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\lower.5ex\hbox{$\mathcal M$}\kern-.125em$\mathcal S$}
\newcommand{\AmSTeX}{\AmS-\nolinebreak\TeX}

\newcommand{\LL}{\LaTeX~2.09}
\newcommand{\bb}{blackboard bold}
\newcommand{\GF}{German Fraktur}
\newcommand{\WW}{\texttt{WinWord}}
\newcommand{\WfW}{\texttt{Word for Windows}$\sp{\circledR}$}
\newcommand{\SP}{\texttt{SigmaPlot}$\sp{\circledR}$}
\newcommand{\Microsoft}{\texttt{Microsoft}$\sp{\circledR}$}

\newcommand{\verybad}{$H$\kern-0.7em\raise0.7ex\hbox{$\exists$}}

\title{Writing on a computer: \\ some discouraging experiences}

\author{Mikhail B.~Sevryuk \vspace{3mm} \\
\textit{Institute of Energy Problems of Chemical Physics,} \\
\textit{The Russia Academy of Sciences,} \\
\textit{Lenin prospect \textsl{38}, Bldg.~\textsl{2},
Moscow \textsl{117829}, Russia} \\
\textsl{E-mail}: \texttt{rusin@chph.ras.ru}}

\date{December~2, 1998}

\begin{document}

\maketitle

\begin{abstract}
Apart from great advantages, preparing a scientific paper on a computer has
also undesirable side effects. In the present text, we point out some of
down sides of electronic writing and discuss how one can avoid them.
\end{abstract}

\vspace{1mm}
\baselineskip=12pt

\begin{flushright}
\AmSTeX\ also provides a font as a concession \\
to perverse notational usage. \\
Mathematicians used to write things like $\mathbb R$ on the blackboard, \\
or in their manuscripts, to indicate boldface. \\
Now some of them use similar symbols in print, \\
so \AmSTeX\ has a ``\bb'' font \verb+\Bbb+. \\ \vspace{1mm}
---~\textsc{M.~D.~Spivak}, The Joy of \TeX\ (1990) \\ \vspace{3.5mm}
Blackboard bold, as in $\mathbb A$, $\mathbb B$, $\mathbb C$, \\
is provided in the \textsf{amsfonts} package \\
with the \verb+\mathbb+ command. \\ \vspace{1mm}
---~\textsc{G.~Gr\"atzer}, Math into \LaTeX\ (1996)
\end{flushright}

\vspace{5mm}
\baselineskip=18pt
\parindent=5mm

Modern text processors such as \Microsoft~\WfW\ and markup languages such as
\TeX\ and its descendants \LaTeX\ or \AmSTeX\ have revolutionized the process
of writing, especially in mathematics and physics. I remember those remote
times when mathematical papers were prepared by a typewriter and formulas were
filled in by hand, all the special characters, fonts, sub(super)scripts being
marked by underlining, encircling, and penciled notes. I disliked filling
in the equations in manuscripts, this seemed to me the most unpleasant part
of a mathematician's life, and I dreamt of an equipment that would save us
from that distressing duty. One of few reveries that have come true
completely!

A lot of books, brochures, manuals, and articles are devoted to computerized
writing and typesetting, the advantages they offer, and their role in the
modern organization of scientific researches. However, my experience as well
as the experience of many of my colleagues show that one should use such
powerful systems as \TeX\ or \WW\ rather guardedly. Preparing papers and
books electronically may cause (and does cause!)\ some errors and troubles
entirely impossible in the past, in the era of typewriters and handwritten
equations. Other misprints (e.g., an unwanted hyphen in the middle of a word)
have become much more frequent. It is easy to avoid these troubles, one must
just be aware of them. Nevertheless, I have never encountered any mention of
those down sides of electronic writing in standard manuals for authors of
mathematical papers. I therefore consider it expedient to share my impressions
with others.

There is a widespread opinion that \TeX\ is almost infinitely portable. This
is perfectly true in the sense that \TeX\ documents are not corrupted in
e-mail transmission---just because they are \texttt{ASCII} files. But there is
no guarantee that the same \TeX\ file would lead to the same printing output
after having been processed on two different computers using two different
\TeX\ interpreters and font packages. This is probably the case if, say, the
file at hand is a \LL\ document containing no commands beyond Leslie Lamport's
standard 1986 manual. But even in this situation, \LaTeX\ systems installed
on different computers break the text into pages rather differently
(according to my experience)---without any modifications of the standard
\LaTeX\ styles.

On the other hand, the fonts and symbols provided by the standard \LL\
packages do not meet all the needs of a mathematical user. Those packages
include a vast variety of symbols, dozens of them being whimsical signs
hardly ever used in actual works, and miss the \bb\ font (``open font'') and
\GF\ (``Gothic'') font, so usual in mathematics. Some people find the \bb\
symbols unattractive (I disagree with that), but in any case, almost all the
users working in mathematics are forced to add additional fonts to the
standard \LL\ set of fonts to be able to produce the \bb\ characters. The
problem is that those additional fonts and the corresponding \TeX\ control
sequences installed on different computers are often incompatible, and this
gives rise to many troubles. The absence of the \bb\ font in the \LL\ packages
has been a real computer malady.

