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From: George A. Heintzelman (georgeh_at_[hidden])
Date: 2001-10-05 13:56:12

Kevin Lynch wrote:
> "George A. Heintzelman" wrote:
> > I disagree. If we develop tags, then I think these things have an SI
> > unit of Amount<>, which can be measured in units of moles, or
> > individual items. Anything can be measured in this units, not just the
> > atoms and molecules of chemistry.
> >
> > And as is very natural with other types of SI unit Amount<>, the
> > conversion factors are important. Treating it this way may make some of
> > these things clearer.
> Alright, I might be able to buy that argument. Like I said, I'm not
> sure what I'm missing just yet, and this may be one of those things.
> Just to make sure that I understand, you're saying that "number of
> things" has is a quantity of type Amount<>, and the unit here is "number
> of cartons". So it is not "unitless", but Amount<> is still
> "dimensionless" since it is a counting "unit".

No. Amount<> is not dimensionless. The seven SI dimensions are Length,
Duration, Mass, Temperature, Luminous Intensity, Electric Current, and
Amount of Substance. I think these -- what I will call 'inventory
quantities' -- are aspects of Amount of Substance. Using inventory
quantities is really no different from counting atoms in chemistry, it
is just that the 'molecules' in use are really big and not as uniform.

The way to see that these inventory quantities are not dimensionless is
that it is completely senseless to take sin(number_of_cartons). Or to
make something exponential in the number of cartons (without dividing
by a number of cartons to set a scale).

Angles, binomial coefficients, and such are examples of truly
dimensionless numbers. I still think something needs to address the
difference between an angle and other dimensionless units, but that's a
different question.

George Heintzelman

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