# Re: [LEAPSECS] The real problem with leap seconds

From: Mark Calabretta <mcalabre_at_atnf.CSIRO.AU>
Date: Thu, 19 Jan 2006 11:29:31 +1100

On Wed 2006/01/18 08:17:54 -0000, Francois Meyer wrote
in a message to: LEAPSECS_at_ROM.USNO.NAVY.MIL

>Maybe it should be, but this is far from being
>obvious from its current definition.

I agree that the current definitions leave a lot to be desired in terms
of clarity and rigour - an uncharitable person might even describe the
extract of ITU-R TF.460-6 cited the other day by Michael Deckers as
inconsistent. However, you have to consider how UTC is actually used in
practice and this is what my comments are based on.

>1. UTC and TAI share the same rate, the same
> origin, the same second. And therefore :
>
> UTC - TAI = 0

They both count SI seconds but the question of the origin is a bit
muddy.

You could argue that there is a fixed 10s offset between UTC and TAI
because UTC post-1972 (everything I've said about UTC only applies
post-1972) started with 10 leap seconds, and before 1972 UTC wasn't
simply a representation of TAI. There's no simple way of fudging
radixes that I can think of to make them match up, but if this worries
you then simply think in terms of proleptic UTC (post-1972),
see http://en.wikipedia.org/wiki/Proleptic.

However, this is not important and really only confuses things further.
(It's why I couched the original example as a graph of a person's age
vs UTC rather that TAI vs UTC.)

>2. UTC only differs from TAI by its definitions of
> the minute, hour and day.
>
>3. the TAI day, hour, minute are the SI
> day, hour, minute of 86400,3600,60
> SI seconds.
>
>4. the UTC minute is defined to ensure that dhms
> expressions of UTC match UT1 at .9 s; it can be
> either 59, 60 or 61 SI seconds long. This
> definition of the minute is realized
> by (positive or negative) leap seconds and
> ensures that the mean UTC day is the mean solar
> day in the long term. The UTC hour has 60 UTC
> minutes, the UTC day has 24 UTC hours.

OK, but using the word "definition" doesn't seem quite right, I'd couch
it in terms based on counting seconds.

If you consulted the wikipedia entry for "Factoradic" that I referenced
the other day you will see that each digit in the factoradic
representation of a number has a subscript indicating its (fixed) radix.
The fields (not the digits!) of a UTC representation should have
something similar (likewise calendar dates written as 2006/01/19),
except that for the seconds field (and the day field) the radix would
be variable and there's no simple way to write it, so people assume
it's 60 which is what you do anyway if you want your approximation of
UT1.

>>From that point of view, the sentence from the ITU460-6 :
>
> "[UTC] ...differs from it [TAI] from an integer of seconds"
>
>
>"representations of UTC involving minutes, hours,
>days differ from equivalent representations of TAI
>by an integral number of seconds"

I agree that the ITU-R TF.460.6 text needs fixing, but I would argue for
a stronger statement emphasising that a UTC representation (of TAI) has
two interpretions, one giving TAI (exact) and the other UT1 (approx), the
latter being offset from TAI by an integral number of seconds.

Mark Calabretta
ATNF
Received on Wed Jan 18 2006 - 16:29:57 PST

This archive was generated by hypermail 2.3.0 : Sat Sep 04 2010 - 09:44:55 PDT