On Sep 3, 2010, at 1:04 AM, Ian Batten wrote:

> I have a clock ticking SI seconds at arbitrarily high precision and 
> resolution.

Examine your premises.  At some point in the past five years or so there was a 
thread discussing the distinction between clocks and timers.  I won't attempt 
to recover the subtleties of that thread at this time of night.  (Though I 
suppose the ITU would assert that my biorhythms are immaterial :-)

> How do I find out how many SI seconds I should count in order to count ten 
> UT1 seconds?  Can I determine that value prospectively, or only 
> retrospectively?


Suppose a timer to be a standalone source of ticking SI seconds.  A "clock" 
implies subjugating that timer to an external discipline such as mediated by 
NTP, for example.  Supplying a discipline from an ensemble of officially 
blessed atomic clocks is no better than applying a discipline from the wobbling 
Earth.  (The clocks may be more stable, but they are guaranteed to be shorter 
lived if nothing else :-)  In particular, constructing an ensemble timescale is 
as retrospective a task as measuring the meridian transit of fiducial stars in 
support of calculating UT1.

Here's an interesting preprint (http://arxiv.org/abs/1008.4686) with pertinence 
to the feasibility of fitting a model to data of putatively "arbitrarily high 
precision and resolution".

Rob
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