With respect to the Sowa/Johansson John F. Sowa debate, I am of two minds. (01)
I agree with Ingvar that the notions of measurement units that we have
are dependent on current science and have changed as the scientific
knowledge and measurement technologies have changed. (I would point out
that much of NIST's research is based on precisely that concern -- that
continuous improvement in measurement science and technology is
necessary for the industrial application of new scientific knowledge.)
The unit definitions become more precise and occasionally change basis.
The underlying concepts that make this possible without wrecking
50-year-old products and traditions are "uncertainty" and "tolerance". (02)
Uncertainty is the maximum possible difference between a measured value
and the actual value (which we cannot know). All measurement
technologies beget uncertainty. Improved measurement technologies
reduce the uncertainty over the previous technologies. This allows us
to define units more precisely, because we know that we can measure
things with uncertainty that is less than the precision of the definition. (03)
Tolerance is the rules we apply, whether legally or in our industrial
designs, as to what the uncertainty plus error is allowed to be without
infringing the value of the product. (Occasionally one sees ignorant
tolerance specifications that require variance less than the uncertainty
of the usual industrial measurement equipment.) (04)
So when we improve the precision of the unit and reduce the uncertainty
of measurements without changing the tolerance, business and industry go
on as usual. In effect, reducing the uncertainty just increases the
allowable margin of error within the same tolerance. But new products
may depend on the higher precision and demand much finer tolerances. (05)
OTOH, I would be very concerned about attempting to create an ontology
that addresses the "uncertainty" literature in any detail. You have
only to look at the BIPM publications (the VIM and the GUM) to
appreciate the magnitude of the problem. We need to address
uncertainty, and we should try to produce axioms that are correct in the
presence of a real theory of uncertainty, but I would prefer to leave
the real "uncertainty" ontology to experts that we haven't yet attracted. (06)
And "tolerances" should be entirely out of our scope. There is nothing
fundamental about tolerance; it is all business rules and engineering
design choices. (07)
So I agree with John that treating measurement units as constants,
whilst realizing that their definitions may change over time, is
probably what we want to do. To borrow another term, the "intention" of
the measurement unit does not change when its precision or its reference
phenomenon changes. I agree with Pat Cassidy:
> I think that for the UoM we can adopt the principle that the dimensions
> (time, distance, mass, temperature, etc.) that are standardized by the basic
> units are themselves "primitive" and logically undefinable, whose meanings
> and usage in programs are generally understood.
Being careful, that doesn't mean that the class 'measurement unit' or
the class 'base unit' don't have axiomatic formulations; it means that
those specific instances are primitive. But the class 'base unit' is
defined by a 'system of units' -- the population is defined
extensionally. "Base units are made, not born." (08)
John wrote:
> To be precise, the standards documents that include such definitions
> should clarify limit terms such as 'infinite', 'negligible', 'vacuum',
> and 'absolute zero'. They can be replaced by limiting statements:
>
> 1. 'infinite length' means a length that is sufficiently long that
> no further increase has a measurable effect.
>
> 2. 'negligible' means sufficiently small that no further decrease
> has a measurable effect.
>
> 3. 'vacuum' means sufficiently rarified that no further decrease
> has a measurable effect.
>
Yes. This is the intent, although the literature will show that the
intent is rather more complex than this, and has specific
interpretations of "measurable effect". In essence, it means that the
uncertainty becomes worse than the value. And in some cases the intent
is to define the unit as the asymptote of a curve that has a precise
mathematical formulation and can be specified to some effective
precision by measuring much more tractable points. (But what that means
is that the measurement technologies and the mathematics of the physical
theory do in fact affect the definitions of the measurement units.) (09)
John also wrote:
> To get back to the UoM topics: physicists (and ordinary people)
> use the same words and units of measurement for Newtonian mechanics
> and the many newer variants that were developed during the 20th
> century. However, the equations that relate those measurements
> have become more complex. That is why I would keep equations
> like F=ma or E=mc^2 out of the upper level ontology. I would
> put them in lower-level microtheories that could be invoked
> for solving particular problems.
>
> But note that the definition of 1 inch = 2.54 cm is independent
> of and holds for any version of physics. Therefore, it can go
> in a separate microtheory that can be combined with multiple
> theories of physics.
>
>
The problem with this view is that there is a fundamental difference
between E=mc^2 and F=ma: the joule is not defined by the first formula,
but the newton _is_ defined using the second. That is, the "base units"
can indeed be defined as if they were independent of physics, but the
definitions of _derived quantities_, and thus "derived units", do depend
to some extent on these mathematical formulations of physics. (Ingvar
started to say this, but never quite finished the thought.) (010)
It may be that the solution is to relegate the whole idea of "derived
units" to "microtheories", but if we do that, then we must formulate at
least the Newtonian one if our ontology is to be useful to any purpose. (011)
-Ed (012)
--
Edward J. Barkmeyer Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263 FAX: +1 301-975-4694 (013)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (014)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/uom-ontology-std/
Subscribe: mailto:uom-ontology-std-join@xxxxxxxxxxxxxxxx
Config/Unsubscribe: http://ontolog.cim3.net/mailman/listinfo/uom-ontology-std/
Shared Files: http://ontolog.cim3.net/file/work/UoM/
Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?UoM_Ontology_Standard (015)
|