Re: ncdigest V1 #416

Harvey DAVIES (hld@dit.csiro.au)
Fri, 25 Jul 1997 15:28:48 +1000 (EST) 

In ncdigest Volume 01 : Number 416 (Thursday, 24 July 1997) I said:

> I am trying to think of a better example of an INTERVAL variable.  The above
> temperature example is confusing in that it is the unit which makes it
> INTERVAL, not the nature of the variable itself.  Perhaps a better example
> would be altitude measured relative to an arbitrary datum whose absolute
> altitude (height above standard sea-level) is unknown.

I have now thought of a much better example, which was so simple and obvious I
could not see it! It is simply time!  A natural origin for time would be the
time of the big-bang, but that is not known accurately enough to use it to
define absolute time.  (I suspect there may also be other difficulties due to
relativity, etc.) So we have to choose some arbitary datum (origin) such as
(a) 0000 hours on Jan 1st 1970 or (b) the birth of Jesus.

So absolute times expressed relative to such an arbitary datum are only
INTERVAL level measures.  

For example say I have a vector of years A.D. as follows:
1956 1900 1944 1997.
It makes sense to calculate the ARITHMETIC-mean as follows:
(1956 + 1900 + 1944 + 1997)/4 = 1949.25
But it is NOT legitimate to calculate a GEOMETIC-MEAN as follows:
(1956 * 1900 * 1944 * 1997)**(1/4) = 1948.94
This case may appear to give a reasonable result, but what if we
had a negative year (for B.C.) - the result would be complex!

Harvey

Harvey Davies, CSIRO Mathematical and Information Sciences,
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