Several years ago, I prepared a long work in \LL, the \bb\ symbols occurring
in that text very frequently (which is typical of mathematical papers). The
local \TeX\ system I used included a beautiful \bb\ font. The final file was
transferred to another computer because the printer attached to the latter
was better (the authors were supposed to submit the manuscript in the
camera-ready form). It turned out that the \TeX\ commands invoking the \bb\
symbols on the first computer corresponded to other symbols within the system
on the second computed. Neither my coauthors nor I were aware of that
circumstance. Without any warning messages, our \LaTeX\ file was compiled
and printed, and, of course, nobody read the final manuscript obtained---the
text had already been checked very carefully on the first computer! The
manuscript was sent to the publisher and was published with incorrect symbols
throughout.

By the way, contrary to the general opinion, the \bb\ problem does not confine
itself with the five letters $\mathbb N$, $\mathbb Z$, $\mathbb Q$,
$\mathbb R$, $\mathbb C$. In addition, one should consider at least $\mathbb H$
for quaternions, $\mathbb O$ for Cayley numbers (octonions), and $\mathbb A$
for algebraic numbers, as well as $\mathbb F$, $\mathbb K$, or $\mathbb D$ for
an arbitrary basic field (the notation $\mathbb F\sb q$ is also used very
often for the finite field of $q$ elements and the notation $\mathbb D\sb q$,
for the dihedral group of order $2q$). The symbols $\mathbb S\sp n$ and
$\mathbb T\sp n$ for the $n$-dimensional sphere and torus, as well as
$\mathbb A\sp n$ and $\mathbb P\sp n$ for the $n$-dimensional affine and
projective spaces (over an arbitrary field) are sometimes utilized. On the
other hand, $\mathbb A\sb n$, $\mathbb B\sb n$, $\mathbb C\sb n$,
$\mathbb D\sb n$, $\mathbb E\sb 6$, $\mathbb E\sb 7$, $\mathbb E\sb 8$,
$\mathbb F\sb 4$, $\mathbb G\sb 2$ denote, in some works, the Weyl groups of
the root systems of types $A\sb n$, $B\sb n$, $C\sb n$, $D\sb n$, $E\sb 6$,
$E\sb 7$, $E\sb 8$, $F\sb 4$, $G\sb 2$, respectively. The notation
$\mathbb H\sp n$ can mean the $n$-dimensional hyperbolic (Lobachevski\u{\i})
space. One occasionally uses the \bb\ letter $\mathbb P$ for the probability
measure and the notation $\mathbb L\sp p$ for the space $L\sp p$ of functions
$f$ such that $|f|\sp p$ is integrable, as well as the notation $\mathbb H$
for the space $L\sp 2(\mathbb T\sp n,\mathbb R\sp n)$. I have encountered the
symbol $\mathbb D\sp n$ for $\mathbb R\sp n\cup\mathbb S\sp{n-1}$, the
compactification of $\mathbb R\sp n$ by an $(n-1)$-dimensional sphere of
``infinite'' radius. In a PhD thesis I read recently, the author denoted
respectively by $\mathbb T$, $\mathbb O$, and $\mathbb I$ the tetrahedral,
octahedral, and icosahedral subgroups of $SO(3)$. In a preprint I read very
recently, the author used the \bb\ characters $\mathbb E$ and $\mathbb G$ for
certain subsets of $\mathbb C\sp N$ and $\mathbb Z\sp N$, respectively,
as well as the \bb\ $\mathbb E$ for any Banach space over $\mathbb R$ or
$\mathbb C$, etc.\ etc.

Another difficulty is that in many particular installations of the \bb\ font,
its letters do not reduce in size properly while appearing as
sub(super)scripts or in footnotes (the same refers to the \GF\ characters).
Of course, the wide availability of the \AmS\ fonts would easy and
eventually remove all these troubles.

The reason for my two-computer disaster described above is obvious. But I
have also encountered other \TeX\ calamities (not connected with \bb\
symbols) which I cannot explain. Once, I refereed a paper prepared in \TeX\
(judging from the fonts used). I pointed out in my report that some
equations in the paper were wrong. The author agreed with my criticism and
in the revised version, he corrected those equations, but other several
equations turned out to be totally corrupted: they became senseless
combinations of symbols! The latter equations were OK in the initial version.
I had and still have no idea of how this mysterious phenomenon could happen.
It was clear that the author had not read the revised version throughout, but
it is so natural not to read the sections that have not been modified\ldots\
(Of course, I eventually made the author produce a version where all the
equations were correct.) Such a case had been impossible in the pre-computer
times.

One sad event more, this time without any enigmas. A paper prepared in
\AmSTeX\ contained arrows created by the \verb+@>>>+ and \verb+@<<<+
commands. To obtain the final camera-ready output, one processed the file by
\LaTeX. Instead of arrows, $@>>>$ and $@<<<$ themselves were gotten, and nobody
paid attention to these meaningless symbols.

