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+% \interval is used to provide better spacing after a [ that
+% is used as a closing delimiter.
+\newcommand{\interval}[1]{\mathinner{#1}}
+% Enclose the argument in vert-bar delimiters:
+\newcommand{\envert}[1]{\left\lvert#1\right\rvert}
+\let\abs=\envert
+\newcommand{\wt}{\widetilde}
+
+\title[Somethin' there is about you\ldots]{Somethin' there is about you,\\
+ That I can't quite put my finger on}
+
+\author{Chris Rowley}
+
+\begin{Article}
+
+I have been stimulated (goaded?) into penning these thoughts by Peter
+Cameron's expression of concerns about the future utility of \TeX{} to
+mathematicians. Many of these I share and, indeed, feel all the more
+pressing since I have set myself up as being responsible for them (and
+even, in some cases, I do directly bear that burden).
+
+I shall first consider some particulars of speaking mathematics and,
+in particular, voicing division; then conclude with some more general
+thoughts about communicating with and via computers.
+
+\section{Talking divisively}
+
+Peter, in company with Don Knuth, wants to write his \TeX{} ``as close
+as possible to the way [he] pronounces'' it (I added the ``he''
+deliberately, see below).
+
+Well, he may say `x over y' for $\frac{x}{y}$ or even `n-one-factorial
+n-two-factorial n-three-factorial, over, n-one + n-two + n-three' for
+$(n_1!\,n_2!\,n_3!)\,/\, (n_1+n_2+n_3)$ but I suspect that he would
+not say `x overwithdelims \ldots' for
+% $x \overwithdelims() y$
+$ \genfrac{(}{)}{}{}{x}{y} $
+(\verb|$x \overwithdelims() y$|)---and how would he cope with this (selected
+``at random'' from an AMS paper)?
+\[
+\left\lvert\frac{\hat v(s)-\hat
+v(t)}{\abs{\wt{D}u}(\interval{\left[t,s\right[})} -\frac{f(\hat
+u(t)+\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t)
+\abs{\wt{D}u}(\interval{\left[t,s\right[}))-f(\hat
+u(t))}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}\right\rvert
+\]
+
+Of course, Peter may put only very simple fractions into his letters
+but an average physicist is not so fortunate (or so communicatively
+challenged?).
+
+The problem with `over' (in the sense of `divided by') derives from
+the development over time of the notation for division; the use of
+built-up fractions is one of the more bizarre of the many usages that
+historical accidents have bequeathed us. If the good old `division
+sign' (whose \TeX{} name I have, I suspect, never known) had won out
+then life would have been much easier for coders and typesetters of
+mathematical documents, and possibly also for mathematicians. I also
+have a feeling that our generation were perhaps the first to adopt
+such a sloppy mode of mathematical speech---the phrase `quotient of x
+by y' seems only a little old-fashioned to me.
+
+In practice, mathematicians can often speak to each other in many
+abbreviated forms just like `over'. For example, in context I could
+say to Peter:
+\begin{quote}
+For t greater than $0$, $-1$ $0$ $1$ t is non-singular.
+\end{quote}
+and I would expect \emph{him} to very easily (sic) understand that
+the `$-1$, $0$, $1$, t' should be formatted as:
+$ (
+\begin{smallmatrix}
+ -1 & 0 \\ 1 & t
+\end{smallmatrix}
+) $
+
+My `day job' (but I do it evenings too) involves me in spending more
+time than your average mathematician communicating notation over the
+telephone, so I have become quite adept at inventing methods of
+speaking math notation to a fairly wide variety of people---this often
+involves private codes which I would not expect anyone else to
+understand. This has little to do with talking or writing to either
+computers or general mathematical audiences, nor should it have, but
+for me it has illustrated very clearly the fact that any particular
+convention, however well it works in a restricted context, is not a
+good paradigm for a general way of making mathematical documents
+portable. I would, of course, place the method that Don and Peter use
+to talk mathematics to each other firmly in this category of ``private
+codes''.
