%lucidity-supplem.tex

%***************************************************************************

%  Further notes on lucid writing, pattern perception, and scientific thinking

%  M. E. McIntyre

%***************************************************************************

  %This is an ASCII file in plain TeX.  In case TeX is not available on
  %your system, note that the unprocessed file is legible if you (a) ignore
  %the backslashed TeX commands, (b) ignore pairs of braces and a few other
  %spurious-looking symbols, and (c) ignore the commented-out lines,
  %those beginning with %.  To print a TeX file like this you can usually
  %type (after checking that your working directory contains this file, named
  %lucidity-supplem.tex)
  %                            tex lucidity-supplem
  %then
  %                          dvips lucidity-supplem
  %
  %and then, on some systems,
  %                            lpr lucidity-supplem.ps

   \font\eightrm=cmr8
   \font\eightit=cmti8
   \font\eightsl=cmsl8
   \font\eightbf=cmbx8
   \font\eighti=cmmi8
   \font\eightsy=cmsy8
   \font\sixrm=cmr6
   \font\sixbf=cmbx6
   \font\sixi=cmmi6
   \font\sixsy=cmsy6
   \font\ttt=cmtt8


\def\eightpt{\def\rm{\fam0\eightrm} \def\it{\eightit}   %  \def\sl{\eightsl}
  \textfont0=\eightrm \textfont1=\eighti \textfont2=\eightsy
\scriptfont0=\sixrm \scriptfont1=\sixi \scriptfont2=\sixsy
  %   \newfam\bffam % \bffam=6 already assigned by plain.tex
   \def\bf{\fam\bffam\eightbf}
  \textfont\bffam=\eightbf
\scriptfont\bffam=\sixbf
 \rm\baselineskip9pt
 }

\def\display{\parindent=2em\par\narrower\par\noindent}

\magnification\magstep1
\hfuzz 30pt
\eightpt
\parindent=0pt
\parskip 10pt plus 5pt minus 4pt


 \line {\sevenrm Version of 15 November 1999, including RPC, NW;
refs. still need tidying
 \hfill lucidity-supplem.tex}
 \bigskip

\leftline{\bf
Further notes on lucid writing, pattern perception, and scientific thinking
}
\medskip\leftline{Michael McIntyre
}
\bigskip

\centerline{``Verbing nouns weirds language.'' --- Anon.}

\bigskip


These string-searchable notes supplement the main line of argument in
{\ttt lucidity.ps}, which was about lucidity principles and perceptual
phenomena and about the biological reality that underlies them ---
i.e., how a little scientific thinking can help you to improve your
communication skills, such as writing skills.  The notes begin with a
draft-repair toolkit, still under development, that I have found
useful as an editor and PhD thesis supervisor.  This is followed by a
miscellany of notes --- for reference only, not designed to be read
sequentially --- expanding on, or supplementing, various points in the
main argument beginning with the `safety first in first drafts'
principles.

There is some overlap and duplication here, and the notes do not add
up to a systematic exposition.  But they have proved to have a degree
of usefulness; and so I am making them available on the Internet now
rather than waiting until I find time to restructure and polish them
(no doubt well into the Millennium). The main headings are in capitals
to aid string searching.  Try for instance COMMAS, STRAY ADJECTIVE,
EQUATIONITIS, GRATUITOUS VARIATION, LEVEL, MATHEMATICAL WRITING, STUCK, WE.


  {\obeylines\parskip=0pt\medskip

  Michael McIntyre
  Centre for Atmospheric Science at the
  Dept. of Applied Math. and Theoretical Physics,
  Cambridge CB3 9EW, United Kingdom.

  Tel (+44-223-) 337871/0; also (+44-223-) 565283, 8-10am and 8-10pm UK time
  Email {\ttt  M.E.McIntyre at damtp.cam.ac.uk}
  }

\goodbreak\bigskip


A TOOLKIT FOR REPAIR WORK BY EDITORS AND THESIS SUPERVISORS (or,
better still, for pre-emptive work by graduate students):  This takes
the form of a table summarizing the acronyms and other symbols that I
have found useful as ringed marks in the margins of draft texts.  They
cover what I have found to be among the commonest traps into which
inexperienced writers fall.  The marginal mark (ringed, and in capital
letters, to distinguish it from suggested changes to the text itself)
points to the reason for the suggested change.  This is an experimental
system and is still under development.  It is not, by the way, meant
to suggest that the writing itself should be peppered with acronyms.
It is simply that there is not much room in the margins of some
manuscripts, nor time, in today's world, to write full explanations of
the same thing again and again.


AA: ambiguous antecedent (to ``this'', ``it'', ``them'', ``ones'',
``former'', ``latter'', etc).  The antecedent, the noun or noun-like
entity indirectly referred to, is not, of course, ambiguous to the
writer;  but it is VERY OFTEN ambiguous to the reader --- to an extent
that even an experienced writer can scarcely credit.  Hard experience
of being misread teaches one to regard any pronoun as potentially
dangerous, and ambiguity as highly probable, unless, perhaps, the
antecedent is the last thing mentioned and the only thing just
mentioned.  The most dangerous pronouns are the demonstrative pronouns
``this'' and ``these'', because of their wide reach, hence wide scope
for ambiguity.  (They can even point forward.)  Consider using LR
instead!  Or consider inserting a noun after the demonstrative pronoun
to make it into a demonstrative adjective, as in ``This paragraph
should be considered most carefully by all writers, especially
inexperienced writers.''

A word processor that made pronouns like ``this'' and ``these'' flash
a warning when typed, or made them turn bright red, would be a
significant aid to lucidity.  In default of such aid, cultivate the
habit of making pronouns flash in your mind's eye; ``this'' and
``these'' should flash the fastest, and ``it'', ``them'', ``ones'',
``none'', etc., somewhat more slowly.



AS: Ambiguous syntax.  For a typical example, string-search
``However it is done'' below.  Commas can be far more important to the
reader's pattern-perception efficiency than inexperienced or careless
writers imagine.  In that connection see also next item:


CP: Comma pair (parenthetical or quasi-parenthetical); use both commas or
no commas; see MORE ON COMMAS (a) below.


EX:  The typical need to be more explicit than you might think;
e.g. string-search ``Neptune'' below.


GV, GPV  etc (formerly EV, EPV, etc): gratuitous variation, perhaps the greatest
single impediment to lucidity, as defined and discussed below: string-search
``literary faults'' or ``GRATUITOUS VARIATION''.


IJ: incongruous juxtaposition, the use of a related pair of words
for two unrelated things,
as with ``dilute'' and ``concentrated'' in ``The experiments concentrated
on dilute solutions.''


IR: incongruous repetition, the use of the same noticeable word for
two different things, especially in the same neighbourhood.


IRW: ``incongruous royal we''.  As defined and discussed below.


LFC: Lazy Figure Caption.  This is an anachronism, a hangover from the days of
metal type, when repeating all or part of a caption was a significant expense.
LFC means that the caption to Fig. n  contains a phrase like ``As in Fig. m'',
or ``...Same as in Fig. m''.  The worst cases are those where the reader has to
turn many pages to find Fig. m  and thus tell what is in Fig. n.  With modern
word-processors there is no excuse --- indeed, it is a discourtesy to the busy
reader --- not to repeat the material in full in the caption of each relevant
figure.  See also RI below.


LR: lucid repetition: consistently using the same word for the same thing, and
not being afraid to repeat it as necessary. ``GV $\rightarrow$ LR''  % ``GV -> LR''
is, in my experience, the ringed marginal mark that is needed most often.


LPR: lucid pattern-repetition, as defined and discussed below.
E.g., by using the repeated word-pattern ``what
helps A... what indulges B'', it instantly signals that two
comparable things are being compared.  It works best when
the sub-patterns A and B have closely similar forms;
Strunk and White call it ``parallel construction''.
String-search ``Vigorous writing'' below.


CO: Ordering needs attention: something has been introduced with
inadequate prior preparation.  The typical result is failure to set
the context that would make the thing comprehensible to the reader.  A
typical fault is an explanation, or terminological definition,
inserted too late, with no attention to the first occurrence of the
term or concept involved.  This is naturally a common feature of first
drafts. Worse still is a disguised ``explanation'' in the form of a GV.

A basic, and indispensable, routine check is find the {\bf first occurrence}
of each important term whose meaning could be ambiguous to the
reader, and to make sure that the required sense is established at
first occurrence.  Even technical terms that one might hope would convey
unique accepted meanings fail to do so, more often than not --- a fact
of life associated with the nature of human communication and
specialization.  The older I get, the more examples of this I find.


NW:  Needless words.  Omit them!  String-search ``Vigorous writing'' below.


P: Plainness.  This could be said more plainly, hence more effectively.


RI:  Redundancy of (critical) information.  Such redundancy is
desirable both for readers' convenience and for robustness to
copy-editing and printers' errors.  Examples include an important
numerical magnitude. A single typographical error can destroy the
information, unless it is mentioned both in the text and in a figure
caption.  It could well be shown on the figure itself as well.  See
also LFC, and string-search ``insurance policies'' or ``agony'' below.


RPC: ``revolting parenthesis construction'' explained below;
string-search ``dislike (like)''.  This seems, so far, to have
infected only part of the scientific literature; its purpose is
the writer's convenience at the reader's expense, and in terms of
communication skills it is a gross amateurism.


SA:  stray adjective or adverb.  This interesting linguistic
phenomenon is important in poetry but dangerous in scientific writing.
String-search ``disabled toilet'' below.


SC:  Simplicity of construction.  The problem is usually a sentence that has
become too elaborate.  String-search ``terrible odds'' below.


SLR, SLPR:  Shortened lucid repetition and pattern-repetition. A version
of LR or LPR in which only a portion of the original phrase is
repeated.  This can satisfactorily substitute for LR provided that no
gratuitous variation is introduced, nor extra words.  There is an
example of SLPR under SIMPLICITY VERSUS ELABORATENESS OF CONSTRUCTION
below.   SLR is well exemplified, on page 4 of {\ttt lucidity.ps}, by the phrase
``experts in bad writing'', which echoes ``experts in the art of bad
writing'' on page 3.


SP:  Standard pattern.  Where usage permits a choice between a word-pattern
having standard (regular) form and a synonymous pattern having irregular form
 --- a good example is ``A is true provided that B is true'' (regular form)
versus ``A is true providing B is true'' (irregular form) ---
it is best to choose the regular form, if only because it helps non-native
speakers.


SS: Side-slip, as in Lucidity Part I, Example 7 (using a mixture of
two word-patterns where a single standard pattern would do):
``Skilled writers distinguish what helps the reader versus indulging
themselves.''  The pattern-variation is gratuitous: there is no reason
against sticking to the one standard pattern ``distinguish A from B":
`Skilled writers distinguish what helps the reader from what indulges
the writer.''  Fowler Two gives some more subtle examples.


SU: Seriously unclear or incoherent, suggesting the possibility of a
serious incompleteness of thought.  (Contrast ``U''; see also ``COHERENCE,
COMPLETENESS OF THOUGHT, CONSISTENCY OF LEVEL'', etc.)  The problem
might be, on the one hand, an extreme case of an explicitness (''EX'') failure,
or perhaps, on the other hand --- for all the reader can tell --- a case
of the writer actually not understanding, or not being aware of, something
crucial.  (See the extreme example under ``LEVEL OF EXPERTISE'' below.)

