[QUANTITY] The quandary

[David Barnes]

Arnold et al.,

first up let me say I wasn't at the meeting, so if I repeat
things already discussed please say so.

Ray's powerpoint proposes a Quantity as a value, an error and
a unit.  Arnold has extended and modified this to be a 
value+unit/s, error+unit/s, resolution+unit/s, size+unit/s,
and pixelsize+unit/s.  

I believe a Quantity is simply a value and a unit.  Nothing
more, nothing less.  The unit can be "null" if necessary, 
and the value may be a vector.  This is the AIPS++ way, and 
I hope that I don't put people off reading the rest of my 
comments because I've now mentioned the "AIPS++" word.

What Ray and even more so Arnold seem to me to be describing
is something like a "measurement", not a "quantity".  It is 
in the process of measurement that you introduce concepts 
like error, resolution, pixelsize - they are in general not
fundamental to the quantity itself.  

At this point, I wondered then if you simply renamed your
Quantity to be a Measurement, and then each of the fields
in your Measurement become Quantities like I have described
then we might agree.  However, there are two further properties
involved in measurements:

- the frame (eg. crucial for converting observed line frequencies
     to radial velocities)
- the sampling which is chosen by the user and is consistent with
     the instrumentation and processing (eg. the pixelsize concept)

AIPS++ deals with the frame by introducing its concept of a 
Measure.  An AIPS++ Measure is one or more Quantities and a
reference frame.  For example, a DirectionMeasure comprises
two Quantities with angular units, and a reference frame which 
might be "J2000" or "GALACTIC".  I personally don't prefer the
semantics here, and it might be more explicit to call something
like this a FramedQuantity.  If it were a truly measured thing
with associated error and/or resolution (for which an object 
doesn't exist in AIPS++) then I would call it a FramedMeasure.

Beyond this, I think the sampling is intrinsic to the way the
data is stored, and is generally independent of the resolution
and/or errors.  In fact isn't the sampling (pixelsize) a function
only of the CoordinateSystem, ie. the mapping of an ordered set
of values in storage to real world values?  So the sampling is
handled if you use FramedQuantities or FramedMeasures to define 
the location of eg. the centre of your image, and plain old 
Quantities (with units like arcsec/pix, MHz/pix) to define the 
pixel increments.

I'm not sure if the above will make much sense, but I basically
wanted to alert this group to the path AIPS++ has taken down
this route, and promote a simpler starting point for quantity
(just a value plus a unit) which can be built upon to derive 
measured things with errors, resolution, and reference frames.

Perhaps there is a good reason already discussed about why a 
quantity needs error, resolution, ..., but I haven't heard it.

If anyone is interested in the AIPS++ approach, you might like
to see the "quanta" and "measures" sections of the AIPS++ 
reference manual:

http://www.atnf.csiro.au/computing/software/aips++/weekly/docs/user/Refman/Refman.html

- David.