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  1. OMG Issue

DTV11 — inconsistent statements on day index

  • Key: DTV11-88
  • Legacy Issue Number: 19280
  • Status: closed  
  • Source: ( Michael Deckers)
  • Summary:

    section 11.2, last Note on p 126:

    [a] "The calendar reform instituted by
    Pope Gregory XIII [Inter Gravissimas]
    deleted 10 days from the
    Gregorian calendar, starting on
    5 October 1582."

    [b] "The previous calendar day had
    index 577 739 on the Julian calendar,
    computed as 1581 years of 365 days
    plus 395 leap days + 279 days
    from 1 January 1852 to
    5 October 1582."

    [c] "The following day was
    15 October 1582."

    [d] "From that date to the Convention du
    Mètre on 20 May 1875, there were
    106 870 calendar days including
    leap days."

    section 11.7, in a Note on p 141:

    [e] "685 263 is the index of
    1 January 1601,
    computed as 684 609 (index of
    15 October 1582) plus 6654 days from
    15 October 1582 through
    1 January 1601."

    section 11.7, in the 2nd Example on p 141:

    [f] "The first calendar day of 2010
    is Gregorian day 830 991"

    The assertion in [a] is misunderstandable:
    no days were deleted from the Gregorian
    calendar by any pope. In fact, the
    proleptic Gregorian calendar without
    any "deletions" is
    used by ISO 8601:2004, by computer
    software and by some historians.
    What really is meant is:
    'The calendar reform instituted by
    Pope Gregory XIII and promulgated in
    the bull [Inter Gravissimas] started
    the use of the Gregorian calendar with
    the date 15 October 1582, which is the
    same as 05 October 1582 in the Julian

    As for [b]: The "previous calendar day"
    would be 1582 Oct 04 in the Julian
    calendar, not 1582 Oct 05 as suggested in
    [b]. Whichever of the two is meant, the
    following computation in [b] is
    incorrect: the number of days from
    1582 Jan 01 until 1582 Oct 05 is 277 and
    not 279, as can be read directly from
    [table 11.3, p 146].

    As for [c]: It appears as if the
    "following day" means the day
    after J1582-10-05. This
    following day is
    J1582-10-06 = G1582-10-16,
    not G1582-10-15 as asserted.
    (We use prefixes
    J and G to distinguish Julian and
    Gregorian calendars.)

    The computation in [d] is incorrect: the
    number of days from G1582-10-15 to
    G1875-05-20 is 106 868, not 106 870
    as asserted,
    because G1582-10-15 = JD 2299 160.5
    and G1875-05-20 = JD 2406 028.5.

    Assertion [e] is clearly
    self-contradictory since
    685 263 - 684 609 is not 6654.

    Inconsistencies between [b, e, f]: If
    1 January 1601 is the day number 685 263
    as asserted in [e] then
    day 0 is JD 1620 550.5 = G-0276-10-25,
    and if day 684 609 is G1582-10-15 as
    also asserted in [e] then
    day 0 is JD 1614 551.5 = G-0292-05-23.
    Still another zero point follows from [f]:
    day 0 is JD 1624 206.5 = G-0266-10-29
    and finally, if [b] is meant to refer to
    G1582-10-14 as day number 577 739, then
    day 0 is JD 1721 420.5 = G0000-12-27.
    That last date might indicate that day 0
    was actually meant to be still another
    date, viz J0001-01-01 = G0000-12-30,
    but this is just a wild guess of mine.

    The inconsistencies may come from
    several sources:
    • from typos (though I am not able to
    figure out which);
    • from the error in the formula for
    the duration of successive Gregorian
    years (eg in [d]);
    • from the use of intervals on the
    "time axis" instead of points on it.

    The time axis is an affine space whose
    translation space, formed by the
    differences T - T' for points T, T' on
    the time axis, is the vector space of
    "duration values". Intervals of
    lengths > 0 s, however, do not form an
    affine space. So one has to take the
    lower or the upper bounds of the involved
    intervals consistently to arrive at valid
    date arithmetic (eg, satisfying the rule
    T - T" = (T - T') + (T'- T")).

    An error in numerical examples for
    non-trivial specifications is particularly
    unfortunate because such examples are
    often taken as the very first test cases
    for an implementation. It is therefore
    appropriate to check all the examples
    before publishing. Many calendrical
    calculators are available online for that
    purpose; the one at [
    is particularly useful.

  • Reported: DTV 1.0 — Fri, 7 Mar 2014 05:00 GMT
  • Disposition: Resolved — DTV 1.1
  • Disposition Summary:

    The suggested text clarification is accepted. The erroneous numbers will be corrected.
    Because the changes made necessary by this resolution overlap those made in the resolution of Issue 19281, this issue is merged with Issue 19281.
    Disposition: See issue 19281 for disposition

  • Updated: Fri, 6 Mar 2015 20:58 GMT