Re: Unicode and math symbols

["Martin J. Duerst" <mduerst@ifi.unizh.ch>]

Hello Chris,

On Mon, 24 Feb 1997, you wrote:

> Martin wrote --

> > In general, I agree with Chris that for systematic form changes
> > in the alphabet, additional information (such as font information
> > on a lower level, or structural information on a higher level)
> > should be used. On the other hand, if there is a well-used
> > Math symbol that isn't in UNicode, I would suggest to make
> > a formal proposal for putting it in, with all the necessary
> > data.
> 
> What makes it well-used;? If you look at something like formal methods
> or logic, you find all sorts of symbols and the number increases
> rapidly: are these "well-used"? are they "maths"?
> 
> The general problem is that mathematical notation is by its nature
> not standardised, in either form or meaning.  

Well, what was in TeX, at a certain stage, got accepted as
"well-used". If you can come up with textbooks, journal articles,
reccomendations from some standard bodies,... (e.g. Z), then
you should have a strong case.


> > One thing not really clear in the Math area is the distinction
> > between semantics and abstract form.
> 
> And also the relationship between them.
> 
> Please do not let Unicode become caught up in the problem of
> expressing the semantics of mathematical notation.
> 
> The only semantics that Unicode gives to 0061 is a standard name and
> the fact that most people expect something with that name to look like
> "a" or "the rounder form used in some fonts"; it does not say that
> "when used in English as the only letter in a word it is the definite
> article", nor should it.
> 
> So please leave the meaning of math symbols (which is also highly
> context-dependent) to the mathematical reader.
> 
> Another reason for keeping such discussions out of the Unicode area
> right now is that a lot of effort is going into decding what can and
> should be standardised at the DTD level (in particular HTML-math).
> 
> I think that this fits in with bb's comment that there are standard
> SGML public-entities for math notation and with the way users are used
> to encoding maths: at least for the moment it should be the only place
> where we try to standardise any sort of semantics.

I agree very much with you. However, I read Barbara's comments
as to that she wants to be closer to semantics than we would.


> One reason for this is that the natural structure of even quite simple
> typeset maths is visually much more complex than the Unicode model
> (for Latin-based systems) of "base+diacritics" and it is not closely
> related to the more complex visual structure of other writing systems.

If you mean *text* writing systems, then they all use lines/columns.
Many of them have some more complicated structure on a micro-level
(i.e. Tibetan stacks, ligatures, diacritics,...) which Unicode
deals case-by-case (you need separate rendering logic for each of the
more complicated scripts, or a very general mechanism).

If you mean other symbolic writing systems, such as mathematical
notation and musical notation, then you are right. Unicode is
not designed for them nor plans to address these.


>   What are the practical benefits of having some set of mathemtical
>   symbols in Unicode?  Is it the canonical name that is important?
>   Or assigning a standard code-value to that name, or both?

The practical value may be that you can use such symbols in
text. You won't be able to write nice formulae, but you will
be able to write formulae with lots of parentheses.

Regards,	Martin.