Thank you, Gunther, for providing some specific examples. We won't agree on the
generalities and abstractions until we can agree on the specifics. (01)
> 1 N.m = 1 N.m : true or false? (02)
So, suppose I have two software applications that need to communicate and I
to check if they would pass the same "type" of information to each other.
I check on both sides and I find that they will exchange something of type
"R x N.m" (outer product of a Real and N.m). Is this sufficient to believe that
they will be exchanging like quantities? (03)
The answer is "Maybe". If you don't like multi-valued logic and prefer to play
it safe, then the answer is "No", particularly in this case because torque and
energy are sufficiently closely related that they may be easily confused. (04)
The solution is then to use the additional mapping, "Kind", to distinguish
between torque and energy. (In my opinion, SI does NOT equate "N.m of torque"
with "N.m of energy", just N.m with N.m). In this case Kind(torque)=torque and
Kind(energy)=energy. To support type-checking, my type needs to be
"R x Unit x Kind", where Kind represents the set of possible values that that
mapping can return. The types are the same if the Unit part AND the Kind part
are the same.
Now when I check the types of data used by the two aforementioned applications
can distinguish between torque and energy.
Is this sufficient? I don't think we can say what is sufficient, just what is
safer and safe enough for now. It's definitely safer to use Kind and that's
SI/VIM gives us to distinguish any otherwise indistinguishable units. (05)
There's only one hitch: Kind is defined in SI (generally) with some examples
given, but the full range of values Kind can take is both *not specified* and
appears unbounded. I don't think this is too big a problem: we just need a list
of everyone's favorites. (06)
As for the question (07)
> 1 m = 1.00 m : true or false? (08)
A computer scientist would say: "True, to within floating point precision". (09)
A physical scientist would (verbosely) reason: The default assumption of
standard uncertainty tells me that
"1" means "1 +- 0.5" and
"1.00" means "1.00 +- .005".
Of course, this assumption is only valid if the definition of the set of
numerical values supports it. A physical scientist understands, however, that
values devoid of uncertainty are largely meaningless, and, so, proceeds with
To answer the question of equality one must have a definition of equality
the definition of uncertainty.
A problem with this question is that physical scientists don't usually ask it:
there is no standard definition of equality.
To define equality, one needs to go back to the meaning, which is that these
numbers are estimates (based on measurements and perhaps some calculation as
The question is more like: "Are these measurements the same value to within
measurement uncertainty?" (011)
Since the standard practice is to apply probabilistic reasoning under the
assumption that the quantity is a random variable with a normal (gaussian)
distribution, where the mean and standard deviation are given
("1" means "1 +- 0.5", etc.) the only way we can get a "Yes/No" answer is to
define an acceptance threshold to the overlap integral. An acceptance threshold
is a real number on the interval [0,1]. Having specified a threshold, and
finding that two values pass, we would say: "The measurements are the same to
within measurement uncertainty."
This usual practice has problems. It assumes that the estimates are
In practice, estimates are often not independent, and the degree of dependence
is unknown. (012)
In this case,
> 1 m = 1.00 m : true or false? (013)
I believe that the physical scientist and the computer scientist will often
agree, but they would do so for different reasons. It is the physical
scientist's reasoning that we must support. (014)
What is required to answer this question? A definition of one or more
uncertainty representations and corresponding definitions of equality. The
definitions of uncertainty are standard, but definition of equality, I don't
think that is standard. (015)
Joe C. (016)
Gunther Schadow wrote:
> ingvar_johansson wrote:
>> one more comment. You asked:
>>> 1 N.m = 1 N.m : true or false?
>> and I said 'true' (and so did Pat H). But this does not imply that 1 N.m
>> of energy = 1 N.m of moment of force, since energy and moment of force are
>> different kinds of quantities (despite having the same dimension).
> and that's precisely my point and why I disagree with Pat Hayes
> that this is not useful. I was asking if 1 N.m = 1 N.m and
> the answer is ambiguous. The unit is newton-meter, it is not
> newton-meter-of-energy, therefore, I would argue, that the unit
> is the same even if the kinds of quantity are different. Unless
> we agree on this (by either one of us changing our mind) I don't
> see a value at looking at ontological constructs.
> I don't want to discuss the N.m issue in particular at this
> time, only that it's pointless to proceed if there is
> disagreement about this matter.
> The question remains what we believe jointly that UoM concepts
> should do for us. You may want them to preserve the difference
> between torque and energy, I don't. So the question remains
> open on the list. But there is no point in proceeding if we
> don't agree on this. We might, however, agree if we use these
> example to be more clear about why we have the desire for the
> UoM concepts to do what we want them to do and possibly how
> else we might get our desires fulfilled.
> In my experience with dealing with scientific equations and
> computations, the units were incredibly useful for (a) converting
> to a unit that I needed and (b) giving assurance that I probably
> didn't make some gross error in my equations. Thus, in my
> experience with dimensioned terms it does not matter in the end
> whether the m in N.m, was the length of a lever or a distance
> of displacement, that is all in the concerns that led to my
> equations. The units function more like a check-digit at the
> end: if the unit term does not agree with the expected kind of
> quantity, something went wrong in my calculation or the formula.
> This is why around UCUM implementation I use the concept of
> a "DimensionedQuantity". A Quantity is any set of values
> where at least some values have a difference operation. A
> DimensionedQuantity is essentially a number with a dimension.
> Such a quantity for example is 16 N.m. Units are themselves
> DimensionedQuantities with a name (and the name can be complex
> such as N.m or even 16.N.m) So, my ontology behaves exactly
> like the symbols that I write on a sheet of blank paper when
> I compute my scientific equations. It does not do more nor
> less than what the units do on paper. I.e., 1 N.m = 1 N.m
> = 1 kg.m2.s-2 = 1 J.
> There is nothing you can do to separate these concepts unless
> by assuming into your theory the detail of all of mechanics
> (and all of science) which you can't do.
> BTW, it is not true that N.m of torque and joule of energy
> are completely unrelated. Because the torque times angle
> moved is again your energy. Whether or not we maintain a
> dimension for angle in UCUM is also besides this point. Of
> course: by adding more distinct dimensions we may be able
> to preserve more distinctions and by having less dimensions
> we lose distinctions that we can make by just looking at
> number and unit. But because I do not expect much more than
> the function of a "dimensional check digit" and defined
> conversion rates from the units, I can give or take a few
> dimensions without much trouble. The only place were I really
> get into trouble is where we haven't even started to discuss,
> i.e., idiosyncratic "procedure defined units".
Joseph B. Collins, Ph.D.
Code 5583, Adv. Info. Tech.
Naval Research Laboratory
Washington, DC 20375
(202) 767-1122 (fax)
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