Dear Ingvar Johansson, (01)
it's been a pleasure to receive your paper. I have not fully digested
it. (02)
"Dimension 1" is a misnomer. Think of a 3-d space, there are 3 dimensions:
width, height, depth. There is no such thing as a 4th "dimension" here.
Every point in this space can be reached by multiplying a number with a
unitary vector. That number itself is of no unit. It is merely an
abstract number. (03)
I haven't followed recently, but there was some proposal to add a unit
for "1", they even wanted to call it "u". It's a disaster if that were
to happen. (04)
The UCUM assumes a very simple view: every physical quantity is expressed
as a scalar value and a unit. The unit is constructed from a vector of
exponents of the base units in the unit system. Units, being nothing but
quantities conventionally picked and named, too are composed of scalar
number and the dimension vector. (05)
"Dimension 1" in this notion of dimension vector is the origin of the
coordinate system, i.e., all dimension vector components are zero.
Mathematically it is the neutral element of multiplication, i.e., 1.
Hence one can call it "dimension 1" but really it is not a dimension. (06)
I'm sorry your paper got rejected. SI people seem to be very protective
and seem to shy away from fundamental discussions. They worship the
principle of "coherence" and hence seem to have been unable to see that
by questioning amount of substance as a base unit you were not abolishing
mol as a unit. For us (because I share the view), 1 mol is just defined
as Avogadro's number. And since "coherence" has no value in itself in
my view (though the decimal system has), it is perfectly fine to keep
the mol and use it in the definition of other units. (07)
I think the Editor should have asked you to revise your paper and submit
it again. Something good would have come out of it. (08)
Other things you had pointed out:
> 1. You write: "A reference standard is merely a choice agreed upon for
> whatever pragmatic motivations, but the meter does not change." Yes, but
> this reference standard can only be chosen because - as a matter of fact,
> not pragmatic choice! - lenghts can be ordered in such a way that a ratio
> scale can be constructed. (09)
I didn't think I was precluding agreement with your statement about the
ordering of lengths. The pragmatic choice is to use this particular
length as a unit (Historically it is no accident that 1 yard is quite
close to 1 meter.) All the candidate units that could have been picked
also are all of the same kind of quantity, and hence share ordering and
scale type, etc. (010)
> 2. You write: "This ontology should not add or remove anything from this
> meaning of a unit: i.e., it must remain a quantity that can DIVIDE
> other quantities to yield a number, or multiplied with a number to yield a
> quantity." This is true only of the units of ratio scales, not the units
> of interval scales such as the Celsius and the Fahrenheit scale. They
> require TWO reference standards. In the Celsius case, '0 degrees C' is
> ascribed to the freezing of water, and '100 degrees C' is ascribed to the
> boiling of water. (011)
In the UCUM we have addressed all those other units. They are all
traced to their base unit but an arbitrary function is applied to
the values. This function pair (function and inverse) is provided
in addition to the base reference to define these units. (012)
> 3. You write: "and in middle school we learn that each kind of such
> particles has a mass which can be computed as the sum of the mass of its
> constituents." Not EACH kind of particle. Photons and neutrinos have no
> mass. (013)
responded to earlier ... "SUCH" is the operative word. (014)
Now I have more comments on your paper. (015)
I agree with your introduction of the count-noun subject. But later
you state: "First now to be noted is the fact that all metrological
units such as m ∙ m-1 and m3 ∙ m-2 are count noun entities". (016)
I do not agree. Counting and measuring are different. (017)
Count nouns are used with cardinal numbers.
Measurement units are used with rational numbers. (018)
that's a big difference. (019)
You could counter that you could have fractions of an entity, but
that to me violates the notion of "entity", i.e., a unitary thing.
Once you start cutting saussages, they seize to be entitic, because
a half saussage is not the same as a saussage (it cooks differently). (020)
Measuring is comparing the particular to be measured quantity with
the reference standard, that is by division. Hence your resulting
number is a rational number (one divided by the other). (021)
Regarding your proposal of parameter units, I have great reservations.
It is in essence what we are fighting against in the UCUM where
people want to leave annotations on units to retain a notion of the
kind of thing that was measured. (022)
One very important piece of any measurement is that it must be
stated WHAT has been measured. If that is stated, the unit no longer
has to retain this sort of detail. Only by abstraction can we compare
the heights of different school children. We benefit from not
retaining all this in the parameter. (023)
In some standards on measurements and units, a "numerator" and
"denominator" component is preserved. This is a bad idea in my
view, as it makes a special case of division. Raising measurements
to powers must be possible (as in computing kinetic energy from
velocity.) And retaining all those parameters would limit the
utility of using quantities in complex relations of invariances.
How could we use the invariance of energy to compute the velocity
needed to shoot a rocket to the moon if not by abstracting from
the parameters that go into the expression of velocity, and the
integral of the gravitational force across the distance through
the gravitational field. Can you do all that while retaining your
parameters on the units? (024)
regards,
-Gunther (025)
--
Gunther Schadow, M.D., Ph.D. gschadow@xxxxxxxxxxxxxxx
Associate Professor Indiana University School of Informatics
Regenstrief Institute, Inc. Indiana University School of Medicine
tel:1(317)423-5521 http://aurora.regenstrief.org (026)
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