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From: Kevin Lynch (krlynch_at_[hidden])
Date: 2001-10-04 14:41:07

wb_at_[hidden] wrote:

> | But, user defined quantities like "apples", "oranges", "fruits", etc
> | are important from the programming perspective.
> (5) I think that "apples" qualifies
> neither as a quantity nor as a unit, but I'm willing to be convinced
> to the contrary.
> (8) At the moment, I can't satisfactorily answer these questions, and
> hence I tentatively conclude that the concept of qualifiers is
> orthogonal to the concepts of quantities and units. Can someone argue
> otherwise?

I would agree that calling these things "qualifiers", "modifiers", or
"unit tags" is a probably a good terminology to use. One question you
could ask is, "What do they qualify?" I would argue that they qualify
the units, and not the physical quantities. I suggest looking at them
this way, since it then makes sense for the "modified units" to decay to
a less modified "base unit" under certain circumstances, but to "stick"
to their unit in other circumstances. Example time:

Consider a manufacturing plant that makes two types of pipe: copper pipe
and iron pipe. you measure the output of the plant in "meters of copper
pipe = mpc" and "meters of iron pipe = mpi". They take as input to
their process copper and iron, and these can be measured in "kg of
copper = kgc" and "kg of iron = kgi". The owner of the plant can ask
the following types of questions:
-> "How much pipe did we make last year?" The answer is Lc + Li which
would have units of "meters of pipe"; the outermost modifiers have
decayed away.
-> But if the owner asks the question "How much copper pipe did we make
last year?" and you tried to accidentally added Lc + Li, you should be
told that the units of the operands are incommensurate with the expected
units of the result.
-> "How much material did it take?" The answer is Mc + Mi which would
ahve units of "kg"
->But "How much copper did it take?" would again give an error if you
added Mc+Mi.
-> Consider "What is the linear mass density of copper pipe?" means
Mc/Lc which has units of "(kgc)/(mpc)" (truth in advertising: this
example is causing me conniptions, because I can't decide if the
"copper" modifier should cancel or decay or not)
->"How much is your pipe?" The result would be in dollar/(mpc)

In other words, if the result expects a certain "modified unit", the
expression should result in that modified unit; this is no different
than what you expect in other methods of considering units - you should
not be able to assign a result with units of area to an expression which
expects a length, for example.

So I don't think that "modifiers" are units or quantities, but they are
not actually orthogonal, either, because they are intimately connected,
and behave in many ways like, units. I think that this isn't such a
problematic issue, either, because we all attach these modifiers to the
units we use in our daily lives: How much does lettuce cost? 1.99 per
head. How much did I spend at the grocery store? $90 How much did I
spend on lettuce at the store? 1.99 per head x 2 heads (notice the
modifier on a dimensionless quantity!) = 3.98 (that truth in advertising
thing is a similar situation where the modifier clearly
DOES cancel. should they always cancel? probably....). The solution,
I think, is to treat the modifiers differently than units, but not THAT
differently, because they really aren't that different.

I hope that made some sense.... I feel like I'm grasping at straws here
to get ideas across that I feel like I intuitively understand.

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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