>>> I take a third way: I am agnostic on 'true' values.
>>> Why do we need such an hypothesis, anyway?
>>
>> Because communication is virtually impossible without this hypothesis,
>> and because it underlies virtually all of science. Equations like e=mc2
>> do not refer to measured values with tolerance ranges and probabilities
>> of error, they refer to mass and energy. That these quantities can only
>> be measured to a certain degree of accuracy is true, but irrelevant to
>> what the equations say. DIfferential equations, in fact, only make sense
>> when the reality they purport to describe is assumed to have
>> differentiable fields in it, which are *inherently* unmeasurable with
>> complete precision. Still, people do use the equations to make predictions. (01)
And "garbage in, garbage out" will apply.
The notation of physics, such as e=mc2, looks good on a marquee, but is
notoriously terse.
There is no specification of dimensions and units, either: does that mean they
are unnecessary to specify?
Anyone who has tried to apply e=mc2 to a real-world problem will tell you that
"of course you must account for the uncertainty..." (02)
>>> In a model, any numerical value you bind to the quantity, Q, that
>>> suggests that that value is the unique, true value of the object in
>>> physical reality that Q refers to, is a lie. You can only bind a
>>> received value to Q, and those values are ultimately received through
>>> some form of measurement process.
>>
>> This is a philosophical position, but (with respect) you are not making
>> a very good philosophical argument in its defense. Rather then engage in
>> this debate, which I don't have the energy for, all I can say is, your
>> view is the minority, and ontology-writiing simply isn't workable
>> without basing it on a more realist perspective. (03)
I think we disagree on what a realist is. (04)
The philosophical perspective I am defending is close to what I believe the
metrologists that authored the SI & VIM had in mind.
I took it that the SI & VIM should serve as a basis for a UoM ontology.
Without much justification you are picking and choosing what may be ignored
from
that standard. I am defending the position that uncertainty is an essential
part
of the standard. (05)
>>> It seems you are saying that the model we create has more importance
>>> than the knowledge that proves the validity of the model.
>>>
>>> I believe it is antithetical to a scientific perspective to accord
>>> more importance to any single model of reality than to our measurement
>>> data upon which the models rest.
>>
>> Fair enough. I disagree (and I suspect most scientists would), but I'm
>> happy for you to believe that Im not a scientist. We aren't doing
>> science in this forum, we are building an ontology. (06)
If you are building models that can be validated, then, in my mind you are
doing
science. This encompasses applied science (engineering) as well. Application of
the scientific method is not so esoteric as you make it sound: it is essential
to sound engineering practice. (07)
If you are building models with no intent to validate them or that cannot be
validated, then you are not doing science or engineering. (08)
The only validation you can perform in your ontology without expressing
uncertainty is strict equality. You'll have no other notion of closeness or
close enough. In any practical sense this means that your model can never be
validated: you will almost never see values exactly equal to what you predict,
and you'll have no idea how far off your model is in its predictive capability. (09)
What use is there for a model that cannot be validated? (010)
>>> Earlier on this reflector the case of the problematic concept of
>>> "boiling temperature of water" was pointed out. You may have a nice
>>> model/theory of phase transitions, but since a (unique) boiling
>>> temperature can be difficult to measure, reality shows itself to be
>>> messier than the model. We cannot just assert in the face of the
>>> evidence that there is a true boiling temperature.
>>
>> Actually, yes we can. And people do, and the business of the world
>> depends on such assertions. Not every user of units is a scientist with
>> a non-realist metaphysics. (011)
Ouch! Have you just thrown me into a philosophical dungeon? (012)
This reminds me of Feynman's description of cargo cult science.
If you build a model with no expectation of being able to validate it, your
activity is on a par with that of a cargo cult practitioner.
