# Dimensionless units

Pedro Osuna Pedro.Osuna at sciops.esa.int
Thu Feb 17 07:33:37 PST 2005

```Dear all,

the example case mentioned before about comparing Jy with Jy/sr, has to do with
point versus extended source information. Whether a
source is extended will have to be stated in the metadata, and if a
source is extended and the flux is given in Jy/sr, the solid angle
subtended by the observation under which the flux is being given
(basically the extension of the source, I guess) should appear there.
Then, clients would get this piece of information (from the SED data
model, for example) and handle it. There is no other way to compare Jy
with Jy/sr, as the second is a relative measurement (relative to a
certain area). This problem is inherent to the type of data, and not to
whether you use dimensional analysis or unit string parsing to make the
comparison.

On the other hand, in case one wanted to compare Jy/sr with
erg/cm^2/s/A/sr, the dimensional analysis machinery would work without
problem, and in this case the comparison would make sense.

We don't pretend dimensional analysis to remove the unit names, nor
We are not against people converting from, e.g.:

W/cm^2/um to erg/cm^2/s/Angstrom

using string parsing, but we prefer to use their dimensional equivalents:

1.E10 ML^-1T^-3  to  1.E7 ML^-1T^-3

which simplifies the conversion.

Cheers,
P.

On Thu, 2005-02-17 at 12:15, David Berry wrote:
> On Wed, 16 Feb 2005, Brian Thomas wrote:
>
> > Good point and true. There are such things as "dimensionless" units
> > (e.g. "angle" and "number of <thing>") which *do count* as
"dimensions".
> >
> > If you look carefully at systems of units, you will find (I think)
two
> > or so dimensionless dimensions exist (I may have missed a third..
Ed
> > might remember).
>
> Tables 5 and 6 in FITS WCS Paper I includes the following
dimensionless
> units:
>
> deg  (plus rad, arcmin, arcsec, mas)
> sr
> mag
> count (plus photon, ct, ph)
> pixel (plus pix)
> Sun
> chan
> bin
> voxel
> bit
> byte
> beam
>
> Obviously, not all of these are equally important (the top 3 in the
list
> are probably the most important), but it makes the point that almost
any
> noun could be used as a unit. A string parsing scheme has no problems
> with this, but I'm not sure how a dimensional analysis scheme would
handle
> it.
>
> David
--
Pedro Osuna Alcalaya

Software Engineer
Science Archive Team
European Space Astronomy Centre
(ESAC/ESA)
e-mail: Pedro.Osuna at esa.int
Tel + 34 91 8131314
---------------------------------
European Space Astronomy Centre
European Space Agency
P.O. Box 50727
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