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Re: Miscellany

regarding confusion between $a$ and a, the example given has both
of them, so the distinction should be clear.  but what if there's
only one?  as in
     For infinitely many values of $a$ goldfish can be
     $a$-automatically generated.
(apologies if this is utter nonsense; my mathematical education was
channeled through calculus and never got beyond it or out of the rut.)

the actual mechanism used in metafont to generate the different shapes
is to increase the value of certain parameters, in particular the
unit width.  the shape of the cap I simply doesn't have enough
distinct features that such manipulation will yield an instantly
perceptible difference.  i doubt that knuth thought much about the
likelihood of I being used in theorems as a pronoun, but he did
have distinct preferences for the shape of italic letters used as
symbols.  i recommend (re)reading his gibbs lecture, "mathematical
typography", published in the bulletin (new series) of the ams,
march 1979, v.1, no.2, pp.337-372, and reprinted as the first
section of the digital press/ams manual "tex and metafont: new
directions in typesetting", pp.1-45.  the techniques used in mf84
(the present implementation) are different from those described in
the prototype, but the basic goals are the same -- an answer to the
question ``If the great type designers of the past were alive today,
how would they design fonts for the new equipment?'' [knuth, gibbs
lecture, ibid, p.17]
                                                -- bb