Many \TeX\ users often forget typing a backslash before the names of Greek
letters and then do not check the printed output carefully. A lot of
manuscripts I refereed were choked with the English names of Greek letters
in place of the actual Greek letters (and it was in fact almost impossible
to examine such papers on their mathematical merits). This ``misprint'',
extremely popular in the present age of \TeX, did not occur at all, of course,
in the good old days of typewriters and handwritten formulas. As a rule, it
cannot filter through the refereeing and copy-editing system of the best
journals, but I observed the names of Greek letters in the formulas even in
Springer books. I also encountered \TeX-prepared manuscripts with blank spaces
in place of some formulas, the origin of this misfortune being unclear to me.

Up to now, I discussed \TeX, but similar effects happen to \WfW\ documents as
well. As a rule, the rich variety of \texttt{Windows} fonts the \texttt{Word}
exploits does not include the \bb\ font. I experienced the cases where the
\texttt{WYSIWYG} principle failed for \WW\ (the printed text exhibited blank
spaces instead of characters perfectly visible on the screen---even in the
preview mode). Transferring a \WW\ file (as well as a graphic \SP\ file) to
another computer may destroy the document almost completely. I myself
encountered the following effects:
\begin{description}
\item [a)] several symbols in equations were corrupted in a horrible and
entirely irregular way (e.g., $\hbar$ and $\widehat{H}$ turned into $\eta$ and
\verybad, respectively, while $1$ and $W$ were replaced with blank spaces),
of course, this refers to the \texttt{Equation Editor} rather than to the \WW\
itself;
\item [b)] additional symbols appeared;
\item [c)] some Greek letters were replaced with the ``corresponding'' Latin
ones (e.g., $\alpha$ with $a$ or $\gamma$ with $g$).
\end{description}
Needless to say, all this occurred without any warning messages. Such
symbols as \verybad\ (with overlapping $H$ and $\exists$) were unknown
before sophisticated text processors conquered the world.

Curiously, in all the (not numerous) \WW\ installations with the \bb\ font
I have seen, the \bb\ characters do not reduce in size automatically while
appearing in footnotes---like in some \TeX\ installations.

How can one overcome all the above-mentioned unpleasant side effects of
computerized typesetting? The following two very simple rules seem to be
sufficient:
\begin{description}
\item [1)] \textsl{Print the whole document and read carefully through it after
\textit{every} change in the environment you use (installing a new version
of the system, adding a new font package, transferring the file to another
computer, etc.).}
\item [2)] \textsl{Read carefully once more through the final manuscript before
submitting it to the journal or sending it to the publisher.}
\end{description}

Nowadays, many journals ask their contributors to send a diskette with the file
of the paper along with the hard copy. In the instructions for authors, it
is often pointed out that electronic submission enables one to avoid
introducing errors while processing the paper. This contradicts heavily the
experience of many contributors, including my own. A lot of my papers were
submitted together with the electronic version (either in \TeX\ or in \WW).
I strictly followed all the instructions of the journals. The result has been
always the same---numerous misprints in the proofs, as if the text were
rekeyed. I do not know the origin of this fact.

Moreover, using electronic versions of the papers leads sometimes to rather
specific errors. Beginning users of \LaTeX\ often ignore the \LaTeX\
cross-reference system for numbering equations and other elements of the text.
They create numbered displayed equations by the \texttt{equation} environment,
but in a text reference to any particular equation, type the explicit
number of the equation instead of using the \verb+\ref+ command. Journal
copy-editors sometimes change the equation numbering (e.g., via breaking a
numbered equation into two parts occupying two lines, in which case each part
gets its own number provided that the new environment is \texttt{eqnarray},
this would shift the numbers of all the subsequent equations). Since the
manuscript is formally prepared in \LaTeX, the copy-editor does not bother
about the necessity to change the text references accordingly. The result is
highly regrettable---the actual equation numbers and the references to the
equations within the text do not match. I experienced this twice.

One should therefore follow the third simple rule:
\begin{description}
\item [3)] \textsl{Do not trust electronic submission. Check the proof as
carefully as you can even if the printed final version of the paper was
accompanied with the file.}
\end{description}

On the other hand, when the publisher uses the file supplied by the
author(s) without carefully copy-editing (not to mention when a camera-ready
output is utilized), the result is often unsatisfactory as well. The
authors' files seldom meet all the standard printing conventions---e.g.,
a uniform style of the references or (in the case of \TeX) the right size
of the ``delimiters'' which is ensured by typing \verb+\left+ and
\verb+\right+ commands---and a certain intervention is almost always needed
to produce a professionally designed paper.

Finally, here is my latest experience. Some time ago, I submitted two papers to
a journal---with \LL\ files. Both the papers were accepted, and when I received
the proofs, I was really shocked: the reference lists turned out to be
interchanged! The reference list for paper \#1 was attached to the body of
paper \#2, and vice versa. Of course, the references within the papers were
``unsolved'': there were `[?]' instead of correct numbers in brackets, but
the publisher seemed to have paid no attention to that. However, these were
the proofs only; I hope that eventually in the issue my papers will be OK!

\end{document}
