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Re: the nature of \sin

Yannis writes:

> Suppose that the word 
> `sinus' appears in text, and a line lower one finds $\sin$; wouldn't it be
> unhappy if these two were written in different fonts? don't forget that not
> all maths are in display mode. 

and again

> Their proliferation is the best proof: besides the ones given by DEK
> you can find Hom, Iso, Aut, bij, and many new ones are constantly invented.
> When you wite something like
> 
>    The set $\Aut(E,E)$ of automorphisms of $E$ into itself
> 
> wouldn't it look strange if ``Aut'' inside dollars and ``aut'' outside dollars
> look different? for me it wuld look like some publications which force the use
> of some PostScript font (usually Times) but cannot avoid authors using CMR
> in math, producing a not very orthodox typographic mixture.

I disagree; I don't think it would look "unhappy" or "strange" for, say,
"sinus" and "\sin" to appear in different fonts. Of course, they'd have to
appear in compatible fonts (eg not one in Times, one in Helvetica).

\sin and friends are funny animals, because tradition says they are set in
roman even when the rest of maths is in italic. Leaving aside the special
nature of these items... In my line of work, I often use words as names for
functions, the words themselves having meaning. Thus, I might introduce the
function $tails$ by

   ...the function $tails$ returns all the {\em tail segments\/} of
   a list, in order of decreasing length...

and having used the term "tail segments", I might well subsequently talk
about "the tails $tails(x)$ of the list $x$". I don't think it appears
unhappy or strange for the two occurrences of the word "tails" here to be
in different (but compatible) fonts---indeed, it would be most confusing if
they weren't. I typically set my text in a roman and my maths in a
compatible sans (to mimic handwriting, as much as possible); I really like
Lucida Bright, because the sans is very compatible with the roman.

I tend to set all my maths in sans, so I presonally would set "sin" in sans
too. Some of my colleagues set some functions like $tails$ in a "maths"
font (eg sans) and some in a "text" font (eg roman)---I think to
distinguish between "user-defined" and "pre-defined" symbols, analogous to
"f(x)" and "sin" in normal mathematics; I'm not sure I think this is
defensible, because I'm not sure I can draw a distinct line between the
two. Yannis writes:

> It is also doubtfull if \sin, \cos belong to the math "language" or to the
> "English language". They are not variables, they escape to the usual rules
> of mathematical notation (a letter=a mathematical object), they *are* beginings
> of words. 

and I think I would have to say that \sin etc belong definitely to "maths
language":

   *  They *are* "variables" (they just happen to be functions, not
      constants).  

   *  I don't believe that mathematics insists on having a *letter*
      for each mathematical object; words are fine. 

   *  Sure, they are the beginnings of words, but so is the "f" in "suppose
      $f$ is a function from $A$ to $B$"; that's just a reminder to the
      reader of the meaning of this piece of notation. 

Moreover, 

   *  they are not "real words"; you'd say "the sine curve" rather than
      "the sin curve"! 

Jeremy