The writing might, for instance, contain a bare assertion, with no
adequate indication of where the assertion comes from and of the
circumstances or sense in which it might be true.  Or there might be
something seriously incongruous.  For example, the assertion might be
an unqualified assertion of the form ``Fact A implies fact B'' in a
case where fact B is well known to be true exactly, but fact A true
only to some approximation, or in some special limit or other special
circumstance.

Such omissions or incongruities may make the reader wonder whether,
in increasing order of seriousness, (a) the writer is using an
important word without understanding of its dictionary meaning --- is
``implies'' being used to mean ``suggests''? --- or (b) the writer's
elementary sense of logic has failed, or (c) the writer has quoted
something from the literature, such as fact A, without a sufficient
understanding of what is quoted.  Or the writer may be betraying
ignorance of something else that is well known and closely
relevant.  If case (c) seems probable to the reader, then, in the
reader's eyes, the writer, justly or unjustly, could be in danger of
losing all credibility.

   ``The master said, Yu, shall I tell you what knowledge is?
   When you know a thing, to know that you know it, and
   when you do not know a thing, to know that you do not know it.
   That is knowledge.''  --- Analects of Confucius.

See also Leopold Kohr (1993) ``The Academic Inn'', Aberystwyth, Y Lolfa Cyf.,
remarks on ``precision'' (versus mere pedantry) on page 104.



U:  Unclear in some way.  It could be just muddy writing,
forcing the reader into re-reading or guessing.  Or it could be some
incompleteness of thought but, as far as can be seen, not as
serious as in cases of ``SU''.  For instance it could be that
an important point left tacit, so that the reader has no clue
whether the writer appreciates it or not.


UC: Unnecessarily complicated (e.g. sentence needs splitting --- search
``terrible odds'' below.


UP: Unnecessary parentheses (...).  Parentheses have a tendency to
appear in first drafts, marking late explanations and other
afterthoughts.  One usually finds on re-reading that most parentheses
are best eliminated, re-ordering as necessary.  Sometimes they creep
in merely as a sort of punctuational GPV, in which case they can
usually be replaced by standard constructions using semicolons, full
stops or commas.

Parentheses, like italics, are best used very sparsely if at all.
They strongly interrupt the reader.  The interruption is stronger
even than that of a parenthetical pair of em-dashes, which in turn is
stronger than that of a parenthetical pair of commas.  See Fowler Two on
``stops''.

Example: ``An additional plot (not shown) was obtained in order to
check convergence.''  This is not specially objectionable, but one
can still give the reader a smoother ride by writing ``An additional
plot, not shown, was obtained...''



US: Unclear syntax.  Milder cases of AS; the reader can probably get
by with one backtracking.


\medskip

*****************************************************************************


\goodbreak\bigskip

ADVICE TO YOUNG WRITERS on scientific topics, less condensed than the
version in {\ttt lucidity.ps}, and leading to the principles of
`safety first in first drafts':

Lucid, informative writing is the only defensible kind of
scientific writing.  Lucid, informative writing minimizes the
computational load on the reader's pattern-perception machinery.  It
tries to save the reader's time, not the writer's.  It is like good
road signposting, boringly explicit and unvaried from the writer's
viewpoint.  The lie of the land is what interests the reader, not the
signposts as such.  Lucid writing minimizes the clutter of needless words,
gratuitous (pseudoelegant) variations and pattern-variations,
long-winded jargon, over-elaborate symbols, marginally relevant
ideas, and other distractions.  It does not minimize repetition,
other than incongruous repetition, and it does not take lazy short
cuts that miss out essential information.  It achieves conciseness
not only by minimizing distractions, but also by finding an efficient,
coherent order of presentation so that each new point is preceded
by any necessary preparation.

The process of striving for lucidity is a practically indispensable
check on the consistency and completeness of the writer's own thinking.
(Again, string-search ``Neptune'' below.  There are countless other
real examples of the same kind.)

Achieving lucidity, consistency, and completeness of thought is
difficult.  But it is often made far more difficult than necessary by
ignoring the following principles; also string-search
``diarrhoea stage of writing'' below:

SAFETY FIRST IN FIRST DRAFTS: The idea --- after making an overall
plan of the main points in coherent order --- is to keep the mud off
the windscreen from the start.  This may seem boring to the writer,
but it saves everyone's time in the end.  Remember (you can say to
yourself) not only that readers might miss your intended meaning, but
also that the copy editor might change it altogether and make a hole
in your scientific reputation,$^{15}$ unless your writing is, to mix
metaphors, impregnably explicit.  Forget elegance to begin with, and
make lucidity the priority.  If elegance is to be achieved as well, it
can be achieved later.

Write as plainly and explicitly as possible.  (I find that EX,
``explicitness needed'', is the ringed marginal mark most often
needed besides ``GV $\rightarrow$ LR''.)  Eliminate gratuitous
variation and incongruous repetition as you go; this forces you to
decide what to call things.  Establish terminology at first
occurrence, then use it consistently.  If you can't decide what to
call something, put down a dummy word such as  XXX  and globally
replace it later.  Remember Littlewood and forget any worries about
insulting the reader's intelligence.  Err on the side of being
downright pedestrian, exactly as in example~{2} of {\ttt lucidity.ps}.
With modern word processors there is little labour in repeating words
and patterns fully.  Doing so helps to check that you are thinking
clearly, and helps to expose problems of ordering and preparation.
Shorten mainly by replacing long, elaborate words with their shorter,
plainer equivalents, and by eliminating needless words.$^{7}$  If you
must shorten by replacing nouns with pronouns, or by telescoping
repeated patterns, do so with the utmost caution.  These are the most
dangerous kinds of shortening.  Shorten in these ways only if you are
certain it is safe.  If such shortening is not done, it will not
matter.  Don't try to judge whether it is safe to shorten further until
you have had time to forget, re-read, and show the draft to a friend.

\goodbreak\bigskip

PRE-EMPTION OF GV (gratuitous or pseudoelegant$^{8}$) variation):
You might ask, do we want to avoid such variation altogether?  Don't
masters of writing use truly elegant variation?  Yes, I reply,
occasionally and perilously, for special reasons (see ``Masters..''
below).  But again, you say, words have complicated sets of
associations, and many ambiguities, and there just mightn't be a
single word or phrase that carries the required meaning.  We might
want to use two terms to mean the same thing just to signal, or
stimulate, lateral thinking. And again, to be widely understood one
might need to mention accepted terminologies that happen to be
misleading, or otherwise unsatisfactory, for the purpose at hand.  Yes
indeed, I reply, but the worst way to deal with any of these problems
is by sneaking the alternatives in as gratuitous variations.  The
reader's brain needs to know whether it is meant to be fitting one
model or two.  So it is much better to pre-empt the problem.  As
already mentioned, and as Strunk and White might have written,

{\display

        ``Rule 23:  Establish terminology at first occurrence.''

}

Write, for instance, ``We shall use the idea of such-and-such, also
known as so-and-so...'', followed immediately by references or
further explanation, if needed, and thereafter sticking to
``such-and-such''.  In cases like example~{2} of {\ttt lucidity.ps}, it
might be enough to write

{\display

        Ex. 2a. ``Gibbs fringes, i.e., truncation oscillations, are
                 produced by the pseudospectral method but
                 not by the TVD method.'' (And thereafter stick to
                 ``Gibbs fringes''.)

}

It is also idiomatic English to write ``Gibbs fringes, or truncation oscillations,...''
But there is a slight danger of the sense of ``or'' being misread as indicating
alternatives rather than, as here, equivalence.  This danger is greatest
with non-native speakers of English; but good scientific writing must allow for
non-native speakers.

Sometimes a word or phrase needs to be understood in a truly
difficult or special sense.  Nevertheless, some indication of that
sense should be given at first occurrence, and the reader
warned that a full explanation must await subsequent developments.

Explanations at first occurrence can also be used to restrict, or
expand, the desired set of associations, some of which come from one
word or phrase and some from the other.  It can be made clear whether
the words or phrases are to be read as strict synonyms, or as subtly
different.

Masters of writing occasionally use elegant variation, as already
mentioned, for sufficiently strong reasons of euphony, rhythm or
emphasis.  (I am prepared to call such use ``elegant'' rather than
``gratuitous'' or ``pseudoelegant'', without being ironical.)  For
example, there is an inconspicuous elegant variation within Strunk and
White's paragraph under ``Omit needless words'', page 23 in the third
edition.$^{7}$  The variation is not only inconspicuous but is also
justifiable, exceptionally, as contributing to an exquisite control of
rhythm and emphasis.  Try reading the paragraph aloud, in measured
tones such as Professor Strunk might have used in his lectures at
Cornell University:

{\display

   ``Vigorous writing is concise.  A sentence should contain
   no unnecessary words, a paragraph no unnecessary sentences, for the
   same reason that a drawing should have no unnecessary lines and a
   machine no unnecessary parts.  This requires not that the writer make
   all his sentences short, or that he avoid all detail and treat his
   subjects only in outline, but that every word tell.''

}

Notice the strong use of LPR (lucid pattern-repetition) in the second
sentence, where the word-pattern ``no unnecessary...'' is repeated
four times.  Hiding next to the third occurrence of this pattern, the
variation echoes the conspicuous word ``contain'' with the
inconspicuous word ``have''. You might even, at a stretch, argue that
this is not a gratuitous variation, on the grounds that there is a tiny but
genuine difference in meaning --- but that would argue against
the sameness or parallelism signalled by the lucid pattern-repetition.
In any case, the use of the conspicuous word ``contain'' at the
start gives a delicately judged emphasis, slightly slowing the reader
just before the crucial phrase ``no unnecessary words'', which one
can imagine Professor Strunk uttering with some gravity.

It is instructive to try replacing the word ``have'' by the word
``possess'' in the second sentence.  This spoils the lightness of
touch, in two ways.  It produces first the muddiness of an ordinary
gratuitous variation, and second an inept emphasis on what is
unimportant, made worse by an inept assonance (possess, necess..).

Strunk's mastery of writing technique, and good ear for word-patterns,
also lets him get away with the conspicuous variation ``unnecessary''
for ``needless''.  The usual gratuitous-sounding muddiness is again
avoided.  This may be partly because the two words ``unnecessary'' and
``needless'' are not only closely synonymous, but unambiguously so.
The variation would nevertheless seem gratuitous, even if not muddy,
were it not justified by the powerful rhythmic and emphatic effects.
Gratuitous variation from ``unnecessary'' to ``needless'' {\it within}
the second sentence of the paragraph would, by contrast, spoil the
rhythm and emphasis and weaken the whole effect.


The control of {\bf rhythm}$^{8}$ in writing is, of course, another
aspect of the control of word-patterns.  The patterns exist in time as
well as in space.  Rhythm can contribute to, or detract from,
lucidity. Here we have an especially plain example: the
sequence ``...no unnecessary words... no unnecessary sentences... no
unnecessary lines... no unnecessary parts'' almost sets itself to
music.  So does the sentence ``Omit needless words.''


