Dear Ed, (01)
Could you please specify GUM (a NIST pub, "Guide to Units and Measurement, or
something?). (02)
To quote your signature message
"We must strive to make things as simple as possible, but no simpler."
- Albert Einstein (03)
In this case, regarding uncertainty, the question is, what complexity is
necessary? As you point out, a theory of uncertainty supporting some reasoning
capability could take significant work, but simply capturing expressions of
uncertainty is easier. The two most significant expressions that come to mind
are the interval and standard deviation. These meanings are pretty common; even
universal. (04)
> But the grocer's scale reads 1.0, 1.1, etc. and the needle is between 1.0 and
> 1.1. What does that mean? Is it OK if he presumes that it is accurate
> enough to satisfy both of you that he is honestly selling you 1 kg? Once you
> start adding 'uncertainty' ideas, we bring in the question of when the scale
> was last calibrated. Neither of you wants to think about that. (05)
In this case, the grocer will often say "It's between 1.0 and 1.1, is that OK?".
At my grocer's, the weights and measures calibration date is affixed to the
scale (by law in many locales). While I may not examine that sticker when
buying
lettuce, you I certainly may when buying truffles. (06)
> (4) We don't want to confuse tolerance with uncertainty in the model. A
> specified quantity value has tolerance (and usually ignores uncertainty,
> sometimes with serious consequences); a measured quantity value has only
> uncertainty. An abstract ideal 'quantity magnitude' has neither. It is the
> use or source of the quantity value that acquires the tolerance or
> uncertainty property. (07)
I agree we shouldn't confuse tolerance with uncertainty. (08)
Like functions that are non-computable, the "true" value of a physical quantity
is non-measurable and therefore not knowable. We only know the values of
quantities by measurement and we always measure to some limited precision.
Tolerances, also, are always non-zero. The source (via measurement) or use
(e.g., tolerance) are the sources of any knowledge we have on physical
quantities: we don't really know any more about "true" or "ideal" values. I
don't see how to relegate the representation of uncertainty to a microtheory:
it
is an essential part of the thing we claim to be knowledge. I'm not convinced
that the interpretation is necessarily specialized, either. (09)
If as you assert:
> If we go only one
> step down that path, we will have a model that has a nearly undefined slot
> for "uncertainty", which means that any two uses of it are likely to be
> semantically incomparable. If we go further, it will take a few years to get
> a correct ontology in the area. (010)
I think the more important questions are "Must it be done?" and "Can it be
done?" rather than "How long will it take?". (011)
My answers are "Yes", "Probably", and "I don't know", respectively (012)
> Yes, in the abstract, 'uncertainty' is well-defined. It is the expression of
> uncertainty that is interesting. Presumably we would include the concept so
> that uncertainties can be expressed. Would you be happy with a
> 'quantity-value has-uncertainty simple-quantity-value' property (with the
> basic SI definition = the maximum amount by which 'quantity-value' may differ
> from the actual value)? What about conditions, e.g. "at standard temperature
> and pressure"? (013)
So, when is something completely unambiguous? Almost never.
How much qualification is enough? As much as it takes for the user to be happy.
Does the user always specify what it takes to make him happy? No.
I think that an expression of uncertainty is a first level of qualification. (014)
So, my wife hands me a grocery list. It says "milk, bread, eggs". Suffice it to
say that my wife is not easily trained to my expectations: she never specifies
amounts, let alone a range of acceptable quantities. I do like to keep her
happy, though, and, as important, I don't want to have to repeat the shopping
trip daily.
I have learned that, having 3 kids, a quart of milk is insufficient, and ten
gallons is excessive. I've even narrowed it down better than that. Perhaps she
has trained me to her expectations. (015)
I am happy to report, however, that, even after untold man-years of effort,
computers are dumber than I am (stay tuned?).
I'm pretty sure that if computers are ever able to deliver on such a request,
then to keep my wife happy they will have to have a rudimentary capability to
process uncertainty. Until they can, I still am useful. Perhaps I am trying to
put myself out of a job? (016)
R/jbc (017)
--
_______________________________
Joseph B. Collins, Ph.D.
Code 5583, Adv. Info. Tech.
Naval Research Laboratory
Washington, DC 20375
(202) 404-7041
(202) 767-1122 (fax)
B34, R221C
_______________________________ (018)
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