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Re: Mathematical Typography

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Fri, 28 Mar 1997 14:14:35 +0100

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 Johannes Kuester <[log in to unmask]> 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