\goodbreak\bigskip

ON BEING STUCK, including writer's block:  Being stuck need not
be a bad thing.  The point is is well explained in a book by Robert
M. Pirsig.$^{22}$  It is an autobiographical psychophilosophical
thriller of, I think, great human as well as intellectual interest.
It contains much insight into creative, `lateral' thinking, the
partly subconscious pattern manipulation and pattern perception
involved in scientific research and scientific writing, and in all
kinds of problem-solving.

About halfway through Pirsig's chapter 26, pp 311--312 in the
original edition, there is a perceptive discussion of how to
cultivate lateral thinking.  Littlewood calls it ``giving the
subconscious every chance.'' [ref.\ {10}, p.196].
Pirsig refers to the typical experience in which a seemingly
unimportant ``little fact'' becomes noticeable some time after
getting stuck on a problem.  It becomes noticeable, at least, if you
are patient enough to give it a chance.  It is ``asking in a timid,
humble way if you are interested in it.'' Pirsig continues, ``Be
interested in it.  At first try to understand this new fact not so
much in terms of your big problem as for its own sake.  That problem
may not be as big as you think it is.  And that fact may not be as
small as you think it is.  It may not be the fact you want
but... often... has friends who are right next to it and are watching
to see what your response is.  Among the friends may be the exact fact
you are looking for.''

The same goes for the problems of writing, and the exact word, or
phrase, or thing to say, that you are looking for.  Part of the trick
is to recognize and overcome `value-rigidity'.  Pirsig goes on to
give the classic illustration of the monkey-trap.

``Stuckness... the predecessor of all real understanding.''
[Near end of chapter 24, p.286 in the original edition.]
Of course one can be getting on with other things, at least part
of the time; the trick is to keep the stuckness at the back of one's mind
and to revisit it now and again.

On writer's block, see for instance chapter 16, p 191 in the original
edition: ``Start with the upper left-hand brick.''

Edward de Bono's books are very good on stuckness etc.  E.g. de Bono (1993).

Pirsig's book also tries to get at the related question of what we
mean by words like quality, integrity, and excellence in the deepest
sense.  Lucidity in writing (or in musical composition or in any other
creative activity) is a natural part of such quality, integrity, and
excellence, even though art may also aim to portray confusion and
incoherence.  The related remarks in {\ttt lucidity.ps}, on our
instinctive interests in coherence and in incoherence, help to make
this understandable from a biological viewpoint.


\goodbreak\bigskip

STRAY ADJECTIVE or adverb, SA: Examples: `disabled toilet', `isentropic
potential vorticity maps'.  The adjective `isentropic' was meant to qualify
`maps', and similarly, `distributions', `gradients', `fluxes', etc.
But, in most readers' minds, it strays on to `potential vorticity'.
It is I who have to take the blame for muddy writing here ---
it was my idea!  What was intended as a neat built-in reminder of
closely relevant ideas ended up as a mere proliferation of terminology:
`isentropic potential vorticity' became merely a longer way of saying
`potential vorticity'.

SA is used in poetry to produce quasi-musical `contrapuntal' effects, when
lucidity is not in question.  Example: ``dogs in the wet-nosed yards'' (Dylan
Thomas: ``Under Milk Wood'').  This marvellous effect probably has no place in
scientific writing.

Another example of SA from our field is `mean mass-weighted potential
vorticity'.  This is a slightly muddy version of the standard, and perfectly
clear, idea of a `weighted mean'.  The adjective `weighted' has strayed on to
the thing whose mean is taken.  A lucid version is `mass-weighted mean
(of the) potential vorticity'.  `Mass-weighted mean'
is explicit; it can signify only one thing in the usual context.  In the muddy
version, `mean (of the) mass-weighted potential vorticity', the `mean' could
be any kind of mean.  In the examples I have encountered, avoidance
of trouble relies on a tacit convention that `mean' is a volume mean, and that
the `mass-weighted potential vorticity' is shorthand for potential vorticity
times mass per unit volume.  Then, of course, the `volume's can be seen to be
irrelevant because they cancel.

In summary, `mass-weighted mean of the potential vorticity' is a clear,
simple, straightforward, standard concept, whereas `mean of the mass-weighted
potential vorticity', taken literally, is a muddier version of what, on
consideration, amounts to the same thing.

This relatively harmless piece of muddiness has sometimes led to a far worse
muddiness, in a typical way.  It is sometimes useful to consider the analogy
between potential vorticity and the mixing ratio of chemical substances.  This
leads, unavoidably, to the idea of `potential-vorticity substance', an
imaginary quasi-chemical
`substance' whose mixing ratio is the potential vorticity.  By
analogy with the total amount of a real substance, one can speak of the total
amount of potential-vorticity substance.  This coincides with what is often
called, muddily, the `total mass-weighted potential vorticity'.  The adjective
`mass-weighted' has now strayed one step further from its original home next
to `mean' (and, by implication, `sum'), and has become stuck even more tightly
to `potential vorticity', insidiously suggesting a repeated pattern of the
form `total something' where `something' is either `substance' or
`mass-weighted potential vorticity'.

So far there is nothing definitely inconsistent.  But, so powerful is
the suggestion from the repeated pattern --- the suggestion of
comparable things being compared or otherwise dealt with --- that it
is easy to begin assuming, unconsciously, that `potential-vorticity
substance' and `mass-weighted potential vorticity' are two names for
the same thing! It is here that something definitely inconsistent has
crept in.  It is logically self-contradictory.
The self-contradiction is underlined by the consideration that `water
substance' would then have to be the same thing as `mass-weighted
water-substance mixing ratio'.  In the context of a volume integral, one would
have to consider that `water substance' is the same thing as `water-substance
mixing ratio times mass per unit volume', or `amount of water-substance per
unit volume'.  By extension to other additive, conservable quantities in
physics, one would have to consider that `energy' is the same thing as `amount
of energy per unit volume', that `mass' is the same thing as `amount of mass
per unit volume', and so on.  This leads to even starker absurdities,
such as ``Energy per unit mass can be destroyed, but not energy
per unit volume.''

The problem comes from {\it seeming} to use the analogy signalled by the use of
the word `substance', yet using that word differently for the two things that
are meant to be compared in the analogy.  This is not a matter of `mere
semantics'; it is an inconsistent, and therefore logically incorrect, use of
words, no more justifiable than an inconsistent, and therefore
logically incorrect, use of mathematical symbols.  It leads to incorrect
conclusions in the same way.  Humpty Dumpty (see below) might object that one
is entitled to define `potential vorticity substance' to be anything one
likes, as long as one doesn't do something mathematically incorrect
--- something incorrect with the equations.  But this supposes,
incorrectly, that mathematics is the only significant language we are using.


\goodbreak\bigskip

EQUATION-BOUND THINKING, OR EQUATIONITIS:
(See also the remarks on ``hypercredulity'' in {\ttt lucidity3.ps}.)
There is a widespread propensity in the physical
sciences to think that mathematical equations and symbols have some
kind of special authority, or numinous quality, in themselves, that
gives them some kind of precedence over the components of other
languages, including words and pictures.  This can lead to an
exaggerated respect for mathematical equations and symbols, accompanied by
insufficient respect for the components of other languages.  Mild
forms of the condition --- let us call it ``equationitis'' for want
of a better name --- include believing that the mathematical
structures are the physical reality, rather than something that
{\it represents} reality more or less closely.  Acute forms include believing
that a particular form of the equations and boundary conditions, with
a particular choice of coordinates and other variables, are the
physical reality.  You might be surprised, but I have actually read,
in draft papers written by bona fide researchers, statements of the type
``This conclusion [about the physical system] holds in isentropic
coordinates but not in pressure coordinates.''  The cogitive illusion
that led to this incautious statement is related, I think, to the
`hypercredulity instinct' discussed in {\ttt lucidity3.ps}.

Indeed the acute forms include forgetting that even a single {\it
mathematical} structure admits an infinite number of mathematically
equivalent, but superficially different-looking, descriptions.  For
instance the Eulerian and Lagrangian descriptions of fluid dynamics
are transforms of each other, but look very different. Even more
different --- as Feynman once put it, ``psychologically very
different'' --- are Hamilton's variational principle and the dynamical
equations to which the variational principle is equivalent.
Professional historians and philosophers of science also seem prone
to missing this point among others --- further discussion
in {\ttt lucidity.ps}.

The acute forms also include forgetting that $ A = B $ implies $ B = A $
and tacitly assuming that the thing on the right hand side CAUSES the
thing on the left-hand side.  This confusion may come from
inappropriate pattern perception; the same pattern
$ A =  B $ has different meanings in mathematics and computer programming.
(There has been much trouble from this in my field of atmospheric
dynamics, at least.  Anyone who happens to be interested can consult the recent
review article by Holton et al.$^{3}$)

Mathematical equations and symbols deserve great respect.  They deserve exactly
the same respect as the components of other languages.  Mathematical equations
and symbols provide us with a set of languages distinguished by
remarkable precision, manipulability, logical consistency, and logical
power, giving them a most remarkable utility for certain purposes.  But this
remarkable, and impressive, power and utility can seduce one into forgetting
 --- for instance --- that physical entities like mass and energy exist
independently of the symbols used to represent them.  One can forget
that the standard phrase ``$E$ is the energy'' is only a convenient
shorthand for saying ``$E$ is the symbol representing the amount
of energy'' or, as the case may be, the amount of energy per unit
mass, energy per unit volume, and so on.  The confusion over
``potential-vorticity substance'' shows that one sometimes needs to be
cautious about using the shorthand.


\goodbreak\bigskip

ON `LATERAL' THINKING AGAIN:

``If you know which facts you're fishing for you're no longer
fishing.  You've caught them.'' --- Pirsig.$^{22}$

Littlewood on the timescales of lateral thinking:

``With a collection of really difficult problems, nothing happens in
a year; much happens in 10 years.''

 ``A. E.  Ingham's yearly pace is snail-like; over 20 years he is
most impressive.''

[ref.\ {10}, p.144]


\bigskip\bigskip

{\bf The following are some still older notes, of uneven quality, and GV and
acronym-ridden. I am not putting these notes forward as examples of
how to write!  But you might find, for instance, MORE ON COMMAS
useful.  I try to bring out why commas are perennially difficult, and
why, for instance, they often come in pairs like the last two.}

\bigskip

Digression: other contrapuntal effects in poetry (cf.\ ``dogs in the
wet-nosed yards'' above) include the famous ``...books in the running
brooks, sermons in stones,...'' from Shakespeare's play ``As You Like It'':

   ``Sweet are the uses of adversity,
   Which like the toad, ugly and venemous,
   Wears yet a precious jewel in his head;
   And this our life, exempt from public haunt,
   Finds tongues in trees, books in the running brooks,
   Sermons in stones, and good in everything.''

