[topicmapmail] loss-less transformation of topic maps

[Bernard Vatant]

[WMJ]

> (1) Is mathematics text based? No! NL text is not even a surface. It is
used
> to put "paint" on the mathematical (symbolic and intellectual) constructs.

I think we have there radically different views of the world. Do you
consider the prose - somehow standardized or ritual, even if in natural
language - used to articulate discourse in mathematical publications, or for
that matter in any scientific publication, and in standards specifications
like W3C or ISO, only a "social paint", and the peer review process, based
on those publications, only diplomatic gesticulation, with no real
importance in the efficiency of the tools? I strongly disagree. The process
of validation and social agreement is essential for the construction of
collective knowledge references. Without that process, there is no
consistent knowledge communities, the same way that there are no consistent
social right-driven communities without aknowledged (written) laws and
regulations, elaborated through peer-review process of the same type. There
is no fundamental difference, IMO, between the human process leading to the
elaboration and validation of a social law and the one leading to the
adoption of a new standard syntax or mathematical tool or so-called
"physical law". It's all about forging a collective tool through
intersubjective agreement. And, like it or not, all those processes are
referencing to TEXTS.
Every bit of mathematical reference is grounded on definitions (text) axioms
(texts) and theorems (text) and weird notations (often difficult to
serialize indeed). Even if mathematical objects are pluridimensional,
geometrical, graphical, functional ... what makes the meaning and efficiency
of these objects and make the mathematical construction consistent is that
text metalevel. Indeed, out of my experience as a maths teacher for more
than twenty years, what I consider to be the real difficulty of students in
mathematics, what is stopping most of them at a very elementary level is not
the comprehension of the mathematical objects, algorithms or
representations, but the comprehension and mastery of this natural language
metalevel.
Moreover, like natural language, syntax of mathematics is often more driven
by historical contingent constructs than formal or logical constraints. I
can point you at many mathematical notations which are known to be
inconsistent, but are kept going on because everybody agrees on their
implicit context and nobody wants to rewrite all the books. Ask the first
programmers of automated calculus the hard time they had with
trigonometrical notations for example, which are completely inconsistent
with other algebraic notations. Ask any maths teacher the hard time it is to
explain to high school children the consistency of things like:
In a(b+c)  a(...) means a multiplication, and (two years after): in f(x),
f(...) means a function!

Every student in maths and science has to go through all that language
contingencies and notation inconsistencies, and master the historically
built collective knowledge and agreements. So he/she has to become somehow a
"text-editing-bigot".

In trying to build consistent and efficient references for Topic Maps, we
are confronted to the same problem of constructing some agreement. We have a
syntax, built out of a mixture of formal and logical arguments, historical
consensus (barely a consensus so far), and available specifications - namely
XML. We have OTOH mathematical and graphical tools, and computer processes
and languages. We try to build something consistent with all that material
to agree about. Where and on what ground will we construct this consensus,
if not at some natural language metalevel? Don't forget we'll have to
communicate afterwards to the rest of the world, every administrator and
editor and end user, what we are about.

Back to the quoted syntax and graph representation below. You claim they are
not equivalent. I'd like you to argument about it, and maybe tell more about
what you mean by "equivalent". What is proposed is a representation. I will
never claim there is any "proof of semantic equivalence", because I really
don't know what it means. What we need is an *agreement* on equivalence,
namely: I understand something in this syntax, and I understand the same
thing in this graph, and it seems I have a process to transform one in the
other, that could be implemented. Do you agree? And if not, why precisely?

Regards

Bernard - not "Bertrand" please :o))


[WMJ]

> (4) To illustrate value of equivalency/redundancy please review
>
> <association>
> <instanceof> <topicRef xlink:href="#web-publication"/> </instanceof>
> <member>
> <roleSpec> <topicRef xlink:href="#website"/> </roleSpec>
> <subjectIndicatorRef xlink:href="http://www.universimmedia.com"/>
> </member>
> <member> <roleSpec> <topicRef xlink:href="#webmaster"/> </roleSpec>
> <topicref xlink:href="#BernardVatant"/>
> </member>
> </association
>
> and attached graph (both copied from
> http://www.mondeca.com/site/products/bernard/semanticgraf.htm.
>
> They are suppose to be equivalent but they are not.
> Those are pitfalls when you join/merge mentally the artifacts that are
> disjoined physically. Integrated text/graph notation helps.
>
> Will Bertrand V. prove me wrong? The future will show -)
>
> Best
>
> WMJ