also, another "moment of force" reference from ISO/DIS 80000-1, "Quantities and
units" (01)
---snip----
3.9
measurement unit (02)
unit of measurement
unit (03)
real scalar quantity, defined and adopted by convention, with which any other
quantity of the same kind can be compared to express the ratio of the second
quantity to the first one as a number (04)
NOTES
1 — Measurement units are designated by conventionally assigned names and
symbols. (05)
2 — Measurement units of quantities of the same quantity dimension may be
designated by the same name and symbol even when the quantities are not of the
same kind. For example joule per kelvin and J/K are respectively the name and
symbol of both a measurement unit of heat capacity and a measurement unit of
entropy, which are generally not considered to be quantities of the same kind.
However, in some cases special measurement unit names are restricted to be used
with quantities of specific kind only. For example, the measurement unit
'second
to the power minus one' (1/s) is called hertz (Hz) when used for frequencies
and becquerel (Bq) when used for activities of radionuclides. As another
example, the joule (J) is used as a unit of energy, but never as a unit of
moment of force, i.e the newton metre (N · m). (06)
3 — Measurement units of quantities of dimension one are numbers. In some cases
these measurement units are given special names, e.g. radian, steradian, and
decibel, or are expressed by quotients such as millimole per mole equal to 10–3
and microgram per kilogram equal to 10–9. (07)
4 — For a given quantity, the short term “unit” is often combined with the
quantity name, such as “mass unit” or “unit of mass”. (08)
---snip---- (09)
Also recall that (010)
joule is NOT a coherent derived unit.
We also need to make use of the mapping Unit, which can map a quantity
(including non-SI units) to the set of "coherent derived units". We cannot
really say that joule = N.m, but we can say that Unit(joule)=N.m. We can also
say that Unit(torque)=Unit(energy).
The Unit mapping is referred to in section 3.2 and is represented using square
brackets. (011)
Joe C. (012)
ingvar_johansson wrote:
>> Thank you, Gunther, for providing some specific examples. We won't agree
>> on the
>> generalities and abstractions until we can agree on the specifics.
>>
>>> 1 N.m = 1 N.m : true or false?
>> So, suppose I have two software applications that need to communicate and
>> I want
>> 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?
>>
>> 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.
>>
>> 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.
>
> Here comes the only passage where the SI brochure mentions 'torque' (pp.
> 119-20):
>
> "In practice, with certain quantities, preference is given to the use of
> certain special unit names, or combinations of unit names, to facilitate
> the distinction between different quantities having the same dimension.
> When using this freedom, one may recall the process by which the quantity
> is defined. For example, the quantity torque may be thought of as the
> cross product of force and distance, suggesting the unit newton metre, or
> it may be thought of as energy per angle, suggesting the unit joule per
> radian."
>
> Ingvar
>
>
>> 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 I
>> 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 what
>> SI/VIM gives us to distinguish any otherwise indistinguishable units.
>>
>> 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.
>>
>>
>> As for the question
>>
>>> 1 m = 1.00 m : true or false?
>> A computer scientist would say: "True, to within floating point
>> precision".
>>
>> 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 the
>> assumption.
>>
>> To answer the question of equality one must have a definition of equality
>> within
>> 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 well).
>> The question is more like: "Are these measurements the same value to
>> within
>> measurement uncertainty?"
>>
>> 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
>> independent.
>> In practice, estimates are often not independent, and the degree of
>> dependence
>> is unknown.
>>
>> In this case,
>>> 1 m = 1.00 m : true or false?
>> 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.
>>
>> What is required to answer this question? A definition of one or more
>> acceptable
>> uncertainty representations and corresponding definitions of equality. The
>> definitions of uncertainty are standard, but definition of equality, I
>> don't
>> think that is standard.
>>
>>
>> Joe C.
>>
>>
>> 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".
>>>
>>> regards,
>>> -Gunther
>>>
>> --
>> _______________________________
>> 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
>> _______________________________
>>
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>
>
>
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> (013)
--
_______________________________
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
_______________________________ (014)
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