Date: Fri, 23 Jul 1999
From: Peter Meyer
Subject: Re: Proleptic calendar conventions

Bill Spencer wrote:

>I think that the common convention for software is to simply run the
>rules from when the calendar was defined backwards to infinity.

Yes. To define a calendar (assumed to use dates which consist of years, months and days, in the usual sense) we need: (i) Rules which allow us to decide how many months are in a given year (e.g. year 1191) and how many days are in a given month (e.g. month 3 of year 921) and (ii) Some way to relate a given date in that calendar to an identifiable day (such as today, or the day designated by some Julian day number or a date in the Gregorian calendar).

Such a year-month-day calendar can be said to be "well-defined" (even if they "years" are not exactly solar years, or the "months" are not exactly lunar months, although we should insist that the "days" are solar days).

A calendar which is actually used always has a date (or approximate date) at which it was first used. Call this its "date of introduction". Strictly speaking the only valid dates in the calendar are dates for days since its date of introduction.

It can, however, be used to specify days prior to its date of introduction, by using (i) and (ii), perhaps in combination with a system of numbering years which permits zero and negative numbers for years. The calendar thus extended is called the "proleptic" version of the calendar. If no lower limit is placed on numbers for years (i.e. if we can use any integer as a year number, and if the rules in (i) work also with negative years) then the proleptic version of the calendar can be extended indefinitely far into the past.

Regards, Peter Meyer