Dimensionless units

[Martin Hill]

Units and dimensions are not ontologies (thank goodness!)

We don't expect the units to fully define what we're measuring, but they are 
an important part of that definition.  So, in this case, we don't expect um 
to tell us we have a wavelength, instead we know 'in some other way' that we 
have a wavelength value, and its units are in um.  

The equivelence between wavelength and frequency and energy in light, say, 
requires knowing that we are dealing with photons (the equivelence is 
different for waves in beer), so we can make use of the units to simplify the 
ontology; if we know 'in some other way' that we have photons, then the units 
can be length, time-1 or energy.

Similarly the difference between surface flux and observed flux need to be 
described, but is a problem for ontologies not units or dimensions.

Units and dimensions allow us to convert and compare things that we know 'in 
some other way' are the same. These need not be simple comparisons; Pedro has 
demonstrated that you can build an SED from dimension analysis, because you 
already know which values go on the 'brightness' axis and which go on the 
'wavelength' axis, even if the units are all different.

Cheers

Martin


On Thursday 17 February 2005 6:33 pm, Ed Shaya wrote:
> Pedro,
>
>     If you are given units of w/cm^2/um then there is no way for a
> computer to know that the um refers to wavelength.  A human can decide
> based on complex reasonable judgement and experiences but it is always
> just a guess.  If I have light emanating from  boxes that are 1 cm in
> height and width and 1 um in depth, then I have the right to express
> this as w/cm^2/um.  Note that this is dimensionally watts/volume.  In
> this case, we would not want a conversion to Janskys with the assumption
> that the um is a wavelength.  You need a system in which the physical
> objects within the units are revealed, such as Light Energy
> Flux/wavelength or Light Energy Flux/Frequency where Flux is already
> defined to be Quantity Flow/Area/Time.  This is to separate it from
> Quantity Change/Area/Time because you do not want to mix up quantity
> sources with quantity motion.   There is also possible confusion between
> Flux at the observer and Flux at the surface of the source, so area
> needs to be more specific.
>    Likewise with the problem of Jy/arcsec^2, this needs to be described
> as Light Energy Flux/Frequency/angle^2.
>     Now, maybe the idea is that the UCD or a more precise class of the
> quantity has this detailed description of what it is and then one
> proceeds to do conversions between two quantities of the same class.
> Any  automated tool will need to understand the class as described here
> to know how to go about a conversion.  After breaking things down to
> just dimensionality, some of the information needed to do the
> comparisons and numerical conversions is lost.  Dimensional analysis is
> what you do when you are ignoring amplitude and want a sanity check that
> unit agree.
>    Does anyone know the origin of the expression "Nothing is simple"?
>
> Ed

-- 
Martin Hill
Astrogrid/AVO, ROE
Tel: 07901 55 24 66