC (whereas in ISO 8601:2000, 1BC is year
> 0000).
> Now the year 1BC in the proleptic Gregorian calendar is a leap year.
> However, appendix E uses the formula
>
>   modulo(Y, 400) = 0 OR (modulo(Y, 100) != 0) AND modulo(Y, 4) = 0
>
> to determine whether Y is a leap year.  But this formula makes year
> -0001
> not a leap year.  If year 0000 was allowed (representing 1BC), then the
> formula would be correct.
>
> James
>
>
```
Received on Tuesday, 23 April 2002 22:34:49 UTC

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