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Date:         Fri, 28 Mar 1997 14:14:35 +0100
From: Hans Aberg <haberg@MATEMATIK.SU.SE>
Sender: Mailing list for the LaTeX3 project
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To: Multiple recipients of list LATEX-L
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Subject:      Re: Mathematical Typography
Status: R

Johannes Kuester <kuester@MATHEMATIK.TU-MUENCHEN.DE> wrote:

>Okay, but there are constant function names as \mu for Moebius function,
>\phi for Euler function (totient) etc., but I think these shouldn't
>be set upright. May be the best example for this is \pi(x), when
>denoting the prime counting function (thus constant or with a fixed
>meaning) versus \pi, the circle number. Here \pi should be set
>upright in both cases, according to Hans Aberg, whereas I suggest not
>to use the `set in upright rule' to functions, whether constant or variable.

  I tried to stress that mathematical typesetting tradition is a dynamic
thing, created by the individual mathematicians, writing their particular
papers; I do not think there are any mathematicians around that would
accept any typesetting rules other than as a guidance. Basically, you are
supposed to invent some typesetting rules which fits the math you are
discussing in that particular manuscript.
  If you try to write manuscripts that cross the borders between different
mathematical fields, you will discover how much these field conventions
collide; I cannot say that any of these colliding rules within these fields
are wrong, in fact, they often turn out to be very right and convenient.

>>   When it comes down to names of constants like "e", "i", "pi", these
>> really were "variables" from the beginning, when they were discovered, and
>> therefore should be typeset slanted. Nowadays, this is no longer the case,
>> being regarded as "constants", and further, any choice of typesetting can
>> most easily be achieved using TeX, so why not change it?
>
>Excuse me? I don't think that they ever were variables.
>Rather mathematical typography wasn't that developed at that time.
>Most of the traditions of mathematical typesetting aren't that old.
>(may be we all should go to the library now and have a look and
>Euler's `Introductio in Analysin Infinitorum'...)

  So, for example, when it comes down to using the letter $\pi$ denoting
the ratio circumspherence length/diameter of a circle, this is very late in
history, just a few hundred years, I think. Just as one might write $x =
2$, people started using some letter for this ratio. So, at this point in
history, the letter you use for this ratio, is not "a name whose meaning is
considered constant", no more than when writing $x = 2$. Later, $\pi$
became the common choice, becoming a "constant" (if the authors decide to
so regard it).
  So we are dealing with ways of dressing the typography up, and not
semantic rules that must to be obeyed.

  One idea to dress things up is according to the terminology
    variable = name that is whose value may not be considered fixed
    constant = name whose value is considered fixed
and typeset constants in upright, and variables in slanted(italic) style.
(If in that particular text you are writing, in that particular instance,
you consider it worth bothering indicating the difference.)

  So, in order to enable this, math families should have both
uppercase/lowercase, and come in upright/slanted(italic) styles.

  But then again, one might use other ways to dress up the typography of a
manuscript.

  Hans Aberg