Units, Dimension, Domain & playing nice with MathML (fwd)

[Andreas Strotmann]

This thread appeared in the www-math mailing list the other day.  Since
this is about extending MathML, and OpenMath is a/the designated extension
mechanism for MathML, but also because this particular topic did come up
in some discussions during the Eindhoven workshop, I'm taking the liberty
of forwarding the message to om at openmath.org.

 --  Andreas

PS: my apologies to those of us who are on both mailing lists.

---------- Forwarded message ----------
Date: Fri, 9 Jul 1999 16:35:42 -0400 
From: "Eisele, Fred" <fred.eisele at eds.com>
To: www-math at w3.org
Subject: Units, Dimension, Domain & playing nice with MathML
Resent-Date: Fri, 9 Jul 1999 16:36:33 -0400 (EDT)
Resent-From: www-math at w3.org

 
Caveat: I will use the term "I" to mean either myself or someone I have
worked with
         (but all the errors are, of course, mine ;-)
 
Goal:  I want a "good" way to associate dimension (length, time, stress,
orientation, interval)
         and an appropriate unit (meter, second, psi, ?, pico-second) with a
quantitative measure.
 
Background:  I develop computer aided engineering (CAE) systems in the
domains of 
         fluid dynamics, heat transfer, noise, vibration, fatigue.  I have
developed many
         proprietary (and brittle) document types over the years.  I wish to
do away with
         as much of this as possible.  To this end I have been working on
some domain
         specific document type definitions.  It have become apparent to me
(and obvious 
         to you) that most of the elements that I have defined are modeled
using some
         mathematical construct.  Nonetheless, the elements are certainly
not 
         mathematical objects.  So, while I see clear benefit in making use
of MathML;
         it is also clear that domain specific elements are required.
 
Proposal:  I propose hat we start a thread to discuss the nature of the
interaction between a
         new domain (tentatively represented by a namespace) and the
existing MathML
         domain (I presume you will have a namespace (MathML?)).  I would
further propose
         that this initial domain be Newtonian physics (most of what I am
working on
         is based on this domain).  I couldn't find a physicsML.
         The principle dimensions could therefore be:
         - mass:        kg, slug, lb., carat, ...
         - distance:   meter, foot, parsec, angstrom
         - time:         second, millennium, day
         - force:        Newton, lbf
         - energy:     erg, watt
         - temperature:  Kelvin, degree Fahrenheit
         It may also be necessary to treat geometry first, in particular the
dimension:
         - angle:        radian, degree, 
         - 3d-orientation:  ?
 
Argument[1]:  It has been proposed in the past that a domain could be
comprehended
         simply by including the units along with a quantity.  
             e.g.   <cn> 5 * days </cn>   or   <cn unit="day"> 5 </cn>
Response[1]: There is no association with a domain.
          There is no indication of the dimension.  It may be argued that
the dimension is
          inferred by the unit but this is not so.  e.g. Kelvin may be
either an absolute 
          temperature or a temperature range.  It may be tempting to include
the 
          dimension as well as the unit.
             e.g.  <cn> 5 * pico-second(distance)</cn>
          But, creating such a (hard to parse) beast when all the XML tools
are at hand
          seems silly.  
 
Argument[2]:  I can represent most of these things as mathematical objects
especially
          things like angle (which can be expressed as a complex number of
magnitude 1),
          or orientation which doesn't even have a proper unit and is
typically indicated
          by a direction cosine which is just a 3x3 matrix.
Response[2]:  Just because something can be represented as a complex number
          does not mean it is a complex number; granted an element named
"force" isn't
          really a force either but ...
 
Argument[N]: ?
 
Note: In the following samples I will show the name spaces but they could be
omitted.
         (Go ahead rip them apart.)
 
Sample[1]:  length is a dimension & belongs to a new namespace but unit is
not.
          <physic:length><mathML:ci> x
<mathML:unit>meter</mathML:unit></physic:length> 
 
Sample[2]:  position is a dimension and the unit attribute is part of an
archetype
         <physic:position unit="meter"
type="mathML:vector"><ci>5</ci><ci>6.7</ci>-5.2</ci><physic:position>
         This representation includes a type which indicates a MathML
element.
 
Sample[3]: From the namespace recommendation < http://www.w3.org/TR/
<http://www.w3.org/TR/> REC-xml-names>sec.4
         
<x xmlns:edi='http://ecommerce.org/schema'>
  <!-- the 'price' element's namespace is  http://ecommerce.org/schema
<http://ecommerce.org/schema>  -->
  <edi:price units='Euro'>32.18</edi:price>
</x>	
         
 
Sample[4]:  Basically, this one doesn't work but maybe the germ of an idea.
    <apply>
        <dimension type="physic:length" unit="foot">meter</dimension>
        <ci> x </ci>
        <cn> 5 </cn>
        <vector><ci>5</ci><ci>6.7</ci>-5.2</ci></vector>
    </apply>