From: Hans Aberg (haberg@math.su.se)
Date: Sat May 14 2005 - 17:29:37 CDT
At 23:58 +0200 2005/05/14, Philippe Verdy wrote:
>May be the distinction is only needed when using these mathematical
>symbols within normal text which would be rendered (with rich-text
>enhancements) in serif or sans-serif style. In that case, there's a
>visual distinction between what is a quoted mathematic formula and
>the rest of the text, if this could cause confusion.
>
>So effectively this is a rendering problem, as the same document
>could use the opposite styles as well.
>
>I really doubt too, that there will be distinctions between serif
>and [sans-]serif symbols in the same set of mathematical formulas:
>see for example how you can make the distinction between a serif and
>sans-serif 'a' or 'e' or 't' with SO MANY fonts.
The principle is that math text should, in principle, be able to mix
them, and they then mean different things. Then I do not that happens
with serif plus sans-serif. So they should not have been added, based
on that.
>A mathematic formula is already complex enough so that it should not
>use confusive notations, which may lead to many interpretation
>errors/bugs and false demonstrations.
>
>I won't say the same thing about the light/bold and roman/italic
>distinctions which are really more convincing visually.
By contrast, the four combinations of plain/bold, upright/italic are
used side by side to indicate semantics differences. The
upright/italic difference is more subtle. The combination bold italic
was often not used in the past, because it was not available. Before
the advent of computer typesetting, typesetters would often
substitute with what was available, as having many fints was
expensive.
>So if one wants to make the distinction between "sh" the hyperbolic
>sinus function name and "sh" the product of the two variables s, and
>h (independantly of the fact that there may be an "invisible product
>operator" or some space between them, if needed to make the
>distinction with named variables with more than one letter in their
>name), its highly probably that the variables will be in italic or
>bold style, and the "sin" operator will be in normal style,
If "sh" is a constant name, then it should be typeset the same as
"sin", namely in plain upright, and kerned together more tightly as
words. The combination as an implicit multiplication should be
typeset as "s h", but the actual space is smaller.
>and in both cases they can be either in serif or sans-serif font
>style, as a matter of rendering preferences.
The TeX fonts are all serif. I think this is traditional math, only
using serif. Sans-serif, if used by engineers for tensors, is
probably then just another style.
>Same thing for the "dt" differential notation: the differentiator d
>will probably by upright (or bold), and the t variable will be
>generally italic, and there will remain the distinction with another
>italic constant d in the formula.
In actual practise, the "d" is likely to be in italic, even though it
should be in plain upright. The "t" should and will generally be in
italic.
>The three usual roman/bold/italic styles (is bold italic really needed too?)
The bold italic has not been used much in math, due to lack of
availability. But if constants should be upright, variables slanted,
then this distinctions should be used in bold as well.
>used in mathematics is often clear enough to make all the necessary
>distinctions, including when a formula is embedded within linguistic
>text.
Otherwise, this is what I think too. But now the sans-serif Latin
variations have been added, and the Greek letters should in principle
should be no different from the Latin.
>In addition, most of the mathematics works is performed manually
>(expect within final reports, and books or publications), with a
>simple pen on a basic sheet of paper or with a marker on a
>whiteboard, and a humane hand can't draw these distinctions easily
>and legibly, even if the hand can often be much better than too
>limited computer programs (like text editors, email agents, and even
>"WYSIWYG" wordprocessors that still depend on fonts, and
>display/print resolutions.)
Already in the eighties, mathematicians started writing papers
without any handwritten intermediates. It depends much on what you
do. Sometimes paper is needed, but as computers becomes better in
representing and handling math, less use of paper is needed.
-- Hans Aberg
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