Warning!  There are copy editors who would be quite sure that
Shakespeare got it wrong, that he meant  ``Sermons in books, and
stones in the running brooks'', and who would change it without a
second's hesitation (e.g. Mermin 1989, ref. 15; my own experience of
publishing in scientific journals bears this out).  The point is a
serious one.  Whether or not you write like Shakespeare, copy editors
can still play havoc with your intended meaning, rhythm, and emphasis.
Aside from numerous factual changes, I recall one case in my experience
where a copy editor, by inserting two small words, turned what was
intended to be a courteous mention of a colleague's work into what
sounded like disparagement of that work.  To cap this, the change was
unflagged --- there was no warning in the margin of the proofs ---
and when, luckily, I spotted the change and asked for it to be reversed,
the copy editor claimed, or seemed to claim, to have a right to the final
decision.  (Policymakers for some scientific journals and their learned
societies may need to reconsider whether it is the author or the copy
editor who, in principle, carries responsibility for the author's
scientific reputation, or indeed potential legal liabilities.  To be
sure, scientific journals are strapped for cash and can no longer
afford the best copy editing; but this makes it all the more important
that the author, whose reputation is at stake, should have the last
word on questions of meaning and emphasis unless there is a grave
reason against it.)

***************************************************************************

                          FOCUSED WRITING

[An early version, apropos of what lucidity.ps
calls ``reducing the combinatorially large tree of possible internal models''.]

Cleaning up a first draft --- the diarrhoea stage of writing --- to
make it not only syntactically sound and well punctuated, but also
well focused, is a difficult art even if one has already found a good
approximate order in which to deploy and develop the ideas.  Why is
this?  One reason is the aura of associations carried by any word.  It
is these associations that give language its functionality, its
comprehensibility, its power to aid associative thought, and indeed
its ability to trigger intellectual excitement.  But associative power
implies associative ambiguity, hence the constant danger of sending
the reader off in the wrong direction.  Most words pull in many
directions: ref.~{21} gives telling examples, such as the word ``line'',
with its 30 or more different senses.

Focusing, an important aspect of lucidity, might be characterized by
saying that the choice of words, and the way they are put together, is
such that everything points toward the set of associations intended
and does so at the level of precision intended.  All the words,
phrases and symbols to pull together in leading the reader's thought
in the desired direction.  Even the choice of mathematical notation
can be significant for this purpose, if mathematics is involved,
because, whatever certain kinds of purists might say, mathematical
symbols often possess associations beyond their overt meaning.  (Here
is an example to prove the point: ``Let  N(.)  be a linear and  L(.)
a nonlinear function.''  The perverse choice of letters hinders
pattern perception and slows the reader.  The effect is what
psychologists call ``Stroop interference'', as with the word ``red''
printed in green letters.)

In the nature of things, first drafts are usually defocused.  After
all, they are merely the result of getting the ideas down on paper
somehow.  It is all too easy to distract the reader with irrelevant,
or even hilariously incongruous, associations (see ``IR'' below).  More
seriously, it is easy to introduce unwanted, misleading associations
that do not, at first reading, even warn the reader by being
incongruous.  Sometimes these unwanted associations are
extraordinarily hard for the writer to spot, even on a later
re-reading, since the writer's thinking is already channelled in the
direction intended.

The confusion, for the reader, is even worse when the writing is not
EXplicit enough: ``TWO trivialities omitted can add up to an
IMPASSE'' (J.E. Littlewood, ``A Mathematician's Miscellany'').

For the inexperienced writer it is essential, if only for the
foregoing reasons, to persuade someone else to read and comment on a
draft.  I remember learning quickly from such exercises at the
second or third draft of my PhD thesis.  Problems are often best
spotted by a non-specialist reader.  My wife, a nonscientist
(but a superb musician), taught me a great deal.

Only experience, then, including the reactions of others, can teach
the art of focused writing.  But one can take a shortcut past many of
the pitfalls by noticing, from the outset, the following simple
points of technique, of which some have already been mentioned
under ``safety first in first drafts''.  Here is a summary, followed
by further illustrations:


THINGS THAT HELP FOCUSING

{\display

   Explicitness, EX in TOOLKIT: remember Littlewood's ``trivialities''.

   Plainness of language, P in TOOLKIT and one of Strunk's main themes,
      including his injunction to ``omit needless words'', NW.

   Simplicity of construction, SC.

   Lucid repetition (of noticeable words).  Further discussion in lucidity.ps

   Lucid pattern-repetition, LPR.  Strunk emphasizes the important
      type of LPR illustrated by the displayed example above (in the
      sentence after ``Vigorous writing is concise''); he calls it
      ``parallel construction'', or
      ``expressing coordinate ideas in similar form''.  Further discussion
      in lucidity.ps, including the conspicuous analogies in music.

   Coherent ordering, CO: finding a good order in which to develop ideas, so
      that each new point is preceded by any necessary preparation.  Difficult but
      overwhelmingly important, because context is overwhelmingly important
      (cf. ``organic unfolding'', p. 13 of lucidity.ps, also
      ``1-1 lexical fallacy'' in Appendix 2 thereof).  And remember
      ``Rule 23'' above: Explain terminology at first occurrence.

}

[Explanations of the sense in which a term is to be understood, if
needed at all, must be given at the first occurrence of the term
unless there is an exceptionally strong reason against it.
Explanations appearing later, as afterthoughts, signal that the
presentation is out of logical order.  This always occurs in first
drafts, and must be fixed.  A typical symptom is too many
parenthetical insertions.  See ``UP'' in TOOLKIT]

[Cf. the imagined, but typical, dialogue between referee and author on
p. 13 of lucidity.ps --- at least my ten years' experience of scientific journal
editing says that it's typical --- ``But if only the referee had
read on, all would have become clear''... etc., etc.]


THINGS THAT HINDER FOCUSING:

   The antitheses of the foregoing, including:

{\display

   Elaborateness of contruction (see below), and the presence of needless words.

   Gratuitous variation, GV, or ``(pseudo)elegant variation''; see lucidity.ps
      (the opposite to LR, the use of different words for the same thing).

   Gratuitous or ``(pseudo)elegant'' pattern-variation, GPV, the opposite to LPR.
      (This has its mathematical counterpart: recall Littlewood's
      quote about Jordan.)

   Incongruous repetition, IR (using the same word for DIFFERENT things,
      especially in the same neighbourhood)

   Incongruous juxtaposition, IJ (as in ``My pear tree has gone bananas.'')

}

The last two are often relatively harmless, since they usually evoke a
laugh, especially IJ.  There is a chapter in Littlewood's ``Miscellany'' on
``Cross-purposes, unconscious assumptions, howlers, misprints, etc.'',
with some more such gems.

IR increases muddiness, but usually not seriously. ``A noticeable word
used once should not be used again in the neighbourhood with a
different application'' (from Fowler's article on ``elegant'' variation (GV)).
One of Fowler's examples of IR is ``a meeting at which they passed
their time passing resolutions...'' An example I picked up from the geophysics
literature is: ``An important feature ...is the absence of a marked
interhemispheric gradient.  This is in marked contrast to...''



FURTHER NOTES:

EXPLICITNESS (EX):  Underestimating the need for explicitness is
common among the most talented beginners, to whom many things may
seem childishly obvious, especially since they have been immersed in
whatever they are writing about and liable to forget that others have
not.  Littlewood's ``Miscellany'' gives gives an example where
``trivialities omitted'' led to a mistake that impeded a major
discovery.  See the two chapters on John Couch Adams,
Urbain Jean Joseph Le Verrier, and the discovery of Neptune. ``Always
answer the trivial questions of your elders (and it is just possible
even for a bright young man to be overlooking something).''  In this
case the bright young man was John Couch Adams, not only failing to persuade
Sir George Biddell Airy, the Astronomer Royal, to point the telescope,
but also making an actual mistake without realizing it.

It is sometimes useful, up to a point, to think of the reader as a bit
ignorant or forgetful, or just plain stupid --- even a reader as
brilliant as Littlewood.  This of course does not mean being arrogant,
or heavily didactic: the trick is often just to slip in a brief
mention or reminder.  It can be important on the simplest level: for
instance it is unwise to expect the reader to remember that the
symbol  $P$  was defined several pages ago to be potential energy rather
than, say, pressure or anything else.

The reader might have forgotten, and the first occurrence of  $P$  might
be time-consuming to spot several pages back.  When  $P$  reappears it
is best to remind the reader with a phrase such as ``The potential
energy  $P$  is...''.  In other words, do NOT write ``The potential
energy is...'', nor ``$P$  is...'', especially since either of the last
two can act as GVs.  ``Which potential energy?'', the reader might wonder,
on encountering ``The potential energy is...'' --- ``Is it the one
that was called  $P$  earlier?''  As with LPR, one or two well-chosen
words may slightly lengthen the writing but can greatly shorten
the reading, indeed can save the reader whole minutes of scanning
earlier pages dense with text and symbols.

None of this need insult the reader's intelligence.  Shortening the
reader's task is what's important; the reader is busy, and if he or
she doesn't get your message in one second flat, you may have lost your
audience.

Littlewood sums up some of this very well, in the passage referring
to the ``two trivialities'':

{\display

    ``...the great thing is to give the educated reader the chance to
   catch on at once to the momentary point and take details for granted:
   his successive mouthfuls should be such as can be swallowed at sight;
   in case of accidents, or in case he wishes for once to check a
   detail, he should have only a clearly circumscribed little problem to
   solve (e.g. to check an identity: TWO trivialities omitted can add up
   to an IMPASSE).  The unpractised writer, even after the dawn of a
   conscience, gives him no such chance...''

}

PLAINNESS (P):  Here there really are straightforward opportunities for
shortening.  A good start is simply to prune superfluous adjectives
and adverbs, and replace long words by short words wherever possible.
See Fowler Two, ``adjectives misused'' and Strunk and White, ``omit needless
words''.

Try to choose the plainest, most literal words and phrases, and,
again, don't be afraid of repeating them.  Try to avoid vogue words
and fashionable in-talk, as far as practicable.  The plainest terms
are often the most self-explanatory as well, for instance ``vortex
pair'' versus ``translating V-state'' or ``modon''.  (The last two terms
are sometimes used to mean certain particular cases of vortex pairs;
but if such distinctions were important they would need to be spelt
out anyway.)  Another example is ``buoyancy frequency'' versus
``Brunt-V\"ais\"al\"a (-Hesselberg-Milch-Schwarzschild..) frequency''.

Vogue words and in-talk are for talking to, or writing for, inner
groups of colleagues who agree on what they mean; they are part of the
tribal or ``we-they'' mechanism, which if allowed to get out of
hand can contribute to the balkanization of science.  But if one is
writing for publication, why not do science a favour and write to be more
widely understood?

For native English speakers, and others who have mastered
conversational English:  Try to avoid colloquialisms; remember that
some of your readers may be colleagues whose English may be
rudimentary.  Once, when writing to a German colleague I made the
mistake of using the colloquialism ``in my book,..'', meaning
``according to the views I hold,...''.  My colleague asked me when it
was due to be published!

The other simple but important technique is to split sentences.  In
the nature of things, most first drafts have many sentences that are
too long.  Mine certainly do (and I equipped my text editor with
a sentence-splitting macro long ago).   ``When you become
hopelessly mired in a sentence,... do not try to fight your way through
against the terrible odds of syntax.  Usually what is wrong is that
the construction has become too involved at some point; the sentence needs
to be broken apart and replaced by two or more shorter sentences.''$^{7}$

At a more advanced level, sentence
length, and paragraph length, are important devices for controlling
signposting, rhythm and emphasis (e.g. Mermin 1989$^{15}$; Strunk and
White,$^{7}$ near the end of chapter II, rule 22 in the 3rd edition).
So also are the positions of key words and phrases; e.g. search
``Einstein'' below).

