The misunderstanding of MathML (Re: The disappointment and embarrasment of MathML)

To all readers of the message below, I would like to refute several of the
arguments put forward there.

 - "MathML reinvents the wheel"

   truth is that pretty much all existing CA system languages have been
   seriously deficient with respect to fundamental design principles
   for content markup languages[1]. OpenMath and MathML are the first to
   fix at least some of the most problematic of those errors.

 - copyrighting the language of maths.

   as anybody in the CA field can tell you, it is extremely ironic to
   put forward Mathematica as an example for a language that cannot 
   be copyrighted.  Indeed, the infamous mma/mockmma incident a few 
   years back (where a well-known researcher was told off by Wolfram 
   lawyers for using Mathematica's proprietary syntax for his own 
   CA system and algorithm design environment) is an immediate
   refutation, and a direct argument for the need(!!!) for
   an open(!!!) language.  Experience has shown that copyleft is a
   necessary ingredient in maintaining openness.

 - "the MathML group didn't deal with the makers of Mathematica (or
   Maple)"

   oh yes they did, even as far back as the beginnings of the OpenMath
   project that provided many of the MathML researchers responsible for
   Content-MathML.  Collaborators have included people with close ties
   with: Maple (Gonnet, who initiated the OpenMath project), Mathematica
   (several developers are members of the MathML WG), Axiom (Sutor),
   REDUCE (myself, Neun, and others)...

It should be noted also that the very idea of OpenMath (and
Content-MathML) is
  - to get away from the babel of CA languages, and define a language
    all can agree on
  - to get away from the unnecessary details that some of them need
    for operational purposes (e.g. Axiom's very detailed type system,
    or the distinction between int and Int in Maple)
  - to get away from an operational view of maths and towards a 
    declarative one
  - to go beyond Computer Algebra and into the rest of mathematics


The message is furthermore rife with misunderstandings of the concepts
employed in the definition of MathML and their relation to concepts in
Computer Algebra languages.  Most fundamentally, the distinction between a
declarative semantics of MathML and the operational semantics of a
Computer Algebra system's user language is completely ignored (see e.g.
the introductory chapter on the design decidions for the KIF (knowledge
interchange format) language -- "why not LISP").  At another place, it
fails to distinguish between import and export convertability.  

The author apparently also fails to realize that his proposal for a
<mathematics use=Mathematica> ... </mathematics> already exists: it is
called the "object" tag.

The author fails to distinguish between content and presentation markup, a
distinction that is utterly vital in this context.

  Conclusion

MathML may not be perfect, as I'm the first to conceed ;-), but it is very
well designed (compared to, say, Mathematica or REDUCE input languages),
and it should be published, even in its imperfect state, as soon as
possible.

  Thank you.

Andreas Strotmann


[1]  L.J. Kohout, A. Strotmann: "Understanding and Improving Content
Markup for the Web: from the Perspectives of Formal Linguistics, Algebraic
Logics, and Cognitive Science."
    in: ISIC/CIRA/ISAS '98 Joint Conference on the Science and Technology
of Intelligent Systems (IS'98), Gaithersburg, MD, 1998. 

____________________________________________________________
"The act of defending any of the cardinal virtues has today 
all the exhilaration of a vice." -
G.K.Chesterton: A Defense of Humilities, The Defendant, 1901 
                           www.chesterton.org/acs/quotes.htm

On Thu, 13 Apr 2000, Thomas Cool wrote:

> Dear Tim Berners-Lee,
> 
> You are probably under the impression that MathML is a good idea.
> May I invite you to read the paper linked below ?
> It isn't too late to stop it - but perhaps I am an idealist like you yourself.
> 
> Kind regards,
> 
> Thomas Cool
> http://www.dataweb.nl/~cool
> 
> http://econwpa.wustl.edu:8089/eps/get/papers/0004/0004002.html
> http://econwpa.wustl.edu/eprints/get/papers/0004/0004002.abs
> 
> also available at http://www.dataweb.nl/~cool/Papers/MathML/OnMathML.html
> 
> 
> 
>

Received on Thursday, 13 April 2000 16:06:39 UTC