From: Henry Spencer <[EMAIL PROTECTED]>
On Wed, 9 Aug 2000 [EMAIL PROTECTED] wrote:
> It is true that font variations carry a meaning in mathematics,
> but it is a meaning that is determined in each book separately.
> One paper will use fraktur c for the cardinality of the continuum,
> another paper will use italic c, while in a third paper a symbol
> is given in fraktur if and only if it denotes a Lie algebra.
An interesting point. This suggests that the mathematicians need to pay a
bit more attention to the text-formatting community, and in particular to
the difference between procedural markup and descriptive markup -- they
are making the same old mistakes.
"Mathematicians"? Which ones?
One reads books and journals. No markup is visible.
Maybe some form of markup was used during production. Maybe not.
Also in private, papers are usually exchanged in PostScript or dvi,
not in source form, so that there are no problems with TeX versions
or missing macro files. The future may be different.
What is wanted is not a way of saying "Fraktur Lowercase C", but a way of
saying "Lie Algebra Lowercase C"... which a particular formatting style
might print as a Fraktur lowercase C.
What you say seems obvious. Still, I am not sure I agree.
(i) The number of mathematical concepts is very large, several millions
I suppose, and moreover grows very quickly. It is not like markup
in a typesetting environment, where a few hundred labels like <titlepage>,
<chapter>, <table> suffice. Thus, expecting a standard markup for concepts
in mathematics is less realistic.
(ii) Mathematics tends to choose a notation that is as compact as possible
and as readable as possible. That means that things that are variable in
principle but constant in a given context are not specified.
Thus, going from complete markup to the desired output is AI-complete.
(iii) As a variation on (ii), there is a certain tendency
to use lower case symbols for the elements one works with,
upper case symbols for sets of such elements, script symbols
for collections of such sets. This makes sure that typography
is as quiet as possible for the basic types. But what is considered
the basic type depends on the article. The sets of objects considered
by the first author, are the basic objects of the second author.
Again, knowing the semantics does not suffice to derive the
desired typography.
Andries
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Linux-UTF8: i18n of Linux on all levels
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