There is a myth that plain, straightforward writing must never use verbs in
the passive voice.  It is true that the passive voice makes it more difficult
to write plainly, other things being equal.  But an absolute prohibition makes
little sense.  For example, it is perfectly plain and straightforward to write

{\display

          ``The integral was evaluated numerically by Romberg's method.''

}

This is one of the useful techniques for avoiding too great an intrusion
of the first person.  [String-search WE below.]

There is, by the way, an equally silly myth that one should never use verbs
in the active voice.


SIMPLICITY VERSUS ELABORATENESS OF CONSTRUCTION (SC):  There are some
telling, and hilarious, examples of ``how not to'' in Gregory, M.W.,
1992 (''The infectiousness of pompous prose''Nat 360,11), including sentences
that are disastrously elaborate as well as far too long.  Gratzer
gives some even more hilarious examples (Nature 306, 134, 1983), full of
ludicrous GVs.

Another example is the ``revolting parenthesis construction'' (RPC), as
one might call it, exemplified by

{\display

  ``Anticyclones (cyclones) rotate clockwise (anticlockwise)
    in the northern hemisphere.''
}

This well illustrates that saving a few words is not the only
consideration.  The construction is ``revolting'' literally as well as
figuratively: the reader is forced to turn back.  Compare it with

{\display

  ``In the northern hemisphere, anticyclones rotate clockwise and
    cyclones rotate anticlockwise.''

}

This version is shorter and clearer for the reader, being better
matched to our pattern-perception equipment, and only eight
characters longer for the printer.  Actually, it can be
made only one character longer:

{\display

  ``In the northern hemisphere, anticyclones rotate clockwise and
    cyclones anticlockwise.''

}

This last is an example of a shortened, or telescoped, LPR (SLPR).  Omitting
the second ``rotate'' is not a GPV.  It works as an LPR because the
shortened pattern comes immediately after the full pattern, and there
are no distractions, such as an GV like ``turn'' for ``rotate'', that
might tend to erase the mental echo of the full pattern.

Similarly, one can use shortened LR's (SLRs), again provided that the
mental echo of the first occurrence is fresh in the reader's mind.

The following extract from a referee's report illustrates more
tellingly the false economy of the RPC.  It is a parody, but is by no
means atypical of the real thing:

{\display

   ``I must confess that I dislike (like) the convention of using
   parentheses (not using parentheses) to indicate alternatives.  The
   space saved (taken) does not (does) seem to be worth the way in which
   the busy reader is slowed down (helped on his or her way).  The problem
   tends to be compounded (simplified) when the sentences get too long
   (are kept short).  Quite often one can be almost as succinct, and
   certainly more lucid, by stating one of the alternatives and then
   using a phrase like `vice versa'.''

}

Littlewood's ``Miscellany'' gives a more sophisticated example of a
fundamentally similar thing, from ``an excellent book on
Astronomy''.  The author is writing about galaxies:

{\display

   ``Many of the spirals, but very few of the ellipsoidals, show bright
   lines due, no doubt, to the presence or absence of gaseous nebulae.''

}

Littlewood gives his analysis of ``this rich complex of horrors''
about two-thirds of the way through the chapter on ``Cross-purposes,..''.
(If you look this up, you may notice that the analysis depends
on reading ``due to'' in its time-honoured adjectival sense.)


LUCID REPETITION (LR): Another good example is ``We will be serious if
you are serious.'' (Fowler Two). Repeating the word ``serious'' helps both
lucidity and plainness. It also gives the word an apt emphasis.

As already indicated, LR also applies at long range.  LR means using
the same word for the same thing throughout the same piece of writing,
repeating it as necessary. This makes it easier for the reader in the
middle of the text to pick up relevant things said earlier.

Crucial pieces of information about diagrams should appear in the
text as well as on the diagram and in its caption, using the same
words or symbols.  This kind of LR is also one of the more important
insurance policies against damage caused by printers or copy editors.  See also
RI, LFC in TOOLKIT.  Had I followed this practice in earlier years, a co-author and
I would have been spared the agony caused by the exchange of two superficially
similar-looking diagrams, at the final printing stage after meticulous proof-
checking, that turned a beautiful and impressive connection --- a significantly
close agreement, carefully discussed, between theory and experiment --- into what
looked like the usual sloppy and wishful thinking about ``agreement''; see
note subsequently published in Acustica, 50, 294-5 (1982).  Both diagrams
showed nothing but experimental data, and there was no clue in either diagram,
such as a label, that might have warned the reader.


GRATUITOUS VARIATION, or ``(PSEUDO)ELEGANT'' VARIATION (GV): As already
mentioned, ``elegant'' is Fowler's chosen word, used not approvingly
but ironically:  ``There are few literary faults so widely
prevalent,'' says Fowler, ``and this book will not have been written
in vain if the present article should heal any sufferer of his
infirmity.''  GV still seems to be encouraged today, indeed imposed,
or strongly suggested, in the schoolroom.  ``It is the second-rate
writers'', says Fowler, ``that are ``chiefly open to the allurements
of elegant variation''.  In particular,

{\display

   ``...the real victims, first terrorized by a misunderstood taboo,
     next fascinated by a newly discovered ingenuity, and finally
     addicted to an incurable vice, are the minor novelists and the
     reporters.''

}

I quote this mainly as a reminder of the vast number of examples with which
we are inundated every day, and which might be unconsciously imitated.
Most of these are harmless in themselves --- only a mild form of informational
pollution.  The real trouble with GV is that, in the worst cases, it can
plunge the reader into a quicksand of confusion, forcing multiple
backtrackings, or even forward scans, to guess whether the same thing
is meant or not.  Some examples are given below.  GV is sometimes
defended as a way of alleviating boredom; but it is the writer's
boredom that is alleviated, hardly ever the reader's.  There are rare
exceptions --- string-search ``Masters'' above --- but the only safe
rule, for most of us, is simply to eliminate GV altogether.  This takes a
conscious effort, even for non-addicts, since a given thing may call several
words to mind and it is easy to switch from one to the other inadvertently.

See also Fowler Two on ``which'' versus ``that'', including the lowest
form of GV: see ``that, rel. pron.'', example (e), about two pages on.


PRE-EMPTION OF GV.  Sometimes, of course, the ideal of using
exclusively the same word for the same thing may be unattainable.  But
then one must take pre-emptive action.  For instance there may be
accepted or fashionable terminologies that are illogical
--- as with the variable ``solar constant'' --- but to which
one might have to refer in order to be widely understood.  If alternative
words or phrases for the same thing need to be mentioned, it is often a
good idea to declare them as strict synonyms near the beginning, as
in ``We shall use the idea of such-and-such, also known as
so-and-so...''   and, if possible, stick to ``such-and-such''
thereafter.

Upfront declarations of this kind can be helpful in any case, since
the introduction of more than one word can both enrich, and more
clearly indicate, the desired aura of associations, some of which
come from one word or phrase and some from another.  It can also be
made clear whether the words or phrases are, indeed, to be understood
as strict synonyms, or whether they are to be understood as subtly
different.

What is dangerous is to use different terms indiscriminately in the
absence of an early declaration, since then the reader may wonder
whether or not they are merely GVs or whether a significant difference
might be intended.  In this connection, it is well to remember that
even technical terms, supposedly having a precise meaning, are often
given different meanings in different contexts, or sometimes even in
the same context.  An example of the latter in my research field is the
word ``source''; see my Fermi review, p 369.

The difficulty is added to by the frequency which ``words with a
precise technical meaning escape into the outside world, are mangled
by journalists and politicians, and are then received back'' [by
scientists!] ``in their new and perverted sense'' (Walter Gratzer
again).  See lucidity.ps, \S4.3 on language evolution, and remember
that some users of words, like Sheridan's character Mrs Malaprop, or
Fred in Ronald Briggs' ``Where the Wind Blows'', are looking for
whatever sounds trendy and/or sells more newspapers.  A recent
example is ``symmetry breaking''.  Nowadays this is often used in the
trivial sense of becoming asymmetric merely because the
externally-imposed conditions are made asymmetric --- as compared with
the original, nontrivial sense of becoming asymmetric DESPITE the
externally-imposed conditions being symmetric!  Symmetry breaking in
the second, nontrivial sense now has to be called ``spontaneous
symmetry breaking'' because of the trivialization of the original,
shorter term ``symmetry breaking''.

When writing, it is a good idea to hold in mind the following idea.
Leaving the GVs lying around in your writing is like driving an
unnecessarily wide vehicle through a minefield: it will greatly
multiply the chances of being misunderstood completely by your
referees, copy editors, and readers.  (See also Fowler Two on `false
scent'.)  The best defence is meticulous care over first occurrences,
and use of LR both locally and globally. This in itself increases the
reader's chances of focusing in on the sense in which a word is being
used, even if that sense isn't immediately clear.

Modern word processors can help with these problems.  For instance it
is sometimes worth holding frequently-used words in buffers, so that
repeating the word takes no more typing than using, for instance, a
pronoun.  One can use mark-type-copy to help construct the second half
of a long LPR.  When making a first draft at the keyboard, one can
avoid most inadvertent GV's from the start, by using backward search to
check for the word previously used for a given thing.

JOURNALISM:  With some shining exceptions, routine journalism provides
a daily avalanche of illustrations of how not to write.  Some styles
of journalism, including much sports journalism, seem to make almost a
fetish of using GVs. Although many journalists are capable
professionals, remember that their aim is often very different from
the aim of anyone writing with a serious purpose.  Indeed the
journalist's aim may well be to impart at most a trivial kind of
information in a very familiar context, certainly nothing that
increases the reader's understanding of anything.  The assumption may
be that the reader is more interested in receiving a sort of
comfortable and slightly confused mental titillation, plus a small
amount of information in a very familiar context, such as the number
of goals scored.  I am tempted, quite unfairly to the best journalists,
to quote Oscar Wilde:

{\display

  ``There is much to be said in favour of modern journalism.  By giving
  us the opinions of the uneducated, it keeps us in touch with the
  ignorance of the community.''   [The Critic as Artist.]

}

There is, on the other hand, a new trend toward psychological
professionalism in the major tabloid newspapers, which are in the
business of supranational political and economic power.  Their writers
are masters of technique and are lucid when they choose to be. Their
techniques are worth studying, as are the techniques used by the
highest-paid advertising copy writers.


              MATHEMATICAL WRITING AND COMPUTER PROGRAMMING

It should hardly need saying --- but papers I have refereed or edited
show that it does need saying --- that many of the same principles
apply not only to languages such as English, but also to the symbolic
languages of mathematics and computer programming, and to any other
symbolic language.  Any language used for scientific purposes needs to
be written legibly as well as merely correctly; and legibility depends
on pattern perception.  There is a pseudo-purist or Humpty Dumpty view
that denies all this and says that one can choose any symbols and
arrange them in any way that is logically correct, write any program
that works, and so on.  For example, ``Let  N(.)  be a linear and L(.)
a nonlinear function.''  Get it?  The perverse choice of letters
hinders pattern perception and slows the reader. The inefficiency and
expense of this becomes obvious to anyone dealing with the writing and
debugging of computer programs, whence the notion of ``structured''
programming, which begins with the idea of being legible in exactly
the present sense.

