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). (01)
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. (02)
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. (03)
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. (04)
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. (05)
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. (06)
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. (07)
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". (08)
regards,
-Gunther (09)
--
Gunther Schadow, M.D., Ph.D. gschadow@xxxxxxxxxxxxxxx
Associate Professor Indiana University School of Informatics
Regenstrief Institute, Inc. Indiana University School of Medicine
tel:1(317)423-5521 http://aurora.regenstrief.org (010)
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