Ineffective as the activity may be, plenty of people may still do it, but
that's
not a valid argument to join the crowd. (013)
>> They are when they ignore questions of how quantities are measured,
>> accuracy, etc., and simply refer to values, which they often do. The
>> weight of my car is given in kilos. It does not come with an error
>> estimate or a tolerance interval: it is expressed simply as a numeral.
>> Now, this numeral, when used in an ontology, must refer to something.
>> What is certainly *seems* to refer to is a weight, specified using a
>> scale calibrated in kilograms. An *actual* weight, *the* weight of my
>> car. If there is no such thing as the actual weight, then I cannot refer
>> to it, and must use some other way to specify what '5647 kilos' means.
>> So, what, in your view, are we to say about such language? That is is
>> simply wrong, and should be rejected? Or that it is an abbreviation of a
>> much more complicated assertion not about actual weights at all, but
>> rather about measurements of weight, perhaps referring to the apparatus
>> that was used to measure the weight of my car? (But what if there is no
>> such apparatus, and the weight has been calculated in some way rather
>> than measured? Is it then no longer a weight, but only a
>> pure-mathematical entailment?) Or that a tolerance interval must exist,
>> even if we do not know what it is, so this must be expressed as an
>> existential claim about an unknown tolerance interval? (But that could
>> be any interval: surely we want to say more about it, perhaps that is a
>> 'reasonable' such tolerance interval for things of this kind - so we
>> need to talk about what kind of thing the car is, and have an
>> overarching ontology of reasonableness of measurements for certain
>> purposes...) But all I wanted to say, and all that the shipping company
>> needed to know, was how much my car weighs, expressed in kilos.
>>
>> There is a deeper argument, in any case. Take a tolerance interval as an
>> example. You want to say that 4.0 'really' refers to the interval [3.95,
>> 4.05] , because exact quantities may not even exist. But that interval
>> expression itself uses exact quantities, viz. 3.95 and 4.05. Indeed,
>> given your rules here, these are more exact than the original, having
>> two decimal places: so each of these must really be an interval: 3.95 is
>> [3.945, 3.955]. And that in turn is [[3.9445 3.9455] [3.9545 3.9555]]
>> And so on ad infinitum. Now, one can indeed make mathematical sense of
>> these infinite nested-interval structures, but its a lot more
>> complicated than the authors of the SI system had in mind, I am willing
>> to bet. The point being that at some point in this descent, we usually
>> want to just toss in the towel and say, OK, I'm referring *exactly*
>> here, just using a numeral to refer to an *actual number*, a *point* on
>> the rational continuum. And if we can do that anywhere, then we can do
>> it right at the beginning. (014)
It seems to me that you ignore the details of how any knowledge of quantities
would actually be used.
The values of quantities will be used to make decisions.
If, for example, I am receiving widgets that the shipping list specifies as
weighing 10 grams, what do I do with that information? If I merely acknowledge
the receipt of the information, it is of little use. On the other hand, if I
use
that information to make a decision, then I must compare it to something.
Let's say that I weigh three received widgets and I find that they weigh 12,
11,
and 9 grams. As a receiving clerk, the only idea I have if these are acceptable
is if they are what is specified on the shipping list. I compare those weights
to what is on the shipping list. Shall I send them back to the manufacturer?
Since in your ontology only strict equality can be used, they are clearly not
what is on the shipping list, and an error must have been made, so back they
go.
If instead I have a range of acceptable weights, and a range of received
weights, then there's a much greater likelihood that some or all of the widgets
would be acceptable.
Your ontology can only work with integer quantities and measurement instruments
calibrated in integers. A difference in weights having value one means the
widgets are not the widgets you ordered. The scales used must be engineered
specifically for widgets (since weights in general do not really occur in
integer gram increments). Now you'll also need a different scale for the next
shipment, because it contains gadgets, and its shipping list specifies them to
weigh 5000 milligrams. (015)
In short, without an ability to express uncertainty, the information you pass
describing quantities will not be practical for any actual use. (016)
R/jbc
--
_______________________________
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
_______________________________ (017)
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