The Littlewood quote about Jordan (lucidity.ps, p.~4 and ref.~16)
illustrates one form of mathematical GPV.  Another is writing a set of
expressions having a common pattern in such a way as to fail to
suggest the pattern.  If you really are a genius, like Jordan, then
you might get away without bothering to fix such things;
but then you increase the risk of becoming a misunderstood genius.

If you can get hold of a copy of Littlewood's ``Miscellany'' (now
reprinted in paperback, in an expanded version edited by B'ela
Bollob'as) it is worth reading beyond the above-quoted passage about
giving, or not giving ``...the educated reader the chance to catch on
at once...''.   Littlewood goes on to give a pertinent example of lack
of plainness in mathematical writing, the kind of thing that arises
simply from a lack of know-how, ``not at all extreme for a draft
before it has been revised by some unfortunate supervisor or
editor.''  The result is that before the reader can spot the point,
``he has to tease his way through a maze of symbols of which not the
tiniest suffix can be skipped...   One slip is practically
certain in this style of writing, generally devil-inspired.''
Littlewood leaves some incidental misprints uncorrected ``for added
realism''.  He then shows how to write out the same example, which is
a proof of the Weierstrass polynomial approximation theorem, in a
``civilized'' way.  [For those interested in the mathematics itself, insert
a factor  f(xi, eta)  into the integrand of the last expression given.]


NOTE ON THE USE OF ``I'', ``WE'', ``INCONGRUOUS ROYAL WE'' etc:
--- more on the Great First Person Debate, and the Great Active
Versus Passive Voice Debate

In a formal publication, aiming to report on a finished, definitive
piece of research, there is a strong case for avoiding the first
person singular, that is, the pronouns ``I'', ``me'', ``my'' etc.  The
reason is that scientific definitiveness ought to be independent of
personal considerations.  The inverse-square law of Newtonian gravitation
holds to the same extent, is testable to the same extent, and is limited
to the same extent, whoever contributed to our knowledge of it.

Some scientists practise total avoidance of the first person. This is
arguably the safest thing to do.  However, there are some common
misunderstandings.  The commonest is that the first person plural
provides a universal remedy, for instance to replace  ``I measured
$g$''  by  ``We measured $g$''  even if the paper has only one author,
or similarly to replace  ``my measurements''  by  ``our measurements''.
These are examples of what might be called the ``incongruous royal
we'', IRW.  The author probably does not want to sound like Queen
Victoria (``We are not amused''), but is inadvertently doing so.  If on
the other hand there are two or more authors, then there is nothing
incongruous.

I suspect that the ``incongruous royal we'', which is absurdly
popular, arises from confusion with a legitimate, and entirely
different, use of ``we'' that is beautifully explained by Ziman.  It
could perhaps be called the ``diplomatic we'' of scientific writing.
This is the use of ``we'' in the sense of ``you and I, dear reader'',
or, in the case of multiple authors, ``all of us including you, dear
reader''.  It is perfectly natural in the context of something,
usually of a theoretical or computational nature, that the reader
might be expected to be able to verify for himself or herself at least
in principle.  The typical example is a statement of the type ``After
a few lines of manipulation, we find that...''.  Used skilfully, this
can be made part of the persuasiveness, and avoidance of egotism, that
characterizes all good scientific writing.

Of course you can play safer and use, to nearly the same effect, the
non-egotistical first person singular:  ``...one finds that...''.  Or
you could even use ``...it is found that...''.  The latter very
slighly reduces plainness by using the passive voice ``is found''
instead of the active voice ``find''.  It is also uncomfortably close
to the incongruity and muddiness of the unattached participle:
``Manipulating such-and-such, it is found that...''.  Does ``it'' do
the manipulating?  The non-royal ``we'', and equally the ``one'', are
neater and clearer in this case.  They can also help to involve and
persuade the reader by making the tone a touch less austere, if that's
what you want.

There is another diplomatic ``we'' meaning ``all of us'', that is to say
the relevant scientific community.  Example: ``Our understanding
of such-and-such has advanced in such-and-such a way.''

If one is prepared to live a little more dangerously, then there is
another, in my view natural, use of the ordinary first person,
especially if it is done with a light touch.  This is the occasional
statement that is genuinely personal.  The most elementary example is
in the Acknowledgements section.  One can appropriately write ``I
thank so-and-so for helpful correspondence.'' There are other
examples, as when offering an intuitive speculation or opinion, as
opposed to stating that something has been definitely established:
``For what it is worth, I think that such-and-such will prove important.''
This can be apt, for example, in the review-and-forward-look type of
article.  With a little care you can do it without letting your ego
get in the way.  There is of course a fine judgment to be made here,
as to whether anyone is likely to be interested in what you think.
If the review article was an invited one, then you might be justified
in assuming that someone is interested.

On the active or passive voice of verbs, there is a silly debate on
forbidding or condemning the one or the other.  Why should a good
craftsperson throw away one out of two perfectly good verbal tools?
The main danger with passive verbs is not so much the passive voice
itself, but the temptation to use a passive verb with a pronoun like
``it'' as subject.  The construction ``...it is found that...'' can
work well, as above.  But beware: every time you use a pronoun, you are
risking ambiguous antecedent, AA --- one of the most insidious risks,
to which the writer is apt to be most blind.  The other example given
above carries no such danger.  Using the passive voice is perfectly
neat, perfectly plain, and perfectly sensible:  the incongrous royal
``We measured $g$'' can perfectly well be replaced by ``$g$ was measured''.

Other sillinesses, such as ``Never start a sentence with `But' '', as
I just did, or ``never split an infinitive'', seek to reduce the art
of rhythm and emphasis to rules of thumb that are unlikely to be
univerally applicable.  Replace such rules by ``Think twice before
splitting an infinitive'', etc.  Starting a sentence with ``But'' can
be rhythmically abrupt, and therefore useful as an emphatic device if
used sparingly and at the right moment.  Yes, it is a good idea to
think twice before shouting.  The same goes for splitting infinitives,
as in ``to BOLDLY go''.

For musicians: split infinitives are the consecutive fifths of English,
sort of.



                      FURTHER MISCELLANEOUS NOTES

(These sketchy notes do not, of course, claim to replace Strunk-White,
Fowler Two and other such classics.)

RHYTHM AND EMPHASIS.  The control of rhythm and emphasis is a
fascinating but tricky art; see also Mermin$^{15}$).  Much of that art
concerns the use of paragraphing, ordering, and punctuation without
doing violence to syntax as in, for instance, ``The cat, sat on the mat''.

Fowler Two has a wonderful article on {\bf rhythm}; see also also note {12}.

Enthusiastic beginners sometimes assume that they can use italics for
emphasis all the time.  One soon notices that this comes across to
the reader like continual shouting.  Some journals, including Nature,
enforce the discipline of not allowing italics for emphasis at all.

A phrase enclosed by a parenthetical comma-pair, suitably timed, is
one of the useful techniques for emphasis:

{\display

   ``I am not, in any way, impressed by these unchecked numerical results.''

   ``The cat did not, at any time in recent memory, sit on the mat.''

}

Both examples are syntactically correct, and emphasise the word
``not'' without using italics.

Many copy editors today would succeed in recognizing the rhythmic
clumsiness of ``The cat did not at any time in recent memory sit on
the mat.''  But some would change it to the syntactically absurd
``The cat did not at any time in recent memory, sit on the mat.''
See note on ``A does B'' below.

MORE ON COMMAS.  There are far worse cases where the copy editor
might change your meaning altogether.$^{15}$  The risk of such damage is
another reason for putting in the commas yourself, as well as writing
as lucidly as you can; and it is best to put them in too generously
than too sparsely.  They tend to be too sparse in any case, in first
drafts.  The chances are that the removal of a few commas will be less
damaging than uncomprehending insertion by someone trying to follow
style-manual rules by rote.  The same goes for hyphens, if your
journal happens to be going through a hyphen-inserting phase.  It is a
good idea to get hold of the journal's style manual, as well as to
skim recent issues, to see which way round the journal is doing
things.  Nowadays, reference to the Chicago Manual of Style
(full reference at end) can be especially useful since many
copy editors have been told to regard the Chicago Manual as
authoritative.  See also \S\S2--6 of Strunk and White, and Fowler Two on
``Stops''.

The difficulty with the comma is that it is a multiple-valued symbol.
By firmly-established convention, it can have any of several different
syntactical meanings, governed by context.  It can sometimes have more
than one of those meanings simultaneously.  In some, but not all,
cases the commas are optional, and are available to use or omit
for purely rhythmic purposes.  Note for instance the following examples,
the first of which has already been referred to under RHYTHM AND EMPHASIS:

(a) Commas can begin or end a parenthesis not otherwise marked.  Such
parenthetical commas, like those surrounding this phrase, naturally
come in pairs (like parentheses themselves).  At least they do so
unless one member of the comma-pair is implicit, as with
THIS phrase beginning ``as with''.

(b) Commas in English can distinguish restrictive from non-restrictive
qualification, the latter being a special case of the parenthetical use,
as in
``The mat, which was under the cat,...'' (non-restrictive, comma
before ``which''; it is presumed that we already know which mat is
in question).  Contrast
``The mat that was under the cat...'' (restrictive, no comma, ``that''
instead of ``which''; the qualification is part of the
definition of which mat is in question).  This is further explained in
Strunk and White, under Rule 3, and in Fowler Two under ``that, rel. pron.''

(c) Commas can be used as simply as separators.  The modules separated
can be, for instance,

{\display

   independent clauses, e.g., ``A did B, and C did D''  or  ``A did B, but
      C did D'',   [comma is optional, available for rhythmic control],

   certain other modules such as opening adverbs,
      e.g., ``However, it is done..'' vs. ``However it is done,..'',

   items in a ``serial list'' (Strunk and White) or ``enumeration'' (Fowler Two)
      e.g., a list of adjectives on the same level, or ``coordinate
      adjectives'', as the Chicago Manual calls them; e.g., ``large,
      scaly, ferocious-looking Komodo dragon''.  A comma before the
      adjective ``Komodo'' would be incongruous: the structure is
      a two-level nesting of adjectives:

      %     {large, scaly, ferocious-looking {Komodo {dragon}}}

      $\{$large, scaly, ferocious-looking $\{$Komodo $\{$dragon$\}\}\}$

}

In this last example (with apologies to the admirable Douglas Adams),
each group enclosed in braces has the character of a noun: it is a
definite ``something''.  By convention, the use or lack of commas
shows the nesting explicitly: the convention says that these commas
act both as separators and also as a kind of glue, almost like hyphens.

Serial lists of nouns --- as in ``dragons, crocodiles, alligators, and
iguanas live here'' --- are usually separated by commas, though there
are two standard conventions on whether there should be a final comma
before the final ``and''.  The example just given follows what is
sometimes called the ``Oxford'' and more commonly the ``American''
convention, well established in the USA and now gaining ground in the
UK.  This convention (Rule 2 in Strunk and White) makes the final
comma the normal practice.  When the convention is followed
consistently, it works well and saves all kinds of trouble.
Fowler's article on ``stops'' (COMMA, subsection B) shows why.

