Unifying Atomic Time and the post-Gregorian calendar corrections

From: Markus Kuhn <Markus.Kuhn_at_CL.CAM.AC.UK>
Date: Thu, 03 Jul 2003 15:20:19 +0100

I recently proposed in my posting "What to do if International Time hits
the International Date Line?" a new approach to solve two calendar and
time-keeping problems at the same time:

  a) the long-term deviation of atomic time from UT (i.e., in the years
     5658, 8462, ... the point where TI corresponds to local time crosses
     the international date line)

  b) the long-term deviation of the longitude of the sun from
     the Gregorian calendar date (i.e., after a few thousand years,
     the spring equinox will happen on 19 March, 18 March,
     17 March, ...)

The crucial idea/observation/hope is: while the daily rotation of the
earth deviates from atomic time strongly enough to cause an offset of
more than one day "relatively" soon, the annual rotation of the earth is
stable enough to remain in sync with atomic time within a day for many
ten thousand years to come.

This opens the possibility that the above two problems can be used to
cancel each other out. At least for the next few ten thousand years,
significantly longer than recorded human history!

It becomes clear from replies that I received that my last discussion
proposal wasn't really understood by many people.

So here is again in a nutshell "Kuhn's Atomic Calendar", a leap-second
free tiny improvement over the Gregorian Calendar:

  a) We adopt Temps International (TI) as suggested in Torino
     (TI = UTC in 2005, with no further leap seconds in TI, i.e.
      TI = TAI - 32 s forever).

  b) TI is what computers, navigation systems, time broadcasts, submarine
     crews, etc. will in the future use as the monotonic uniform international
     reference time (POSIX time_t, etc.) instead of today's UTC

  c) Where TI is converted into a broken-down time of the YYYY-MM-DD HH:MM:SS
     form, we strictly follow the Gregorian rules as specified in POSIX:2001,
     i.e. there is a 29 February if the year is a multiple of 4 unless
     it is a multiple of 100 unless it is a multiple of 400.

  d) For local civilian times, we need to change the offset to TI every few
     hundred years, because TI is detached from the rotation of the earth.
     This is no problem, because we change the offset between local civilian time
     and computer time already twice per year today for summer time, and
     countries keep hopping between time zones for political reason
     (see most recently Portugal's move to British time a few years ago).

     In other words:

          2005: British Time = TI
          2780: British Time = TI - 1h (from start of summer-time that year)
          3330: British Time = TI - 2h
          3712: British Time = TI - 3h
          5496: British Time = TI - 11h

     These changes would be implemented by skipping the deleted leap hour
     normally necessary to start summer time at the years listes above.

  d) Whenever British Time is about to fall 12 h behind TI, UN/ITU/IERS (or
     the Queen of England :) will write to all heads of government worldwide
     and invite them to agree that the next year divisible by 400 shall not
     be a leap year (except for anything living in TI or course) in all

     We do this for the first time when we skip the Gregorian leap day
     5600-02-29 in all time zones. This would be handled in computers simply
     as a part of the normal locale-timezone database maintenance and would not
     even need recompiling of existing mainstream operating systems. It can also
     be easily announced 100 years in advance and when to do it will be
     obvious from even crude UT-TI forecasts.

This will keep local times and TI from diverging by more than about a
day or 25 h (for British Time the divergence will even be limited to
about half a day or 13 h):

     5496: British Time = TI - 11h
     5600-02-28: British time = TI - 11 h (5600-02-29 skipped in civilian time)
     5600-03-01: British time = TI + 13 h
     5658: British time = TI + 12 h
     5814: British time = TI + 11 h
     5963: British time = TI + 10 h
     8332: British time = TI - 11 h
     8400-02-28: British time = TI - 11 h
     8400-03-01: British time = TI + 13 h (8400-02-29 skipped in civilian time)
     8423: British time = TI + 12 h
     8513: British time = TI + 11 h
     8601: British time = TI + 10 h

This way, we have a time and calendar system with three nice properties:

  a) Computers etc. run on a strictly uniform, leap-second/hour/day-free,
     monotonic and predictable atomic Gregorian calendar (TI). GOOD!

  b) The offset between civilian local timezone and TI changes occasionally
     by one hour. NOT MUCH WORSE THAN TODAY!

  c) The maximal offset between between the TI used in computers and
     local civilian times will be limited all over the world to the
     range TI - 25h to TI + 25h (today: local times are in the range
     UTC - 13h to UTC + 13h or so). NOT MUCH WORSE THAN TODAY!

  d) The spring equinox will (hopefully) remain more stable at the same
     day of the year than if we kept UTC with the Gregorian calendar, because
     the year length follows closer atomic time than the UT day length.
     (On the last point, I'm still looking for confirmation from
     astronomers with good knowledge of long-term prediction of the
     longitude of the sun.) GOOD!

Don't missunderstand me, I'm not advocating that we should introduce the
above, as I am not a strong leap-second hater. But I hope that people
will agree that *if* we introduced TI and dropped leap seconds, then
above would be a *far* neater approach than leap hours. I just want to
make sure that each camp in this debate is equipped with the best
possible proposal.

The above atomic-time based modification of the Gregorian calendar seems
to me much more elegant than occasionally floated alternatives of
correcting the Gregorian calendar, such as not having a leap year every
4000 years. But my views may be biased ...

Any comments?


Markus Kuhn, Computer Laboratory, University of Cambridge
http://www.cl.cam.ac.uk/~mgk25/ || CB3 0FD, Great Britain
Received on Thu Jul 03 2003 - 07:20:34 PDT

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