Re: [LEAPSECS] The real problem with leap seconds
On 2006-01-10, Mark Calabretta wrote:
> I can't let this one pass - UTC is continuous and monotonic. In fact,
> ignoring differences in origin, UTC = TAI. Surprised? If so then
> you're confusing a quantity with its representation (though in good
> company in doing so).
I do not understand. As a function of TAI, UTC is neither continuous
nor monotone increasing in the mathematical sense.
In the defining document, [ITU-R TF.460-6], UTC is given as
UTC = TAI - DTAI
where DTAI is a step function of TAI assuming as values only integral
multiples of 1 s. Unless constant, such a function is not continuous
on a connected domain in the mathematical sense. Hence, UTC is not
a continuous function of TAI.
At some instant when TAI took a value in the positive leap second between
2006-01-01 + 00 h + 00 min + 32 s and 2006-01-01 + 00 h + 00 min + 33 s
(the exact instant is not clear from [ITU-R TF.460-6 2002]), DTAI jumped
from 32 s to 33 s; thus, UTC is not a monotone increasing function of
TAI either.
Perhaps you consider UTC as a function of something other than TAI where
it may well be continuous or monotone (eg, as a function of itself, UTC
trivially is both continuous and monotone).
Reference:
[ITU-R TF.460-6] "Recommendation ITU-R TF.460-6
Standard-frequency and time-signal
emissions". 2002 Geneva.
Michael Deckers
Received on Wed Jan 11 2006 - 02:47:56 PST
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