Re: TeX <-> Unicode mapping

[Andries.Brouwer@cwi.nl]

hpa:

> We should point this out to the powers that be.
> If people think they [long arrows, the epsilon variant, ...]
> make sense I could allocate numbers out of the Linux Zone for these.

I a not sure this would be a good idea.

Mathematics is a very greedy symbol user.
It has always been the case that all symbols that were available
in the available technology were used for some purpose.

Look at the epsilon.
In many contexts epsilon is just epsilon.
But in some contexts one uses one variant, perhaps for setmembership,
and another variant, perhaps for a small positive number, or perhaps
for the fifth variable in the sequence alpha, beta, ..
(And if the first mathematician uses \epsilon and \varepsilon
then the next one will use \varepsilon and \epsilon for these
meanings. What is usual differs from discipline to discipline.)

Giving such symbols a separate status causes all kinds of trouble.
Unfortunately, Unicode already does this (your K, is it degrees Kelvin?)
(your A, is it Cyrillic? Greek?) (your capital PI, is it Greek? the
mathematical product symbol?), but I think only in cases where this
was required for roundtrip compatibility with existing standards.
Giving glyphs that are sometimes used interchangeably (or even are
completely identical) separate statuses forces people to choose
where no such choice is meaningful.

If the distinction is by use, then a secretary cannot choose.
And I cannot choose either because my use is not one of the
listed possibilities.
And if the distinction is by form, then are font variations
different symbols? Often in mathematics meaning changes with
font. My R is a ring, but \Bbb R is the set of real numbers.
Sometimes a script R will take the real part of a complex number.
But it may just as well be a collection of propositions to be
resolved. Or the name of an axiom system.

This area is a mess, and Unicode is a strange collection of
compromises, and I cannot see any reason to add to this mess.
It would not help anybody.

Instead, we should view Unicode as a system that helps writing
natural language. Not as a system for doing mathematics.
It will fail anyway - Unicode describes one-dimensional things,
mathematical formulas are two-dimensional.

Andries


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