[LEAPSECS] Terminology question

[Michael Deckers]

    On 2010-03-10 17:54, Steve Allen wrote:


>  On Wed 2010-03-10T16:05:28 +0000, Michael Deckers hath writ:



>  >  On 2010-03-09 17:34, Zefram wrote:

>  >  >  Apparently not.  I'm inclined to use the phrase "faux linear time".

>  >  >  These timescales are really encodings of UTC-wise broken-down time, but

>  >  >  they sufficiently resembles a linear timescale that it's commonly mistaken

>  >  >  for one.  I think it's worth reminding people clearly of the reality.

>  >

>  >  Perhaps "piecewise linear" may also be appropriate -- it is a

>  >  common term in math. TAI - UTC (after 1972) may then be called

>  >  a "step function", which is a "piecewise constant" function.

>

>  Except that to say that any available form of UTC is linear

>  is to invalidate its use as a precision time scale.


   "piecewise linear" is not "linear" -- it is a mathematical way
   to say "faux linear". More precisely, it can express the fact
   that between any two successive leap second events (and also
   after the last such event), a POSIX time scale, and also UTC
   looks like a linear time scale. (Actually, the term would
   even apply to UTC before 1972.)

>

>  Read BIPM's Circular T.

>  http://www.bipm.org/jsp/en/TimeFtp.jsp?TypePub=scale

>  Follow the link to BIPM's TT(BIPM09)

>

>  Plot the numbers.  It's not linear.


    You are right in that "linear" requires a qualification, as
    in "linear function of ..". And so does "piecewise linear":
    UTC would be a piecewise linear function of TAI, and of
    TT(TAI), but not of TT, nor of TT(BIPM), TCB, TDB, UT1,...

    Some nice graphs with d(TAI - TT(BIPM)) are in
    [www.bipm.org/utils/common/documents/tai_2004/TAI-GP-4.pdf].

>

>  All precision time scales must employ empirical lookup tables.

>

>  Leap seconds are just one form of lookup table, and the total number

>  of table entries for UTC is smaller than for the other scales.


    Yes, the relationship between UTC and TAI is simple.
    I also suggest "piecewise linear" as a description of the
    relationship: there are intervals of TAI values on which
    UTC is linear in TAI, and arguably such intervals cover
    the range of all TAI values (except possibly during positive
    leap seconds).

>

>  If the question simply wants "generic" UTC, then from the formal

>  definition we can only expect a precision of 1 millisecond.  In that

>  case I could say "linear within the 1 ms precision of the formal

>  specification of UTC as defined by ITU-R TF.460", but according to

>  that as soon as a computer system clock deviates by more than 1 ms

>  it can no longer claim to be UTC.  In that case what is it?


    If I understand you correctly: my computer gives me UTC(my_computer)
    and I can convert that easily to TAI(my_computer), with the usual
    lookup table. The error and the uncertainty with respect to UTC
    and TAI are the same. I did not want to suggest that UTC(my_computer)
    was a linear function of UTC. It certainly isn't!

    I do not understand how the formal definition of UTC limits its
    precision to 1 ms. UTC can be determined with the same
    uncertainty as TAI.

>

>  This is the vocabulary issue which triggers me to answer "mu", for

>  many of the questions seem to want an answer which is far simpler

>  than required to describe (or even in denial of) reality.


    Hai, you are right, an easy term should not cover up a complex
    relationship.

    POSIX systems use different ways to represent UTC values around
    a positive leap second in a time_t value, and the details
    are not so easy to find out. In the few cases where I (thought I)
    understood the scheme, "piecewise linear function" of TAI was a
    valid description. Also, the time scale UTS proposed by Markus Kuhn
    for use in information and communication systems is a "piecewise
    linear" function of TAI in the exact mathematical sense
    (see [http://www.cl.cam.ac.uk/~mgk25/uts.txt]).

    Thank you for your detailed comments!

    Michael Deckers.