In good modern written English, commas are seldom used to separate subject
from verb, nor verb from object.  The standard pattern is ``A does B'',
not ``A, does B'', nor ``A does, B'', nor ``A, does, B''.  In conversational
passages in novels there are a few standard exceptions to this rule,
of the form ``A said, B'', where B is a string of spoken words enclosed
within quotation marks.  Somewhat similar are a few exceptions of the type
``The trouble is, he's lazy'' and ``Those who can, do.''  These are
seldom important in scientific writing.

Great writers can, and sometimes do, break the usual rules because
their control of word-patterns is powerful enough to permit them to
set their own versions of the rules.  Emily Bront\"e's {\it Wuthering
Heights}, with the original punctuation, is a classic example.  Of
course a powerful writer will tend to apply the altered rules
consistently, and thus intelligibly.


USE OF KEY POSITIONS, such as opening and closing sentences. These
need special care because they leave specially strong echoes in the
reader's mind.  They are precious opportunities for signalling the
most important points, those deserving special emphasis.  Try not to
waste such positions on anything else.  Take an opening sentence like
``The Earth's atmosphere is constantly in motion.'' Does anyone need
to be told this?  It seems to signal that the writer has nothing
interesting to say.  With ten other things to read by tomorrow,
I am likely to go straight to the next thing to be read.

An opening sentence that sends the opposite signal is that of Einstein's 1905
paper on the photoelectric effect, one of the celebrated triplet of papers in
Annalen der Physik Vol. 17.  This is the paper beginning on page 132.  A single
sentence touches the key to a whole new line of thought, by pointing to
a fundamental conflict --- a deep-rooted, far-reaching difference of form,
or difference of kind --- between the theoretical concepts then being used
to describe matter on the one hand and radiation on the other
(translation below):

{\display

   ``Zwischen den theoretischen Vorstellungen, welche sich die Physiker
   \"uber die Gase und andere ponderable K\"orper gebildet haben,
   und der Maxwellschen Theorie der elektromagnetischen Prozesse im
   sogenannten leeren Raume besteht ein tiefgreifender formaler Unterschied.''

}

The paper goes on to argue that studying the photoelectric effect, in
which matter and radiation interact, could open the way to radically
new insight.  The rest is famous history, but one imagines that even in
1905 any knowledgeable physicist would at once feel a spark of interest,
even if not conviction, and would want to read on.

Note how the position at the end of the sentence is used for emphasis.  This
``punch-line'' effect probably works in any language, whenever syntax allows it.
Note further how the control of rhythm and emphasis works within German
conventions.  In German, and in some other continental languages, commas do
not signal restrictiveness or non-restrictiveness.  (Search MORE ON COMMAS
above.)  Here the context shows that the clause between commas is restrictive,
precluding the corresponding use of commas in English.
Therefore in English the control of rhythm would need to
be handled differently.

It is an interesting exercise to consider what this might involve.
The literal structure of the sentence can be sketched in English as
``Between, on the one hand, the theoretical concepts that physicists
have developed regarding [matter] and, on the other hand, the Maxwell
theory of [radiation],... there exists...''.  (Literally, ``...concepts
that physicists have developed/shaped for themselves'', but in English
the reflexive ``themselves'' seems both cumbersome and superfluous.)
For a complete translation it seems necessary to reverse the order, putting
the ``punch line'' first --- the second-best choice --- in order to make
rhythmically tolerable English.  The sentence is already elaborate,
and on top of that there seems to be no single English word for
``tiefgreifender'' (''deep-reaching or touching'', with hints of profound
significance).  Here is the best I can do for the moment, with valuable help
from my colleague Dr Oliver B\"uhler:  ``A deep-rooted, far-reaching and
essential difference exists between the theoretical concepts
developed by physicists regarding gases and other material bodies on
the one hand, and the Maxwell theory of electromagnetic processes in
so-called empty space on the other.''

(The expansion of ``tiefgreifender'' into ``deep-rooted, far-reaching
and essential'' helps to put the emphasis back where it belongs, by
slowing the pace at the outset.  Rhythm and emphasis are inseparable!
Einstein's sentence contains no German counterpart to the explicit
signposts ``on the one hand'' and ``on the other''.  But in the
English translation they seem necessary for safety since, on top of
the rule forbidding restrictive commas, English lacks some of the
bracketing and nesting conventions available in German.)

Other key positions to be used with special care are the last
sentences of paragraphs, of sections, and of the whole paper.

(A classic example is the last sentence of the Crick and Watson DNA paper:
``It has not escaped our notice that the specific pairing we have
postulated immediately suggests a possible copying mechanism for the
genetic material.'' -- except that, on checking (Nature, 25/4/53, p.737)
I find that it ISN'T the last sentence --- though they do make it a lone
paragraph.)

COHERENCE, COMPLETENESS OF THOUGHT, CONSISTENCY OF LEVEL.  There are
several questions of level.  They are aspects of what J.K. Galbraith
has called the ``completeness of thought'' that characterizes masterly
writing.  (Galbraith, an acknowledged master, admits that he finds
writing difficult.)

The LEVEL OF PRECISION intended has already been mentioned in
passing.  One needs to be clear how fuzzy one is.  When exploring
unfamiliar territory one may well be dealing with a large range of
levels of precision, from vague intuitions and heuristic guesses, or
``hunches'', all the way to clear-cut things expressible
mathematically.  Well-focused writing imposes order on this chaos,
and gives the reader a chance to see what level or levels are
being referred to at a given stage in the exposition.

Methods of signalling the level, and changes of level, include the
simplest method of explicit statement.  For instance you might want to
tell the reader, at the first occurrence of a certain word, that it
will be used only in a heuristic sense.  Or you might want to say that it
will be used in a precise sense, whose definition you make clear
somehow.  Other ways include the use of ``signpost phrases'' such as
``Broadly speaking,...'', ``Roughly speaking,...'', ``To be
precise,...'' or ``More precisely,...''.  For instance you might want
to give the reader a quick preliminary idea of what is to be
introduced, and then immediately shift level and make it more precise
for those interested.  This is fine provided you make the shift of
level clear.

Good example from our own field: ``Broadly speaking, the invertibility
principle for potential vorticity states that knowledge of the potential
vorticity and surface temperature implies knowledge of the other dynamical
fields.  More precisely,...'' [and go on to explain for instance that it is the
isentropic distributions of potential vorticity that are relevant, that the
mass under each isentrope is prescribed, and that there is a small but
irreducible ambiguity due to the ``fuzziness of the slow quasi-manifold''].

I have always liked the quotation from the preface of G.K. Batchelor's
(1953) book on turbulence, in which he makes it clear at the outset
that this difficult subject is going to be discussed at more than one
level, and why:  ``The manner of presentation has been chosen, not
with an eye to the needs of mathematicians or physicists or any other
class of people, but according to what is best suited, in my opinion,
to the task of {\it understanding the phenomenon}.  Where mathematical
analysis contributes to that end, I have used it as fully as I have
been able, and equally I have not hesitated to talk in descriptive
physical terms where mathematics seems to hinder the understanding.''

Note, incidentally, the beautiful control of rhythm, which lets Batchelor
get away with two rather long sentences.  Beginners beware!  Also,
this is also one of the few places where ITALICS FOR EMPHASIS
seem justifiable and effective.  The italicization works because it is
used only sparingly, as well as aptly, as you will see if you read the book.
Personally, I have noticed that at least nine out of ten of my italicized
words revert to roman at the second or third draft.


THE LEVEL OF EXPERTISE asked of the reader is another question of
level, and completeness of thought, that the writer must keep in mind.

Here, to make the point, is a rather extreme example of ``how not to'',
taken from the draft that began ``The Earth's atmosphere is
constantly in motion.'' (Yes, it was an actual draft, one that I had
to fix up in the course of work for a Research Council.)

``Weather describes the day-to-day variations in rainfall,
temperature and pressure in an area; climate is the longer term
average of conditions resulting from those weather patterns...  Many
physical processes, including atmospheric ones, come into the
category of nonlinear dynamical systems.  Chaos Theory... suggests
that seemingly chaotic behaviour can be deterministic, and that
aspects of it can therefore be modelled and predicted.'' [sic]

The tacitly assumed level of expertise fluctuates from
that of a small child to that of a fairly sophisticated adult
thinker. The writer gives the impression of believing that there is a
need to define ``weather'' but not, for instance, to define ``chaotic''
or ``deterministic''.

In this case the trouble was, as you may have noticed, that the
writer had little understanding of the things being written about.
Nor was the thought complete even on the small child's level.  If
``rainfall, temperature and pressure'' are meant to be definitive of
``weather'', then has ``wind'' been deliberately excluded?  If ``climate''
is just the time average of ``weather'', couldn't the reader be
informed of the only nontrivial aspect of this, namely what timescale
or timescales the writer thinks we should average over?  To cap it
all, the only nontrivial bit of information that we are given
happens to be dead wrong, missing the most basic point about
deterministic chaos by saying that it is predictable.  This is an
unusually stark example of incompleteness of thought (SU in
TOOLKIT).  Before laughing too loudly, consider how easy it is to
commit lapses oneself, the more so under today's pressures.


                   LEARNING FROM GREAT WRITERS

It is interesting notice the techniques of the great writers of
scientific prose, indeed the great writers in all genres.  Fowler's
article on {\bf rhythm} gives a wonderfully moving example from the
Authorized Version of the English Bible. Emily Bront\"e's classic
novel ``Wuthering Heights'' is an interesting example; for instance
Bront\"e breaks many of the usual rules on punctuation, but in a
consistent way and always to good purpose, carrying conviction through
the power of her imagination and the power of her instinctive control
of word-patterns. (If you had mastery, or genius, of that order, you
surely wouldn't be reading these humble notes.)

The modern novelist and thinker Ursula Le Guin is another writer of
great vision and imagination and, for us, timeliness (and she
breaks the rules too, to a lesser extent).  Her collection of essays
``Dancing at the Edge of the World'' (1989, New York, Harper and Row)
is interesting in that it gives, simultaneously, almost in the style
of Unix ``diff'' output, the original and revised versions of her essay
entitled ``Is Gender Necessary?''.  One by-product is a view over the
shoulder of a master writer: some instructive dissections of writing
technique (and useful tips on how to avoid too many ``he or she''s).
The essay discusses the wonderful novel ``The Left Hand of
Darkness'', which I have also read along with her other great novel
``The Dispossessed'', of special interest to anyone interested in
science and humanity.

See also the many examples discussed in the book by Alter.$^{11}$


\goodbreak\medskip

REFERENCES AND SUPPLEMENTARY NOTES
\nobreak\medskip

{1}. Ziman, J. M., 1968:  Public Knowledge: the Social Dimension of
Science.  Cambridge University Press, 154 pp.
This little book is strongly recommended if you
want to understand fully the importance, for scientists, of learning
to write well.  You don't have to read the whole book to see the
point.  Ziman also offers much insight into how science works, and
what scientific knowledge is.  There are specific implications for
writing technique, such as the use of `we' to mean `you and I, dear
reader', as distinct from the `incongruous royal we' (see above).

Ziman argues that scientific knowledge is not what has been discovered
by any individual, but what has also been communicated and has withstood
the scrutiny and testing of that individual's `jealous peers', especially
the most skeptical but capable peers --- as with Einstein's photoelectric
prediction and Millikan's attempt to disprove it experimentally.


