At 20:39 +0200 2001/05/26, Lars Hellström wrote:
>>working mathematicians ... will use whatever symbols they deem
>>appropriate with no deference to anyone else's notions of propriety.
>
>I my experience, people don't always have that clear ideas about what
>notation to use (at least when it comes to new notationold notation is
>another matter); often the ideas aren't any clearer than "something
>triangular". In _those_ cases, which are what I was thinking of when I
>wrote the above, most people start looking through the tables in "A not so
>short introduction to LaTeX" (or whatever they use as first reference) to
>see if they find something fitting the description.
There are many principles at play here: One is to use what oneself and
other people already use or have used in the past.
If one for some reason needs a new glyph, LaTeX character principles are
not of much authority I am afraid: The most natural is to skim through all
sorts of glyphs, and perhaps design a new one if no suitable can be found.
>>As for examples, they exist  I've seen more than one. If you haven't,
>>and don't want to take anyone's word for their existence, then it is
>>entirely appropriate that you spend the time and effort looking for them.
>
>Do you realize that you are advocating "proof by authority" (or worse:
>"proof by claim", the academic cousin of "guilty by suspicion") here?! The
>normal practice in a scientific debate is that if anyone makes a claim and
>someone else requests the proof for that claim then these proofs should be
>produced (or the claim withdrawn) by the one who made the claim, not vice
>versa.
If there was a mathematical theorem that we were trying to prove, then you
would be right: Those that want two glyphs different should prove that
there has been a manuscript where they are used side by side with different
semantic meanings, and those that want them to be the same should prove
that they never have appeared in a manuscript side by side, or have been
used exchangeably in the same manuscript denoting the same mathematical
semantic quantity.
The proof of either claim will consist of a complete search of all existing
literature, taking into account the fact that the test may come up
inconclusively in view that the practise between authors may be
inconsistent, and the fact that the glyphs may have never appeared side by
side in the same manuscript, and other such complications.
But here we discuss the natural principles of human behavior: It is a known
principle in math authoring that one can take any glyphs looking
sufficiently distinct and the author is free to assign them the
mathematical semantics she deems right for the scientific context.
In the case of Unicode, the searchexistingliterature which in principle
defines what should be in Unicode did not prove practical with respect to
math. So one has instead settled for the principle how mathematicians may
use the glyphs, which is more sensible from the practical point of view.
I do not see why a successor to TeX/LaTeX which anyway is based on Unicode+
should meddle with this.
Hans Aberg
