Please allow me to make the following comments: (01)
A dimension is not represented by a product of powers of base units, but
by product of base *dimensions*. And - although less clear to me but as
far as I can see - systems of units can have different base dimensions. (02)
Furthermore, let me emphasize that a dimension only *has* expressions in
terms of base dimensions of systems of units. It *is* not such an
expression as such. Many dimensions exist that have the same expressions
in terms of other dimenions. (03)
However, presently in OUM many dimensions are merged, but they still
*have* expressions in terms of base dimensions of systems of units.
Depending on the outcome of the discussion I am willing to distinguish
these dimensions again, like used to be the case in previuos versions of
OUM. It is an interesting on-going issue and discussion. (04)
Regards, Hajo (05)
-----Original Message-----
From: uom-ontology-std-bounces@xxxxxxxxxxxxxxxx
[mailto:uom-ontology-std-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Ed
Barkmeyer
Sent: 15 July 2009 21:34
To: uom-ontology-std
Subject: Re: [uom-ontology-std] retitled: magnitude of a quantity (06)
Rijgersberg, Hajo wrote:
> Please allow me to make a comment on dimensions and measures in OUM
> (from the forthcoming concept paper):
>
>
> Units of measure and quantities have a dimension. Dimensions are
> abstract properties of units and quantities neglecting their vectorial (07)
> or tensorial character and all numerical factors including their sign.
> Dimensions can be expressed as the products of powers of base
> quantities of a system of units. (08)
Being careful, this definition of "dimension" specifies what is ignored
in the representation of a "quantity (magnitude)". It doesn't say what
the abstraction _is_. (09)
One possible interpretation of "dimension" is 'quantity kind' -- the
nature of the quantity, the nature of the property being measured, such
as linear spatial displacement (length), or force distributed over a
spatial area (pressure). This is the way Pat Hayes used the word. (010)
The other interpretation is a relationship to 'base quantities'
(quantity kinds) from a 'system of units', which relates the nature of
the quantity to the natures other quantities. (The 'quantity kind' is
_not_ a relationship to base quantities; it acquires that relationship
when a system of units is chosen.) (011)
As Hajo says, this latter interpretation can be "represented by" a
formula that is a product of powers of base units, where each unit
represents a base quantity. But, because that formula is in "lowest
terms", a given units formula does not uniquely identify a dimension.
For example, torque and energy are different dimensions (in either
sense), but they have the same 'dimensional formula' in base units. And
obviously, each choice of a system of units will produce a different
formula. (012)
(The problem is that the nature of 'angle', for example, can be conveyed
by arc length / radius, but the two elements of the relationship are
both lengths, and in the units formula, the result is length to the
power 0. length/length and length^0 are different relationships.
Powers of units alone do not convey the relationships to the base
quantities.) (013)
> The above is mainly based on Cohen, E.R. and Giacomo, P. (1987):
> Symbols, units, nomenclature and fundamental constants in physics.
> 1987 revision. Document I.U.P.A.P.-25 (SUNAMCO 87-1). International
> Union of Pure and Applied Physics, SUNAMCO Commission. (014)
-Ed (015)
--
Edward J. Barkmeyer Email: edbark@xxxxxxxx
National Institute of Standards & Technology Manufacturing Systems
Integration Division
100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263 FAX: +1 301-975-4694 (016)
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