# [time-nuts] Re: UTC - A Cautionary Tale

Mike S mikes at flatsurface.com
Mon Jul 18 09:23:32 EDT 2005

```At 08:34 AM 7/18/2005, Chris O'Byrne wrote...
>>>The kind of "simple arithmetic" that I was thinking about precludes
>>>the use of look-up tables.
>>
>> Yet you consider quadratic equations to be "simple arithmetic?"
>
>Simple arithmetic would give an order of magnitude better ESTIMATE. That
>ESTIMATE would not require the use of quadratic equations.

>My suggestion does not call for a "loosely defined" second - it calls for
>a variable second, PRECISELY tied to TAI. In other words,
>time = a + b*TAI + c*TAI^2, where a, b and c are fixed constants chosen in
>such a way that "time" follows UT in the long term, though drifts against
>it in the short term (the constant "a" would approximate the difference
>between UTC and TAI at the time of introduction, "b" would essentially be
>unity, and "c" would be quite small). All time systems would keep TAI
>internally, and convert it to "time" for presentation to the user as
>needed.

Which means either the interval calculation is based on TAI, and is exact, or it is an estimate based on solving quadratic equations. Since you very specifically referred to it as an estimate, it must be the latter.

>And, from the point of view of programming, quadratic equations are much
>easier to implement than look-up tables.

That depends entirely on the platform. That would not be the case on a microcontroller lacking hardware floating point.

> Not if you have mislaid the piece of paper that has the damn lookup table on it.

Myself, I would store such information in electronic form so it was directly accessible to the program, but suit yourself.

>Yes. Leap seconds are absurd enough, leap hours are 3,600 times more
>absurd!

You forgot to extrapolate that statement to leap days.

```