Dimensionless units

[David Berry]

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
adu
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