[LEAPSECS] alternative to smearing

[Zefram]

Preben Norager wrote:
>        Astronomy then have two different "eternal" timescales, with two
>different starting points for zero:

Many more than two.  MJD, TJD, and the Julian epoch, for example, all
have some currency in astronomy, and each have their own zero point.
("Julian epoch" is a somewhat confusing term: it refers to a linear
count similar to JD, but scaled by a factor of 365.25 such that over the
long term it is frequency locked to the years of the Julian calendar,
and with zero point chosen such that Julian epoch roughly matches the
AD year number of the Julian calendar year.  The zero is nevertheless
not identical to the start of AD 0 in either the Gregorian or Julian
calendar.)

>                                    The one is the proleptic gregorian
>calendar, represented by ISO 8601, with the starting year zero,

That's not really the *start* of the Gregorian calendar.  It extends
back much earlier than that, and there's nothing really special about
the year zero.  In general, the zero point of counting systems such as
this is a lot less special than one might imagine.  It's only rarely
the start of the system's applicability.  It may be a reference point,
the time of some epochal event, but often it's not even that.

Looking at the year numbering used by ISO 8601, this was originally
devised by Dionysius Exiguus in AD 525, and he originally used it with the
Julian calendar.  It's not clear in which year he intended the epochal
event to occur: it may have been -1, 0, or 1.  We're not even sure
which event he intended to define the epoch: it's either the conception
or the birth of Jesus of Nazareth.  We're pretty sure that he got the
computation wrong: it's currently reckoned that Jesus was born around the
year -3 in this numbering.  Dionysius actually defined AD year numbering
by reference to the Diocletian era, a year numbering in common use at
the time.  He defined that AD 532 was the year following Diocletian 247.

ISO 8601 uses neither of these as the reference point.  It fully defines
the proleptic Gregorian calendar.  But to specify its phase it does not
refer to any event in the vicinity of AD 0, nor to the Diocletian era,
nor to any event in the vicinity of AD 532.  Rather, it says

	The Gregorian calendar has a reference point that assigns 20
	May 1875 to the calendar day that the "Convention du Metre"
	was signed in Paris.

So the reference point is actually 1875-05-20.  Definitely not the start
of the calendar, nor a zero date.  It's much more useful than either
of those would be: it's a reference event of which we have very strong
historical knowledge.

>                                         But I don't understand how
>astronomy can cope with two different starting points for zero.

We do not find any difficulty in adding a fixed offset to handle a
difference in epochs.  The mathematical expressions would be only very
slightly simpler if we had the same epoch for everything.  What do you
think is the difficult part?

In fact, astronomers and engineers have repeatedly found greater value
in making the JD-like day numbers that they deal with smaller, than
in maintaining a consistent zero epoch.  MJD is defined as MJD = JD -
2400000.5, such that until AD 2132 MJDs have only five integer digits
rather than the seven of JD.  (The shift from being integral at noon to
integral at midnight reflects a shift in preferences, and also entails a
change of epoch.)  TJD is defined as TJD = MJD - 40000, such that during
the era of its original use (the Apollo space programme) it only used
four integer digits.

>                                                                The
>beginning of time must be a beginning in time,

We're not dealing with the beginning of time, or really of anything.
We are not troubled by negative numbers.  (There *is* a slight convenience
in having the numbers one actually deals with all be non-negative,
as I said before, but it is no more than convenience.)

>                                          I don't know if that is because
>Christmas day (December 24/25), and other important days, are not the same
>JD in the julian, and the proleptic gregorian calendar,

No, we're not at all bothered about that.

>zero point in time must be the same for both the daily, and the annual
>continuous timescale.

"Must"?  Why?

>The new system of GD shall like JD count the days from noon to noon. But
>the zero day shall not be JD:0. The zero day of GD shall be the day from
>-0001-12-31T12:00 to 0000-01-01T12:00. That day is JD:17210159, so my
>reform will be the removal of 17210158 days from JD, to create GD.

It won't catch on.  You're not offering any real value here.

If you personally want a day count with a zero in the vicinity of
AD 0, maybe you'd like Rata Die.  Its zero point is 0000-12-31T00.
Unlike JD, it is conventionally used with timezone-relative calendar
days, not only the days of UT and other technical time scales.  It was
rather gratuitously invented for the book "Calendrical Calculations",
and has some currency among computer programmers, but I haven't seen
it used by astronomers.  (Beware of errors and confusion in the book.
It actually defines three slightly different day counts, all of which
it calls "Rata Die".)

-zefram