Indexes and units

[Tim Bergsma]

Peter,

Yes.  eml-unitDictionary uses "dimensionless" in exactly the way I'm
using "unitless".  I had forgotten that.  When eml-UnitDictionary went
to press, we were still vague about the difference between unitless and
dimensionless, but felt strongly that we didn't need both.  So to revise
my earlier statement...In the context of eml-unitDictionary, I would NOT
hesitate to call (certain) indexes dimensionless.  :)

Tim.

> Peter McCartney wrote:
> 
> Well, i meant "dimensionless" in the terms of our adopted schema
> STMML. i think their use equates to what you called "unitless?"
> 
> -----Original Message-----
> From: Tim Bergsma [mailto:tbergsma at kbs.msu.edu]
> Sent: Monday, June 16, 2003 7:52 AM
> To: Peter McCartney
> Cc: Eml-Dev (eml-dev at ecoinformatics.org)
> Subject: Re: Indexes and units
> 
> I would hesitate to call an index dimensionless, but it very well
> could
> be unitless.
> 
> For example, the shannon-wiener index is clearly a one-dimensional
> concept, whereas there might be some other index that rates diversity
> along two abstract "dimensions", e.g. separate values for richness and
> 
> eveness.  So dimensionality applies (if you can count them, they must
> exist).  However, to make units apply, I find myself starting to say
> things like "plot x has a diversity of 1.2 shannon-wieners", which is
> simply not how ecologists talk.  So it is quite possible for a
> quantity
> to have dimension but not units.
> 
> For better or for worse, metadata about dimensions is relegated to
> attribute descriptions; a rather informal solution relative to EML's
> precision-handling of units, but appropriate nonetheless.  To recap my
> 
> theory on this:  units are a formal subset of dimensions.  This
> becomes
> particularly relevant for attributes that have mixed models, such as
> feeding habits for gazelle.  Consider "Grams per day per animal".
> Grams
> and day are units, since they meet the NIST test:  "A unit is a
> particular physical quantity, defined and adopted by convention, with
> which other particular quantities of the same kind are compared to
> express their value."
> (http://physics.nist.gov/cuu/Units/introduction.html).  The concept
> "animal" is only a dimension, not a unit, since it does not meet the
> NIST test.  In this case, I would make "per animal" part of the
> attribute definition, and register grams per day as "the units".
> 
> The problem with indexes is that they are highly formal (unlike "per
> animal") and yet (potentially) dimensionless.  So I'm not able to
> express with precision the manner in which units are a subset of
> dimensions:  a simple appeal to formality doesn't do it.
> Nevertheless,
> the shannon-wiener index is not expressed in terms of something that
> passes the NIST test, so I'm advocating the postion that it is
> unitless.
> 
> Tim.
> 
> > Peter McCartney wrote:
> >
> > How are we currently recording indexes (for example, a vegetation
> > density index derived by a ratio of the values of two or more bands
> > within a RS image; or a diversity index such as shannon wiener where
> 
> > the value of H' is an abstract measure with little relation to a
> > measurable quantity)? Are these dimensionless?
> >
> > Peter McCartney (peter.mccartney at asu.edu)
> > Center for Environmental-Studies
> > Arizona State University
> >
> >
> 
> --
> Tim Bergsma
> LTER Information Manager
> W.K. Kellogg Biological Station
> Michigan State University
> Hickory Corners, MI   49060
> 269/671-2337
> tbergsma at kbs.msu.edu
> http://lter.kbs.msu.edu

-- 
Tim Bergsma
LTER Information Manager
W.K. Kellogg Biological Station
Michigan State University
Hickory Corners, MI   49060
269/671-2337
tbergsma at kbs.msu.edu
http://lter.kbs.msu.edu