Gunther Schadow wrote: (01)
> Dear Ingvar Johansson,
>
> it's been a pleasure to receive your paper. I have not fully digested
> it. (02)
Well, very nice for me to hear that you have at least taken a look at it.
However, I would like to make some comments and clarifications to the
second part of your mail. (03)
/---/ (04)
> Now I have more comments on your paper.
>
> 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".
>
> I do not agree. Counting and measuring are different. (05)
Two comments. (1) Primitive measuring IS counting. If you measure a
distance with a stick, you COUNT how many times you have to lay down the
stick in order to cover the whole distance. And similar remarks can be
made in relation to weighing and time measurement, too. (06)
(2) I claim that even non-primitive measuring have somewhere to rely on a
(what I call) 'count noun entity'. I claim in my paper that all the terms
for base units function the way so-called count nouns do (p. 10). (07)
> Count nouns are used with cardinal numbers.
> Measurement units are used with rational numbers.
>
> that's a big difference. (08)
I guess you mean 'natural' not 'cardinal' number. And since the natural
numbers make up a subset of the rational numbers, I think you overstate
the difference between counting and non-primitive measurement. (09)
> 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).
>
> Measuring is comparing the particular to be measured quantity with
> the reference standard, that is by division. (010)
Once again, what you say about 'division' is not true of measurements that
rely only on an interval scale. I would say that to measure a particular
of some kind is to give it a value on a scale with a standard unit.
Lengths are measured with a ratio scale, and 5m is five times 1m. But the
Celsius scale is an interval scale, and it makes no physical sense to say
that 5-degrees-C is five times 1-degree-C. (011)
> Hence your resulting
> number is a rational number (one divided by the other).
>
> 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. (012)
Here, I think you have misunderstood me a little; see below. (013)
> 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. (014)
I agree completely. I say in the paper that the SI people should become
more aware of the fact that they treat the mole (and only the mole!) as a
parameter base unit, i.e., they do not allow measurements that simply give
the value 'x mole', it has to be 'x mole of specified elementary entity'.
In other words, the SI system claims (with good reasons) that whereas it
makes good physical sense to compare the heights of different school
children, it does NOT make good physical sense to compare the amount of
substance of different elementary substances. It would be like saying that
'10 cars' is the same amount as '10 apples'. (015)
> 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? (016)
As far as I can see, my proposal to regard standard units for dimensions
such as 'length/length' and 'mass/mass' as parameter units does not
inflict on the kind of calculations you refer to. My (and several
others)point is that, for instance, 'arc length/radius length' (as a
measure of an angle) cannot in a physically meaningful sense be compared
with 'my height/your height' (as a measure of our relative length).
Nonetheless, out of both the dimension 'length/length' can be abstracted. (017)
Best, Ingvar J (018)
> regards,
> -Gunther
>
>
> --
> 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
>
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