+
+Knuth's idea of writing mathematics as he and Peter would say it is
+both impractical (as is well illustrated by most of plain \TeX{}), and
+irrelevant to the real problem of communicating mathematics (not just
+the notation, but the structures), both between people and computers
+and inter-computer.
+
+I shall pick over just one other point in Peter's article before
+moving to more general matters: he complains that some of us are
+``obsessed with the need for all operators to be prefix''.
+
+All operators? No, at least not in the mathematical sense. All
+commands, yes: but that is a consequence of yet another accident of
+mathematical history---if you need general functions with an
+arbitrary, and possibly not fixed, number of arguments then the
+functions should be prefix, otherwise neither the computer (without a
+lot of extra work) nor the user (often, remember, this is not a
+mathematician) will be able to understand (in the sense of ``parse'')
+them. As Leslie Lamport observed, this convention does also have the
+advantage that the syntax of prefix commands often also makes it
+necessary to delimit the arguments; this syntactical nicety is
+essential for human readability but not much appreciated by most
+mathematicians (see my remark about ``What are we summing?'' below).
+If you do not understand the importance of writing commands in this
+very inefficient (from the computer's viewpoint) prefix form, try
+learning more than about a dozen Postscript commands with one to three
+arguments and then try and read a file that uses them.
+
+% Also, of course, to pursue Peter's argument about the paramount
+% importance of how one says things: I do not say
+
+
+\section{Talking to computers}
+
+I shall now make some more general observations concerning maths,
+communication and computers.
+
+Knuth's bestiary of mathematical symbols and constructions is no
+better or worse than any other: from the perspective of anyone from
+outside mathematics they are all both mysterious and infuriating.
+
+I have in other \emph{fora} argued strongly against too much formalism in the
+definition of a language in which computers can communicate
+mathematical notation. I now realise that, for general formatting
+purposes, rather more structure needs to be expressed in the mark-up
+than that which Knuth (and, hence, Lamport) thinks necessary. I say
+`thinks' since recent reports from Florida suggest that Don is
+unrepentant in thinking that he got it right---for example it is,
+apparently, OK (\textsc{TM}) if the computer never knows what is being
+summed by a summation sign, just like it does not need to know when it
+is starting a quotient construction.
+
+Computers need a lot more information than is provided by most schemes
+in order to format notation properly; this is very eloquently and
+dramatically illustrated by the work of T.~V.~Raman, who is getting
+the computer to answer back (audibly!) so that he knows what it cannot
+understand. I can assure Peter that Raman does \emph{not} want his
+computer saying `over' at random places but rather needs it to be able
+to efficiently distinguish and locate the beginning, end and ``type''
+of all substructures. If it is ever sensible to use the phrase ``how
+mathematics \emph{should} be spoken'' (when this is the only available
+means of communication) then the only relevant answers must surely be
+Raman's?
+
+It has been apparent to me throughout my mathematical life that the
+world would be a better place if mathematicians were more respectful
+of an audience's intelligence (rather than of her knowledge of the
+bizarre conventions of the subject itself) when writing about it; it
+would be nice to think that training them to `talk to computers' would
+make them more polite, but I doubt it.
+
+I agree that it would be nice to talk informally about mathematics to
+my computer, and I expect that to happen long before it can understand
+(in any format) all the implicit conventions contained in the way I
+write notation that is to be understood only by other mathematicians.
+However, I am sure that it will never be so good to talk about the
+subject, and others, with a computer as it is to do so with Peter.
+
+\section{Talking to each other}
+
+The article also touches on many other areas which contain genuine
+problems (and I cannot see them becoming less numerous in the near
+future). Amongst them are some that the new standard \LaTeX{}
+attempts to tackle, and others that we know must be tackled by
+\LaTeX3. One of the former is the ability to substitute for fonts
+that you do not have.
+
+Peter's thoughts are of great value to those of us who are actively
+influencing the future of \TeX{}, both as a typesetting system and as
+a mathematical lingua franca. Thus I hope we shall see many more
+articles like this one---and not just from mathematicians, please! I
+don't promise to argue with them all in print but I shall certainly
+read them carefully and, who knows, they may goad someone else into
+explaining a different viewpoint on a controversial issue.
+
+\end{Article}