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Re: [uom-ontology-std] retitled: magnitude of a quantity

To: uom-ontology-std <uom-ontology-std@xxxxxxxxxxxxxxxx>
From: Ed Barkmeyer <edbark@xxxxxxxx>
Date: Tue, 14 Jul 2009 13:30:06 -0400
Message-id: <4A5CC09E.6090802@xxxxxxxx>
Geoff,    (01)

Thanks for this.  It came at exactly the right time to prevent me from 
further misleading David Leal and others, in a private exchange that 
touched on this.    (02)

Geoff Williams wrote:
> David Leal says
> 
> <Aside>
> Evan uses the term "quantity value" which is defined within the VIM. I have
> read the definition many times: "number and reference together expressing
> magnitude of a quantity". I think that this phrase should be read as follows:
> 
>   number_and_reference_together - expressing_magnitude_of - a_quantity
> 
> but it could be read as:
> 
>   number_and_reference_together - expressing - magnitude_of_a_quantity
> 
> Hence is the thing identified by (or "expressed by") 2.54 cm a "quantity" or
> a "magnitude_of_a_quantity"? Somebody must know, or is there a deliberate
> ambiguity. :)
> </Aside> >>>>>>>>>>>
> 
> 
> [GW]  ...
>  I am certain in my own mind that the term means "magnitude_of_a_quantity"
> not "quantity"    (03)

I have come to the same conclusion, from the same sources.    (04)

When the VIM speaks of 'particular quantity', it means a physical 
instance -- the quantity evidenced by a specific phenomenon, not the 
abstraction of that quantity.  The VIM thinks of particular quantities 
as the instances of 'quantity', whereas we commonly think of the 
abstractions that are expressed by quantity values as the instances of 
quantity.    (05)

I (now) think that the abstraction is what the VIM means by the 
'magnitude of a quantity'.  Carefully stated, we want to assert that '10 
metres' refers to an instance of quantity.  The VIM doesn't.  It says 
that the distance from my door to the stairs is an instance of quantity 
that has a magnitude that is expressed as '10 metres'.  That is, the VIM 
has three related concepts:
   quantity  -- magnitude of quantity -- quantity value
     many                  1                many    (06)

One instance of abstract 'magnitude of quantity' is the abstraction of 
many instances of quantity.  E.g., '10 metres' applies to many 
particular instances of distance, including the distance from my door to 
the stairs, and the height of the top diving platform at the local 
aquatic club.    (07)

One instance of abstract 'magnitude of quantity' can be expressed as 
many different instances of quantity value, each of which is 
distinguished by the 'measurement unit' it uses.  E.g., the magnitude 
that is expressed as '10 metres' can also be expressed as '1000 
centimetres', or as '32.8... feet' in English measure.    (08)

> In David's example the quantity is a length and the magnitude is 2.54 cm
> ie expressed as a number and reference (unit).    (09)

This is a bit garbled.  From what Geoff says above:
"2.54 cm" expresses a 'magnitude of a quantity'.  David did not in fact 
identify any particular instance of 'quantity'.  Every (particular) 
quantity that has that 'magnitude' must be an instance of 'length', 
which is a 'kind of quantity' (a subclass of 'quantity').  We know this, 
because the system-of-units being used (SI) assigns the 'measurement 
unit' denoted by "cm" to 'length'.    (010)

And 'measurement unit' is then a subclass of what the VIM calls 
'magnitude of quantity'.  It is an abstract reference amount that is 
defined by a particular quantity -- a reference phenomenon.    (011)

> I can seek clarification of this interpretation from JCGM/WG 2 if this is
> a contentious issue     (012)

Please do.  (And I will consult our NIST expert as well.)
To be fair, I think the VIM is a bit ambiguous in its use of the term 
'quantity'.  But what is important is that there are 4 distinct concepts:
  - particular quantity = a physical instance to be quantified
  - kind of quantity = a category of comparable particular quantities
  - magnitude of quantity = an abstract quantification of particular 
quantities
  - quantity value = the expression of a magnitude as a number and a 
measurement unit (where the number is the ratio of the magnitude to the 
unit)    (013)

And we can argue about which of those concepts gets the term 'quantity' 
in our ontology.    (014)

But we are hardly the first to tread this path, and I strongly suggest 
we begin by looking at the reference ontologies, including the OUM 
ontology to which Hajo Rijgersberg pointed us (his work).    (015)

-Ed    (016)


-- 
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    (017)

"The opinions expressed above do not reflect consensus of NIST,
  and have not been reviewed by any Government authority."    (018)

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