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Re: Semantic information for math representations of physics

From: JB Collins <joebmath@yahoo.com>
Date: Thu, 3 Feb 2005 04:20:17 -0800 (PST)
Message-ID: <20050203122017.8082.qmail@web31103.mail.mud.yahoo.com>
To: RobertM@dessci.com, www-math@w3.org

I am recently familiar with the <csymbol> construct.
As I understand it, it supports user extensibility. I
was also wondering how the process works (if there is
one) whereby some concepts become standard rather than
merely user extensions. I chose the delta function as
an example because it seems to be a purely
mathematical concept with general utility (and I need
it too!). Another capabilty I really need is support
for representing tensors, as metric spaces are a core
bit of mathematics required for physics. (As soon as I
want to use grad, div, curl in non-cartesian spaces, I
really need a metric tensor).

After extensive search, I haven't found much
"ready-to-use" from the physics-specific perspective.
I intend to change that. I believe I need to begin
with MathML and possibly OpenMath, since they are
web-based and provide a lot to build on. From time to
time, such as above, I would like to suggest additions
to MathML and/or OpenMath and would like to know how
to do that.

You mention some things about the relationship between
MathML and OpenMath, which I am interested to hear
more about. I am also recently familiar with OpenMath,
and have spent some hours at their website. (I wonder
if I shouldn't be cross-posting). While I am happy to
receive pointers on the specifics of those standards,
since I am relatively new to both, a significant part
of my participation in the www-math forum is to get a
handle on the philosophy to apply in deciding when I
should, for example, be using MathML and when I should
be using OpenMath constructs. Before you say "use them
interchangeably" let me cast my vote for a unified
standard, or at least a unified set of recommendations
to the user.

Please correct my perception: I see two standards that
are informally linked and promoted by two different
organizations. The cooperation appears to be due to an
overlap of goals and personnel, but is not otherwise
formalized. The result for me, as a user, is
consistency, but also a fair degree of redundancy and
some resulting confusion.
Those things being said, I am going to take your
response as guidance that says something like "when
concepts are defined in MathML, use them; when they
are not, for user extensibility, rely on OpenMath."

As an additional question to throw in, I am also
interested in knowing if MathML / OpenMath borrow or
cooperate with the MIZAR project. While I started this
thread on the MathML reflector, you pointed to
OpenMath and its use for interchanging documents for
theorem provers. The MIZAR project provides a similar
capability. While they seem primarily focused on
supporting mathematicians, there seems to be a lot to
borrow from.

I am a physicist/computer scientist, interested in
representing and supporting the validation of
physics-based numerical models generally, from the
conceptual, mathematical statements, encapsulated as a
coherent model, to the translation of that model so as
to incorporate mathematical approximations, and then
to the translation of an encapsulated, approximative
model to a discrete, numerical model. In the short
term, I think supporting documentation and user access
to physics-based models is a reasonable compromise.
Perhaps this answers your question about what I really
want to do, and that IS the more ambitious goal of
creating a web-based standard - most likely coupled to
the use of TeX/LaTex, the de facto standard for many
technical authors.

I am very interested in enrolling collaborators. Since
I see what I want to do as an application of MathML,
perhaps this (www-math) is an appropriate forum for
doing so.

Joe Collins
Naval Research Laboratory

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Received on Thursday, 3 February 2005 12:20:48 GMT

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