Rata Die

Rata Die (RD) is a system for assigning numbers to calendar days (optionally with time of day), independent of any calendar, for the purposes of calendrical calculations. It was named (after the Latin ablative feminine singular for "from a fixed date") by Howard Jacobson.[1] The same system (including the same epoch) was used earlier, e.g., the REXX programming language since about 1980:[2]

The base date of 1 January 0001 is determined by extending the current Gregorian calendar backward (365 days each year, with an extra day every year that is divisible by 4 except century years that are not divisible by 400).

Rata Die is somewhat similar to Julian Dates (JD), in that the values are plain real numbers that increase by 1 each day. The systems differ principally in that JD takes on a particular value at a particular absolute time, and is the same in all contexts, whereas RD values are relative to timezone. This makes RD more suitable for work on calendar dates, whereas JD is more suitable for work on time per se. The systems also differ trivially by having different epochs: RD is 1 at midnight (00:00) local time on January 1, AD 1 in the proleptic Gregorian calendar, JD is 0 at noon (12:00) Universal Time on January 1, 4713 BC in the proleptic Julian calendar, and the REXX count of days begins with 0 at midnight (00:00) local time on January 1, AD 1 in the proleptic Gregorian calendar.

Forms

There are three distinct forms of RD. In this section they will each be defined in terms of Julian Dates. "Zoff" is the offset of the timezone being used, in fractional days. (For example, in Eastern Standard Time, 5 hours behind UT, Zoff = -5/24.)

The first form of RD is a continuously-increasing fractional number, taking integer values at midnight local time. It may be defined in terms of the Julian Date as

RD = JD - 1 721 424.5 + Zoff

In the second form, RD is an integer that labels an entire day, from midnight to midnight local time. This is the result of rounding the first form of RD downwards (towards negative infinity). It is the same as the relation between Julian Date and Julian Day Number (JDN). Thus:

RD = floor(JD - 1 721 424.5 + Zoff)

In the third form, the RD is an integer labelling noon local time, and incapable of labelling any other time of day. This is defined as

RD = JD - 1 721 425 + Zoff

where the RD value must be an integer, thus constraining the choice of JD. (The fractional part of the JD must have a particular value which depends on Zoff.) This form of RD is used in the book for conversion of calendar dates between calendars that separate days on different boundaries.

The book does not explicitly distinguish between these three forms, using the abbreviation "RD" for all of them.[1]

See also

References

  1. ↑ 1.0 1.1 Reingold, Edward; Dershowitz, Nachum (2007). Calendrical Calculations (3rd ed.). Cambridge University Press. chapter 1.2. ISBN 0-521-70238-0. Retrieved 2015-04-22.
  2. ↑ REXX/400 Reference manual page 87.