{2}. Medawar, P., 1982:  Hypothesis and imagination.  In {\it Pluto's
Republic}, Oxford, 351pp.  Also in {\it The Art of the Soluble},
London, Methuen (1967).
A spirited defence of Popper as well as of the role of imagination.
``The belief that great discoveries and little everyday discoveries
have quite different methodological origins betrays the amateur'', p.124.

{3}. Holton, J. R., et al., 1995: Stratosphere--troposphere exchange.
Reviews of Geophysics, 33, 403--439.

{4}. Rock, I., and Palmer, S., 1990:  The legacy of Gestalt
psychology.  Sci. American, December 1990, 48--61.

{5}.  Marr, D. C., 1982:  Vision: a computational investigation
into the human representation and processing of visual information.
San Francisco, Freeman, 397pp.
``Was the foundation of modern computational vision... still the Old
Testament of the subject'' --- Colin Blakemore.  For more recent work
see, e.g.,
Blakemore, C. (ed.), 1990:  Vision: coding and efficiency.
Cambridge University Press, 448pp.

{6}. Corballis, M. C., 1993: Taking different sides (review
of Hellige, J. B., 1993: Hemispheric Asymmetry:\ What's Right and
What's Left, Boston, Harvard University Press, 396pp.)  Nature 363,
682--683.
Contrary to popular belief, but not surprisingly, both hemispheres
of the brain are involved in language processing.

{7}. Strunk, W., White, E. B., 1979:  The Elements of Style (3rd edn).
New York, Macmillan, 92pp.
This wonderful old concise, lucid, pithy handbook is useful to anyone
who wants to learn to write well for any purpose.  I think it is the
minimum required reading for most writers of PhD theses and early
research papers, if only as a check that you possess the most basic
know-how of effective writing.  The first part, written by William
Strunk, used to be called, with a certain emphasis, `The {\it Little}
Book' at Cornell, where Strunk was professor of English.  It starts
with a quick lesson on the elementary rules of syntax and punctuation,
and goes on to give valuable tips on how to achieve strength and
conciseness.  It does all this, in the edition currently in print, in
thirty-three pages.  It would have saved me much time had I discovered
it earlier in life.

{8}. Fowler, H. W., 1983:  A Dictionary of Modern English Usage, 2nd
edn, revised E. Gowers.  Oxford University Press, 725pp.  I now call
this great classic ``Fowler Two'' to avoid confusing it with what is
called the 3rd (1996) edition, ``Fowler Three'' let us say.  Fowler
Three is an entirely different work with an entirely different aim,
perpetuating Fowler's name but not his work.  Fowler Three (and, even
more, Crystal$^{21}$) is useful for catching up on recent changes in
vocabulary and usage in our hectic world.

For depth of insight, for intuitive grasp of how language works
and how to use it well, Fowler Two is still hard to beat.  It is
distinguished for its penetrating discussions of fundamentals.
See for instance the article on {\bf elegant variation}, a term
that Fowler uses ironically and disapprovingly: ``There are few
literary faults so widely prevalent.''  This is what I now
call {\bf gratuitous variation}, GV, experience having taught me that
the irony in Fowler's use of the word ``elegant'' is often missed.
Beyond this, Fowler Two is a treasurehouse of deep insight into the
workings, and evolution dynamics, of the English language.  It is an
antidote both to pedantry --- see the article on {\bf split infinitive}
--- and also to what Walter Gratzer$^{14}$ called the ``slop of
overflowing neologisms, pleonasms, malapropisms, clich\'es and
unattached participles'' that we live in today.  Two examples among
many are the wonderful articles on {\bf rhythm} and {\bf grammar}.
``It is... despite the grammarians'' [in the Procrustean clutch of the
``ruling language'', Latin], ``not thanks to them, that over the
centuries our language has won ease and grace by getting rid of almost
all its case-inflections; some day perhaps this good work will be
completed, and we shall no longer be faced with the sometimes puzzling
task of choosing between {\it who} and {\it whom}.  But it is going
too far... to say, as Orwell$^{20}$ said, that grammar is of no
importance so long as we make our meaning plain.  We have developed
our own `noiseless' grammar, as Bradley called it...''

{10}. Littlewood, J. E., 1953:  A Mathematician's Miscellany.
Paperback re-issue with further material, edited B.
Bollob\'as 1986, Cambridge University Press, 200pp.
A frank, and sometimes hilarious, inside view of genius.  Littlewood was
a wide-ranging scientific thinker as well as a great mathematician, and
much of this book was written for a non-specialist audience.

{11}. Alter, R., 1989: The Pleasures of Reading in an Ideological Age.
London/New York, Simon and Schuster, 250~pp.
This book vividly illustrates how word~patterns and their deeper
connections function in great literature, including many fine examples
of rhythmic effects. The book is also a literary expert's riposte to
cultural~relativist extremism, emphasizing the coherent as well as the
incoherent aspects of great literature.


{13}. Gregory, M. W., 1992:  The infectiousness of pompous prose.
Nature, 360, 11.

{14}. Gratzer, W., 1983: Usage and abusage.  Nature 306, 134.
Review of Fowler Two and appeal for its wider use.

{15}. Mermin, N.\ D., 1989:  What's wrong with this prose?
Physics Today, 42(5), 9--11.
An appeal against the more idiotic kinds of copy-editing.

{16}. Klauder, J. R., 1972:
Magic without Magic (John Archibald Wheeler Festschrift).
W. H. Freeman.
See page 482; the quotation about genius is attributed to Wheeler.

{17}. This file is at
{\ttt http://www.atm.damtp.cam.ac.uk/people/mem/oldftp/lucidity-supplem.txt}.
The file size at the time of writing is about 100 Kbyte.

{19}.  Alexander Goehr, personal communication.

{20}.  Orwell, George, Politics and the English Language.  (Inside the
Whale.)

{21}.  Crystal, D., 1995: The Cambridge Encyclopaedia of the English
Language London, BCA, by arrangement with Cambridge University Press,
489~pp. Among other riches this lavishly illustrated book contains
many examples, well cross-referenced, bringing out the importance of
word-patterns and their functioning. For instance page 161 has a large
diagram showing at a glance the present-day ``collocational range'',
or cloud of possible usages and associations, surrounding the word
``line''.  There are ``nearly 150 predictable contexts..., which can
be grouped into 30 or so senses'', highlighting the ambiguity of the
word ``line'' when removed from the word~pattern it is used in:
``high-voltage line'', ``brought into line'', ``what line to take'',
etc. etc.

{22}. Pirsig, R., 1974: Zen and the Art of Motorcycle Maintenance. Bodley
Head, 412pp.

*****************************************************************************

\bigskip

FURTHER NOTES AND REFERENCES  (see also lucidity.ps)

Day, R.\ A., 1989:
How to Write and Publish a Scientific Paper, third edition.
Cambridge, University Press, 211pp.
By an experienced biologist and journal editor.  Lively
and informative about scientific and publishing conventions; not much about
writing technique as such, apart from the excellent advice to keep things
simple, and to read Strunk and White.  Reviewed J.\ Fluid Mech. 207, 629.

Chicago, University of, 1993:
The Chicago Manual of Style, 14th edn.
Chicago, University Press, 921pp.
See also Mermin (1989), ref {15} above.  The Chicago Manual is  %^{15}
being increasingly adopted as the definitive reference for editorial offices.
Most of it looks very reasonable, exceptions being the rules on numbers in
text (spelt vs.digitized, see Littlewood) and the illogical (and misnamed)
``American Style'' of punctuation in the presence of quotation marks (see
Fowler Two on ``stops'').  But one can live with these problems if forewarned.
The main problem is that the underpaid copy editors charged with implementing
the Manual's recommendations may not understand the subtler points, and
can all too easily do substantial damage to a carefully written manuscript.
A careful author may find it useful to quote from the Preface: ``Although the
purpose... remains to establish rules, the renunciation... of an
authoritarian position in favor of common sense and flexibility has always
been a fundamental and abiding principle.  At the heart of that principle
is a respect for the author's individuality, purpose, and style, tempered
though it is with a deeply felt responsibility to prune from the work
whatever stylistic infelicities, inconsistencies, and ambiguities might
have gained stealthy entrance.''  Another good idea, when dealing with
copy editors, is not only to be meticulously polite but also
to suggest to them upfront that the authors have taken exceptional care
to find the best wordings, emphases, punctuation, and shades of meaning and
that many of these shades of meaning depend on specialist technical knowledge.

I was relieved to see that the rules on ``appositives'', or nouns in apposition,
are sensible: the Manual does allow one to write ``the potential energy $V$''
without commas around the $V$, as in ``Zadok the priest'',
contrary to what some style manuals might say.
The rule is another case of ``restrictive sense implies no comma(s)'', as in the
excellent ``..., which'' versus ``... that'' convention described in
Fowler-Strunk-White; see COMMAS above.

Higham, N.\ J., 1993:
Handbook of writing for the mathematical sciences.
Philadelphia, Society for Industrial and Applied Mathematics, 241pp.
Specially useful features:
 a chapter for non-native English speakers,
 a chapter giving excellent advice on how to prepare and give a talk
   [see also Nature 272, 743 (1978)], and
 a final chapter and appendices on using TeX, LaTeX, Emacs, Internet
   and simple Unix workstation tricks, with, e.g., a clear-looking table
   of commonly used Emacs commands.
Very thorough bibliography, though with Littlewood a surprising
omission.  Shows respect for Fowler Two and for Strunk and White,
and gives several other references that are probably worth looking at,
including Bernstein 1971.  Decent instinctive view of writing technique,
with much good elementary advice, but some dogmatism and some lapses ---
including an ill-considered, and marvellously muddy, statement that the
opposite to gratuitous (pseudoelegant) variation is incongruous repetition.
Overestimates the skills of today's copy editors --- but suggests the
good idea of using yellow stick-on notes to thank copy editors on the
occasions when they get things right.

Terrible gaffe over pronunciation of ``TeX''!  Donald Knuth insists that the
"X", a Greek Chi, be pronounced as in "J. S. Bach" or as in Scottish "loch".

Bernstein, T.\ M., 1971:
Miss Thistlebottom's Hobgoblins:\ the Careful Writer's Guide to the Taboos,
Bugbears and Outmoded Rules of English Usage.
New York, Farrar, Straus and Giroux (1971); reprinted London, Simon and
Schuster 1984.
ISBN 0-671-50404-5.
This sounds marvellous, but I have been unable to get hold of a copy.
Not in local libraries, and local bookshop says it's out of print.
Second-hand book search in progress.  Probably on the lines of Pinker's
chapter on `The Language Mavens'.

de Bono, E., 1993: Water Logic.  London, Viking/Penguin, 191pp.
Nice approach, as with other de Bono books, to releasing
mindsets (handling STUCKNESS, cf Pirsig$^{22}$).

The full reference for my Fermi review is
Proc.\ Internat.\ School Phys.\ ``Enrico Fermi''
CXV Course, {\it The Use of EOS for Studies of Atmospheric Physics,}
edited by J.\ C.\ Gille and G.\ Visconti.  North-Holland (Amsterdam,
Oxford, New York, Toronto), pp.\ 313--386 (1992). ISBN 0-444-89896-4.
The confusion arising from the ambiguous meaning of words like ``source''
is discussed on p 369.


 \bye

