> Hi all,
>
> This is my first post to this conversation. As the creator / editor of the
> Unified Code for Units of Measure (http://unitsofmeasure.org), I am
> certainly
> interested in what this group comes up as a semantic construction of units
> of measures, but I can't monitor this thread so closely. (01)
Dear Gunther Schadow,
As you can see from the attached paper ("Exchange 'Amount of Substance'
for 'Number of Elementary Entities' and Delete 'Dimension One'"), I
sympathize with many of your views. However, I have some critical remarks
to your mail. (02)
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. (03)
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. (04)
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. (05)
Best, Ingvar J (06)
> However, a few
> things stick out at this time:
>
> 1. the construction of a unit as more than a representative quantity,
> e.g.,
> as a function that takes a length and maps it to a number,
>
> 2. the question of whether certain dimensionless measures (e.g., angular
> degrees) should have a dimension instead and the irrationality of the
> dimensional reductionism.
>
>
> Ad 1: WHAT IS A UNIT?
>
> When Peter Hayes suggests that the unit meter "denotes a function
> from lengths to numbers" would seem to say that any unit is defined as
> a function from its respective kind of quantity to numbers. But that would
> mean you contract the entire definition of measurement into the unit,
> for measurement is a function from the respective kind of quantity to
> measurement results which are numbers given a reference.
>
> That is too much.
>
> A unit is a reference standard for a measurement of a kind of quantity.
> As such it is a defined quantity. 1 meter is the length of <fill in the
> current agreed metrologic standard procedure>. That reference procedure
> may be a factor k times the length of an earth meridian, a particular
> stick stored in a museum, or a factor k times the wavelength of some
> monochromatic radiation. Interestingly, as these reference procedures are
> replaced over the decades and centuries, such replacement is made while
> keeping the unit invariant for all practical purposes. That is, the
> factor k is chosen to keep unchanged all measurement results expressed
> in meter. I.e., if a new reference procedure to realize the meter is
> introduced and if that new meter standard now requires anyone to convert
> their old results from old-meter to new-meter, then the new reference
> standard should be corrected.
>
> Therefore, one would conclude that a unit transcends any of its particular
> reference standard that are used at a time. A reference standard is
> merely a choice agreed upon for whatever pragmatic motivations, but the
> meter does not change.
>
> In the end, one should just define unit as a quantity in its respective
> dimension, abstract from the reference procedure, but at any time
> approximated as best we can by that procedure. A quantity is expressed
> as number times unit, because the unit has that which cancels out
> when we divide a to be measured quantity by the unit to leave only
> a number. 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.
>
>
> Ad 2: THE PROBLEM OF DIMENSIONAL REDUCTIONISM
>
> So what about dimensionless quantities and units which are
> defined as dimensionless by any particular system of quantities and
> units, such as the angular degree?
>
> One could very well say, and with procedure-defined units which we
> encounter a lot in medicine I have been forced to conclude that there
> is really an infinite set of dimensions. This is using "dimension"
> somewhat loosely meaning the class of quantities that can be converted
> into each other. In that sense,
>
> (i)
>
> wave length is in a different dimension from
> body height is in a different dimension from
> distance between celestial bodies
>
> and
>
> (ii)
>
> amount of carbon atoms is a different dimension from
> amount of glucose molecules,
>
> but
>
> mass of glucose molecules is convertible to
> amount of glucose molecules, hence is it the same dimension?
>
> and
>
> (iii)
>
> volume concentration of alcohol is in a different dimension from
> plane angle
>
> and so forth.
>
> In the (i) the length is used to determine entirely different quantities,
> and I cannot divide my body height over the radio station I've tuned into.
>
> In (ii) practitioners often feel the need to annotate units by the
> specific
> thing that is measured of fear that this information is cancelled out
> and lost. On the other hand, practitioners are often oblivious of the
> difference between amount-of-substance concentration vs. mass
> concentration
> for a particular substance, for you can just convert between them.
>
> In (iii) it is striking that we actually find plane angle in the same
> dimension as volume concentration of alcohol.
