[UNITS] Re: Dimensionless units

[Brian Thomas]

 David,

On Thursday 17 February 2005 06:15 am, 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".
> >
> 
> 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

 Right, most of these are in the 'dimension' "number of <thing>".
 "pixel" is in the dimension "number of pixels" and so on. "sr" and 
 "degree" (and etc) belong to the dimension of "angle". Magnitude
 is an interesting case as it is, of course, 'dimensionless' being the
 log of a brightness and scaled relative to a reference source.

> 
> 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.

 For the purposes of dimensional analysis, all of these represent separate
 dimensions I would think, (with the exception of "bit" and "byte" which 
 surely belong to the same 'number of' dimension and differ by a scale factor 
 of '8'). There may be other connections that one may make between the 
 'noun' dimensions (as you refer to them) above, depending on the experiment
 (for example bin equivalent pixel in cases).

 So, at any rate, yes, the dimension "number of <thing>" is not one singular 
 dimension but a 'super class of a type of dimension' wherein each sub-class
 is orthogonal to one another (if properly designed...again I don't thing 'bit' 
 and 'byte' are in different 'dimensions') and <thing> is implicitly defined by
 the conditions under which the measurement was taken ('bin' in one experiment
 is not necessarily equivalent to 'bin' in another). 

 But its not so hopeless that we have to go out and select candidates from a 
 dictionary to build up a set of these 'noun' dimensions.  For the purposes 
 of the VO, I think we would be able to get by quite well with the list you just 
 included above.

 Regards,

 =b.t.


> 
> David
> 

-- 
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|                                     
| Dr. Brian Thomas                    
|                                     
| Dept of Astronomy                   
| University of Maryland-College Park 
|
| Phone: (301) 405-2312               
| Fax: (301) 314-9067                 
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