# Dimensionless units

Martin Hill mch at roe.ac.uk
Fri Feb 18 04:51:44 PST 2005

```On Friday 18 February 2005 10:11 am, David Berry wrote:
> Alberto,
>
> > Sorry, but I don't really get the point.
> > Apples are apples, and bananas are bananas,
> > and the UCDs are clearly stating that those two things
> > are not of the same kind:
> >
> > Jy    ->  phot.fluxDens
> > Jy/sr ->  phot.fluxDens.sb
> >
> > Why would you want to use the units to discriminate between the two?
>
> That's ok if a UCD is always available, but if there are cases where you
> want to do unit conversions when no UCDs are available, then you need some
> way to distinguish "Jy/sr" from "Jy". <snip>

Noooo....  etc.  If we don't know what it's a measure of (ie we have no UCD
or other dictionary/ontology term or 'some other way') then we can only do
trivial unit conversions which share the same dimensions, ie we don't
distinguish between Jy/sr and Jy without some kind of metadata about the
likely to be for human consumption where a set of values are displayed in
units familiar to the user; Europeans might display velocity in m/s,
Americans in mph, and the British in feet per minute.

dictionary/ontology/UCD terms with our values and units, so that we can
describe an apple as an apple and a banana as a banana, no matter whether the
units we count them in are individuals, cartloads, buckets or clumps (a
banana-only unit that can only be averaged out to individual bananas using

> Also, if UCD's are available then why do we need a dimensional analysis
> at all since the UCD will imply the dimensions (we would still need the
> scaling factor though)?

Does *every* UCD imply a dimension?

Also, we often use 'some other way' to describe a value.  For example, a
parameter in a web service call might be described in some human readable
form (eg the RA/DEC of NVO cone searches) so that we understand what the
value is by its purpose.  We then know, and our software can be written to
interpret, that we have an 'angle' and can accept and convert between

So as Pedro says, our dimension-based unit conversions are independent of the
metadata and UCD/dictionary/ontology used to describe a value, and are only
used to convert between values that share the same dimension equation.

Where we do have metadata and dictionary/ontology terms, then our conversions
are based upon our knowledge of physics and those terms as well as their
units.  We may make use of dimension-based unit conversions as a part of
that, but we shouldn't be looking at dimension-based unit conversions to
solve the whole conversion problem.  We need to look at metadata- and
ontology- based converters for that.

For example, most UCDs are a mix of dictionary, incomplete metadata and
sometimes units, so we can use them to do rough conversions and comparisons.
IR band), and PHOT_FLUX_IR values can be compared and converted
(approximately) to PHOT_MAG_IR which also implies similar metadata.

Cheers

Martin

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

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