>
> Having to maintain UCUM and getting many comments and requests by
> practitioners, the most difficult thing is to tell people that their
> distinction does not matter hence it is reduced into the same dimension.
> And at the same time that their unit is not a unit because it cannot
> be reduced into any of the 7 dimensions.
>
> Clearly, the fact that there are fewer dimensions than kinds of
> quantity is because of a reductionist abstraction, by which we find
> that wave length and body height are "just lengths". And where
> frequency is "just" number over time. And where many procedure-defined
> units, such as "Bioequivalent Allergen Units" are just dimensionless
> numbers. It is odd that we try to rescue the dimensional identity of
> plane angle when not also rescuing the dimensional identity of
> "Allergen Units". What is the rationale for this? Over the 10 years
> that I have managed the UCUM system, I have today less a good answer
> than I had before.
>
> Fortunately even the hard physical science has seen a major change
> in system of base quantities and units, that from CGS to MKS, wherein
> the major change is not in these 3 letters but in the approach to
> measuring electromagnetic phenomena. This is something to study when
> making an ontology of units.
>
> In my view today, just as the meaning of a unit transcends the particular
> reference standard chosen for them at different times in history,
> the meaning of a quantity must transcend the particular reductionist
> construction in terms of base quantities and units, from which the
> dimensionality is determined.
>
> The choice of base system of units is entirely arbitrary for a base
> system of quantities. The choice of base system of quantities is
> somewhat arbitrary, but any such reductionist system seems never
> quite sufficient practically. For example, it is entirely irrational
> to me that there should be a dimension reserved for "luminous intensity"
> in the SI, when there is no dimension for "loudness" and no dimension
> for "allergenity". In fact it seems trivial to reduce luminous
> intensity to radiation energy flux (or something related), when it
> is actually very hard to capture "allergenity". Why should there
> be an exception made to photographers but none to allergologists and
> pharmacologists?
>
> The plane angle situation is similarly irrational.
>
> And the most irrational thing in the SI is the amount of substance
> being admitted as a base quantity. It's amazing if you think that
> it is clear to every elementary school kid today that matter is
> made up of little particles called atoms and molecules, 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.
> And that the mass of a block of matter is the sum of the mass of
> the particles that make up such matter. Yet, at the same time
> scientific society affords itself a dimension that means nothing
> more than "number of atoms or molecules". According to this system,
> the number of cars and number of people in them are dimensionless,
> but the number of carbon atoms and number of Amb-a-1 proteins are
> in a common special dimension.
>
> I think this ontology discussion should wrestle with some of these
> irrationalities and anomalies. It should construct its concepts
> so that they may help to explain what is going on here.
>
> In UCUM, the base is currently defined thus:
>
> * length - meter
> * elapsed time - second
> * mass - gram (not kilo-gram, because kilo-gram has a prefix)
> * charge - because elementary charge is the basis of
> electrical phenomena - coulomb as conventional unit
> * temperature - kelvin
> * candela - luminous intensity (just because the SI has it)
> * radian - plane angle
>
> So, you can see, the UCUM is an ongoing experiment to try to uphold
> a different base where amount of substance is just a dimensionless
> count of particles and plane angle is a dimension different from
> length.
>
> Over the past 10 years of running UCUM, there have been 99% of
> discussions about procedure-defined units which are no good units
> at all, and 1% (if that much) of discussion about the lack of
> amount of substance as a base unit. Recently we had to mark a
> large (and most rapidly growing) set of units in UCUM with a
> marker "arbitrary", i.e., defined by a special procedure so that
> there is no conversion relationship to any of the other units
> in the system. This is still an ongoing problem.
>
> When I monitor this ontology discussion, I am most interested to
> seeing how it will strive to align in its principles as much as
> possible with the VIM and metrology convention, yet be able to
> avoid its irrationalities and construct the concepts for kinds of
> quantities and units as transcending any particular historical
> choice of metrologic standard system.
>
> 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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> (07)
--
home page: http://hem.passagen.se/ijohansson/index.html (08)
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