# Re: Units, Dimension, Domain & playing nice with MathML

From: Walter T. Stephens <ceramist@worldnet.att.net>
Date: Wed, 21 Jul 1999 00:27:46 -0400
Message-ID: <006501bed331\$63549b60\$324b4c0c@thecomputer>
To: "Eisele, Fred" <fred.eisele@eds.com>, <www-math@w3.org>
```I advocate the first example because it only quantifies the mathematics
without trying to further describe the mathematical expression.

For example, I often calculate the Reynolds number for flowing gas streams.
The formula for the Reynolds number depends upon properties of the flowing
stream, which have definite quantities, but the Reynolds number itself is
dimensionless.  Understanding this fact allows the user to relate the result
of the mathematical calculation with a physical behavior of the flowing
stream.  If some properties of the flowing stream were expressed in
different units, one term using "inches" and another using "meters", then
the Reynolds number loses its physical meaning but the mathematical formula
is still correct.  Only the user knows that the quantity calculated is the
"Reynolds Number".  Any content evaluating engine is simply using
mathematical operators on some numerical values.  Units thus allow the user
to obtain some additional value while reducing the abstraction of the
mathematical expression.

By using namespace tags such as /position or /orientation, one requires the
MATHML expression to take upon a definite meaning.  For example, one might
define a tag called /force and apply it to a vector F indicating the
application of a force onto another object.  This is an issue of
qualification: how does an expression in MATHML render its definition beyond
its mathematical content? In other words, how does someone completely
express "Let X represent the position of an object in N dimensional space."?
MATHML can descibe X using a vector, but what determines that it is also a
position?

What we have is a discussion about two seperate but valid concerns.
Quantifying the expression and its terms establishes a physical relation to
a known frame of reference.  Qualifying an expression and its terms gives a
further description to the user and possibly the content evaluating engine.
I think both quantifying and qualifying the expression can be achieved by
including attribute values on the value or identifier tags.

"Let X be the position in meters of a particle in one dimension space" would
be <ci unit="meters", definition="position">X</ci>

The content evaluating engine can then make use of each attribute as needed
and the user only need use the identifier X as desired.  Any MATHML
expression that uses X also embeds the definition of X instead of requiring