W3C home > Mailing lists > Public > www-math@w3.org > April 2003

enough structure? and adoption barriers (and the road ahead)

From: Al Gilman <asgilman@iamdigex.net>
Date: Wed, 09 Apr 2003 10:15:55 -0400
Message-Id: <5.1.0.14.2.20030409090110.02027200@pop.iamdigex.net>
To: www-math@w3.org

At 06:51 AM 2003-04-09, William F Hammond wrote:
>[I suggest that follow-ups be directed to www-math@w3.org only.]
>
>Al Gilman <asgilman@iamdigex.net> writes:
>
> > Equations are not very usable when read linearly, even when spoken
> > by a live mathematician.  They must be regarded as complex
> > expressions rather than linear text.  Letting the user walk the
> > expression tree is the way for them to be able to get their ears
> > around the structure that is at hand.
>
>Q1. Do you have text representations of examples of such expression
>     trees?

I believe that you can find this in Raman's work.

>Q2. Do you think that content MathML is rich enough for this or do you
>     have something more in mind?

Raman tells us it captures the formal structure well enough.

Without consumer-grade tools operating at the level of the MathTalk
suite, I can't confirm if this is efficacious as well as effective.
[efficacious is distinguished as "effective under field conditions
of practice, transferrable into widespread practice, as opposed to
effective for which demonstration under laboratory conditions is
sufficient.  This is jargon from health policy, but it is relevant
to the matter of getting authors to practice some hygiene of format,
as 'authors' is a large public and so we are into adoption issues
comparable to those in public health.]

"Rich enough" has too many divergent connotations.  Rich, like
'simple' and 'beautiful' would appear to be in the appreciation
of the hearer, beholder or what have you.

>This issue is certainly related to issues surrounding the design of
>author-level markup, because for author-level markup to be sane for
>translation to content MathML it must expand to such an expression
>tree.
>
>It will be a hard sell coaxing general authors to have new content
>up to this standard, given that the present is typified by PDF made
>from TeX/LaTeX source as found at arxiv.org.
>In addition to the possibility of optimal non-visual rendering,
>however, authors may look forward to:
>
>       1.  better online indexing of their articles.
>
>       2.  better online searchability for their articles
>           (though few realize that searching TeX source for
>            math involves luck).
>
>       3.  better interface between online article content
>           and mathematical software on a user's platform.
>
>The road there still looks rather long because of the need for author
>markup that will be an attractive choice for authors who are now very
>happy with their smooth access through TeX/LaTeX to visually pleasing
>PDF.

According to what I hear from the Math WG, this hard sell is
finally catching on.  I don't have the particulars, but there is
a large and growing corpus of stuff in MathML at this time.

<general rant>

Other than that, algebra is such a formal language, that is to say
pattern-rich rather than atomic-term-heavy, that it is easy for a
linear-text representation to be competitive with direct manipulation in a GUI.
And those with the training to create new utterances in classical
mathematics have the skills to pick up LaTeX quickly and not find it a barrier.

However, as with the spreadsheet and office work: direct manipulation will
open the door to application of more math to more people with less boot
camp.  It will expand the market for math by lowering the barrier to entry.

The market for MathML direct-manipulation tools is more those without the
background or patience to pick up LaTeX than those who are already
acculturated to it.

</general rant>

This is why, from the perspective of supporting the interest of people with
disabilities, I think we have to treat both LaTeX and MathML as a step
forward in capturing the structure needed for user-directed structure
walking, *and* we need to continue to press for better scene graph theory and
experimentation (for which SVG and X3C are good platforms) in the capture of
formal structure while working in a direct-manipulation,
least-formal-visualization context.

<blue sky use case>

One needs to be able to view a magneto-hydro-dynamic event (see the example
of the breakup of a vortex pair in the latest [Vol 19 No 1] enVision from
SDSC/NPACI).  Then one hypothesizes a theory that one might be observing in
terms of the differential constraints that a generator phenomenon for this
evidence obeys, and what potential it extremizes, and then one can get a
grid matched to the multidimensional data that is the application of the new
theory.  And a new visualization driven by this mapping of the data.

Then one can go into schema view and designate a slice of the
problem-definition (constraints and optimizations) space that one wishes to
explore parametrically, and from then on direct manipulation -- tugging on
markers on the existing curve-fit gridwork of analysis coordinates -- will
result in recomputation of the analysis gridding with perturbed vaues of the
constraints and potentials of the theory.

Matching models to experience is the game of Science, and numerical methods
of curve fitting are just one example of how it can be done in a computer
aided way.

Note that what the blind web wanderer needs in terms of formal
infrastructure for the WYSIWYG-created [equation or] page layouts of today
is a small matter of interactively-checked curve fitting.  With curve-fit
(model fitting) routines nominating structural analyses of the WYSIWYG work
in progress, it will be about as easy to get well-structured expressions
from the GUI creator of MathML as it is to get them from the emacs jockey
writing LaTeX.

While I quail at the rhetoric of the NSF about 'computational science'; on
the other hand, in a context like this I have to say we have to take the
truth in that slogan very seriously.  At the rate Moore's law is progressing,
computational processes will be taking work off people in increasingly more
areas.  The computers may not only be hypothesizing and in-silico testing
novel bio-chemical techniques, but also discovering markets for them in novel
business-transaction patterns.

The ethics of science is already a hot topic, and without a computational
science of ethics we may be in deep trouble.

<blue sky use case>

Al


>                                     -- Bill
Received on Wednesday, 9 April 2003 10:44:08 GMT

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