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Re: Questions from the example markup





I wish to applaud Ron, and then Ka-Ping, for marking up an example fully.
I think it helps a great deal to have concrete ones to consider.

The most striking thing to me about the markup done is the extent to which
it resembles the TeX solution that is both widely proposed and opposed.
That said, I think that it also suggests the point that either you do just
enough markup for presentation purposes, or you have to do a lot more.  A
partial enhancement is fraught with opportunities for confusion.

One simple example of what worries me is provided by the case where Ron
carefully put in a "&FunctionApplication;" because he noted that \div  was
an operator, and specially marked <mo>(&nu;\cdot\nabla)</mo>, but did not
make special arrangements in the use of -&nabla;p.  The &nabla; is as much
an operator as \div or \curl (&nabla; is notation for the gradient, \grad,
and
\div = \grad \cdot and \curl = \grad \cross --- in an informal manner of
speaking).  It seems there are lots of possibilities for only partial
markup and hanging ambiguities inherent in trying to distinguish, in ways
that authors and editors are unfamiliar with, parts of the semantics of
math notations.

When it comes to the naming of classical objects that I mentioned, I was
only starting to point out that it seemed natural.  Indeed you'll find that
authors frequently adopt macros for them, in part because their
presentation is often done specially (bold, blackboard or roman, say).  I
don't actually see it as a bad idea to have a certain fairly large list of
classical objects with agreed and documented definitions as part of a
standard.  If you think of Asian languages then you can see that dealing
with a reasobaly large name space for ideographs, which all have widely
agreed meanings, is not an unsolvable problem.

A collection of classical items for math would not be all that large.
Actually I'm not proposing that here, but a small basic collection, say,
including

naturals
integers
rationals
reals
complexes
quaternions
octonions

Classical Groups:
GL, SL, U, SU, O, SO, SP, Osp,

Special functions:
Hermite, Legendre, Bessel (I, J, K, ...), ...
Hahn, Charlier, Krawtchouk, ...

Racah, Clebsch-Gordan

Probability distributions:
Gauss or normal, student, ....

...

wouldn't be that bad to assemble.  In any case we do need to provide, I would
suggest, a capability that _allows_ authors to use such constructions as
these easily and, if at all possible, unambiguously.  Computer algebra
systems already have large collections of common-place objects identified,
as do handbooks and tables.

However, it could well be that all this is rather at the level of the
planned "macro capability" rather than being of importance at this stage in
the deliberations.

I do not at all disagree now with the goals that Ron reiterated:
   (a) render to various sensory media in such a way that a
       "knowlegeable" human can interpret the notation properly
   (b) allow for paths by which authors or others may upgrade the notation
       to one with fuller semantical attributes

It has to be true that we are intending that math notation be read by
people who know something of math: advanced documents are to be read by
specialised readers.   It is just when it is to be read by machinery that
we are more careful.  As the example quoted by Fateman to the DLI list
showed, even what we think is very well-specified may well be wrong or
meaningless.  The more complicated notation or markup is the easier it is
to convince oneself that it is probably right because a machine says so.
That is a problem in teaching and it's going to be a problem with HTML/Math
too.

                Patrick



>
>It's unclear to me whether we have a strong(ish?) disagreement here.
>I'm certainly not in favor of *requiring* that authors name the
>well-known objects of their papers.  This would be too much to expect,
>in my opinion (no one expects the analogue in standard text, I imagine
>a vast menuing system (probably equivalent to ZF) to classify "all"
>objects, and do we expect to name the various non-standard models?  --
>where do we stop?)
>
>I do want to define an HTML-Math wherein authors are able to specify
>such things if they wish.  My view of the project to date has been
>that we are trying to define a language which will (a) render to the
>various sensory media in such a way that a "knowlegeable" human can
>interpret the notation properly, and (b) allow for paths by which
>authors or other third parties may upgrade the notation to one
>with fuller semantical attributes.  If this group has widely
>diverging opinions on the degree to which semantics must be carried,
>we'll probably have difficulty settling on a standard.
>
>But do we differ in this?  Maybe not.  Ping's statement
>
>> It makes the most sense for the conceptual entity "the complex numbers"
>> to be represented by a separate named entity.  It is certainly *not* a
>> variable named "C" in any sense -- and you would need it to be distinguished
>> for it to be properly rendered to speech.
>
>is much stronger than I would have said myself.  There actually is a
>good sense (a formalist or nominalist sense) in which "the complex
>numbers" are adequately represented by "C", and I'm fairly certain
>that Raman reliably distinguishes this "C", as do those who read the
>"C", by context.
>
>
>-Ron