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From: Kevin Lynch (krlynch_at_[hidden])
Date: 2001-10-05 12:51:15

Jonathan H Lundquist wrote:
> > From: "Eric Ford" <eford_at_[hidden]>
> >> Quantities can be measured in bins, cartons, bags, etc., all of
> >> which are user-defined units of measure.
> >
> > These can all be considered pure numbers. You're counting something.
> > You could think of this in terms of qualified units as a number: a
> > pure number qualified by what you're counting (_of_bins or _of_bags)
> > and a second qualification for what's in them (_of_bins_of_apples or
> > _of_bags_of_oranges). In these cases I beleive you're more interested
> > in strong typeing for pure numbers than you are in a unit library.
> I think they have to be more than pure numbers, they're units of
> measure in that bins can be converted to cartons, etc. But the
> conversion factors do depend on the qualifiers.

I wouldn't have said "pure numbers" like Eric did, but I agree with what
he is saying. The quantities being measured here are "dimensionless"
and "unitless", and can decay into "pure numbers" in the appropriate
circumstances, but I would agree that they are not _currently_ pure
number. These things would be called "tags" on "pure numbers" in the
language I've been advocating, but not, I don't think, "units". (So I
realize that I've not defined my terms yet, but I'll get to it soon ...
really :-)

Consider the following question
, which should have a sensible answer: "How many cartons of apples and
bags of pears are in the warehouse?" The answer has units of "" (the
quantity is "unitless", a "pure number"), and you have constructed this
from a "tagged pure number" in the language I've been using, since the
"tags" "carton" and "bags" have decayed. But we didn't need to use unit
conversion here, like "1 meter/3.2 feet = 1"; that is under these
circumstances, "1 carton = 1". "carton" then is not a unit in my
terminology, but that _doesn't_ mean that you can't have a non-trivial
conversion factor. For example, "1 carton/27 apples = 1", so the two
"tags" are not equivalent, even if they can decay.

This is completely at odds with what we normally consider "units". The
following question should have a sensible answer: "How much pipe do we
have in the warehouse?", with an answer of "meters"; the meters can't go
away. If you ask the question "How much pipe and brake pads are in the
warehouse?" has the answer "200 meters of pipe and 27 brakepads"; in
this case, it never makes sense for the unit "meters" to decay. This is
not true of the "tags" used to label the "pure numbers" in our fruit
warehouse above.

That seems most consistent to me, although that may only be because I
haven't _found_ the error in my logic just yet.

Kevin Lynch				voice:	 (617) 353-6065
Physics Department			Fax: (617) 353-6062
Boston University			office:	 PRB-565
590 Commonwealth Ave.			e-mail:	 krlynch_at_[hidden]
Boston, MA 02215 USA

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