# A plehtora of Quantities

Guy Rixon gtr at ast.cam.ac.uk
Fri May 14 04:07:52 PDT 2004

```OK, I guess I meant unit-less.  There are a few quantities which are naturally
dimensionless ratios but have other, perverse expressions:

- Angle: naturally a ratio of arc length to radius; if you measure both
lengths in the same unit, then the ratio doesn't need units; degrees of arc
are a perversion (and _so_ third-millennium-BC :) ).

- Probability: naturally a fraction from 0 to 1 inclusive; using percentage
is a perversion.

- Fraction of good pixels in an image: a ratio in the range 0 to 1 inclusive;
could be perverted to use a percentage.

- Albedo factor: again defined as a fraction from 0 to 1 but sometimes
perverted with percentages.

- Number of, say, CCD within a mosaic camera: no natural unit, but would take
a quasi-unit of "CCD" in Dave's scheme.

- Dimensionless physical constants like the fine-structure constant.

I agree that we have to use a unit for angle since there is so much historical
bad practice. However, inside the VObs, where the machines live, we could use
implied radians throughout and only translate to pervy units for display to
humans.

I suggest "count" and "ratio" for the others. I don't think that putting
quasi-units like "CCD" in a Q is going to work; better to write "count" and
infer the quasi-unit from context.

BTW: "pixel" is not a count but a length in arbitrary units.

Cheers,
Guy

On Fri, 14 May 2004, David Berry wrote:

> Guy,
>
> > What if the real-world quantity is dimensionless? Should we add 'nodims' or
> > something as a kind of quasi-unit?
>
> Do you mean dimension-less, or unit-less? Angle is dimension-less, but it
> has units (rad.s, deg.s etc). Numbers which count something are
> dimension-less, but they can be said to have units of the thing they are
> counting. E.g. the FITS standard for units (see FITS-WCS paper 1) includes
> units like "pixel". Can you think of a quantity which has no units in this
> sense?
>
> David
>
>
>
>
> >
> > On Thu, 13 May 2004, Alberto Micol wrote:
> >
> > > > Want a quantity with errors but no units?  Go right ahead.
> > >
> > >
> > > I think we should forbid such option, really!
> > > Of course, unless you can convince me of the contrary.
> > >
> > > Alberto
> > >
> > >
> > >
> >
> > Guy Rixon 				        gtr at ast.cam.ac.uk
> > Institute of Astronomy   	                Tel: +44-1223-337542
> >
>
> ----------------------------------------------------------------------
> Dr David S. Berry    (dsb at ast.man.ac.uk)
>
> STARLINK project		 |	Centre for Astrophysics
> (http://www.starlink.ac.uk/)	 |	University of Central Lancashire
> Rutherford Appleton Laboratory	 |	PRESTON
> DIDCOT				 |	United Kingdom
> United Kingdom			 |	PR1 2HE
> OX11 0QX                                Tel. 01772 893733
>                                              01257 273192
>

Guy Rixon 				        gtr at ast.cam.ac.uk
Institute of Astronomy   	                Tel: +44-1223-337542