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Re: [Axiom-developer] RE: [xml-litprog-l] Re: noweb, pamphlets, and TeXm

From: michel . lavaud
Subject: Re: [Axiom-developer] RE: [xml-litprog-l] Re: noweb, pamphlets, and TeXmacs
Date: Tue, 26 Nov 2002 14:20:09 +0100

Hello Mike,

> > LaTex is a defacto standard notation for mathematical
> > markup but MATH/ML is rapidly evolving as a more
> > "modern" alternative. Should one attempt to adopt such
> > a radially different (and some say exceedingly verbose)
> > approach as MATH/ML in the design of a new user
> > interface for Axiom?
> LaTeX is fine as a rendering language but it does not have a regular
> syntax and is very hard to manipulate.  I've just spent several months
> working with XML documents with embedded fragments of LaTeX for
> mathematics and the upshot is that we're removing the LaTeX and
> replacing it with MathML.  Also, once you translate to LaTeX, it is
> very hard to have any degree of interactivity such as cut-and-paste
> since the structure of the rendered version may have little or no
> relationship to the underlying data structures.  With MathML/XML you can
> annotate the presentation form with the content form (and vice-versa) or
> use xref to link related parts of different structures.

>From the point of view of software developers you are certainly right, but
from the point of view of users and Science, I think you are wrong :
TeX/LaTeX is a defacto standard notation for mathematics, as Bill Page
noted, and I think that we ought to start from this point, whatever the
difficulties, for many reasons, the main one being that software are for
users, not for developers, so the user's point of view ought to be
prominent (this is a true for commercial software because the aim is to
earn as much money as possible, but I think this ought to be also the case
for free software). I give a few reasons, why users might have an opinion
opposite to yours:

1 - One would have tons of work in maths, physics, chemistry, etc. that
would go to the rubbish heap or would have to be translated, with the
inevitable errors inserted by any translator. Errors of one character in a
text can be corrected automatically by humans and software, but error of
one character in a formula in a scientific article cannot be corrected
(except by reconstructing the proof) and the consequences can be
disastrous.  Let just recall that an error of one character in a computer
program led to the crash of a NASA planetary probe, cf:

There are other examples of this type  (crash of Ariane 5, sink of an oil
platform etc) and one can imagine easily others, for example the
consequences of an error in the chemical formula of a medicine, etc.

Your argument based on your difficulties is quite valuable, but the
question "is a formula in language XXX rendered exactly, today and in the
long term ?" is much more important in my opinion - all the more in the
long term.  No human can read a Mathml formula except very simple ones, it
is too much verbose. So one would be condemned to use software to read
such formulas. Could anybody certify that a MathML formula written with
today's version could be rendered exactly with a software in hundred years
as it is today? TeX formulas on the contrary can be read by humans
directly, and moreover TeX is frozen, so this stability and human-
readability makes it a completely reliable way to transmit math formulas
over very long periods.

2 - Let just consider the denomination of plants, animals, anatomy : all
are in Latin, since Linne's work more than 200 years ago. This stability
in the denomination was a crucial ingredient for the progress of botany,
biology and life sciences, etc. because everybody - whether he is British,
Chinese,  French or from any country - knows a given living being under a
unique name. Botanists can still read descriptions of plants that were
written 200 years ago. Of course, this approach is difficult, as botanists
have to learn Latin, but this is the condition for scientific exactness
and for having a common and stable language, understood by everybody over
a very long period. The "sagesse" of botanists, biologists etc. has been
to keep this (otherwise obsolete) language to allow their science to
progress and to remain rigorous, instead of unceasingly changing their
language, which would have restrained the progress and multiply the
possibility of confusions and errors.

For the same reason, I think we ought to maintain the usage of TeX for
documents with mathematical formulas, as the usage of Latin is maintained
for description of plants, animals etc, despite all the considerations you
give (about your difficulties with TeX) which are, I agree, valuable, but
negligible as compared to the bad consequences of abandoning TeX in favour
of something else, and then 20 years laters abandoning this "something
else" for another "something else", etc., etc...

If this point of view worries you too much, let us consider that there are
people who are working on Scientific OCR, that could reconstruct formulas
from scanned articles in scientific journals. This is a very difficult
job, but this would be very useful and is worth the study. And it is
certainly feasible, as any scientist does it daily with his mind.

Well, instead of starting from scanned images to reconstruct formulas, let
us start from formulas in TeX, to produce MathML output today, and to
produce #!??&@ML output in 20 years (the new language which will have
superseded MathML at that time among learned computer scientists). This is
probably a difficult job, but certainly much less difficult than
Scientific OCR. And it is certainly feasible unambiguously also, as one
can read formulas printed with TeX without any ambiguity.
So, mathematicians, physicists and chemists in 100 years could still be
able to type their articles in TeX and read the articles that were written
in TeX this year. And efforts to build free archives of scientific
articles (which might be unimportant for developers but are of utmost
importance for many users) would not be ruined, too.

3 - Another difference between user's and developer's approaches :
learning TeX is difficult for the user, but it is justified because it is
error-free and could stay for ever (if we are sufficiently wise to decide
it ?). Having to learn a few years later another language is unacceptable
for most users, I think, even though it might be more convenient for

Best wishes,

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