Writers using MS Word tend to make certain standard errors in their typesetting. For instance, they use hyphens instead of em-dashes (ctrl-alt-hyphen or option-shift-hyphen). Mathematical typesetting is especially bad. There is essentially no way to typeset mathematics well in MS Word. The best solution: LaTeX.
For a while, I've been meaning to comment on the "that"/"which" controversy, the claim that "which" should not be used with restrictive relative clauses, nor "that" for nonrestrictive. From a linguistic point of view, it seems clear that this view is descriptively barren. Geoff Pullum provides a convincing and entertaining argument on Language Log, based on the sentence "The key point, that all the popular reports missed, is that FOXP2 is a transcription factor...". The rarity of sentences like these, in which "that" is used for a nonrestrictive relative clause, leads Pullum to refer to it as "ivory-billed".
I suppose, and am happy to stipulate for the purposes of discussion, that the use of "which" for restrictive relative clauses and "that" for nonrestrictive (or supplemental, as Pullum prefers) is grammatical. Nonetheless, the overwhelming preponderance of occurrences of "which" for nonrestrictive clauses means that the use of "that" in that context is much more likely to give pause to the reader, a kind of cognitive setback. For that reason, a charitable writer (and shouldn't we all strive to be one of those?) ought to use "which" for nonrestrictive relative clauses -- not because it is "wrong" to use "that", or ungrammatical, but because the use of "that" is likely to be jarring to a significant fraction of one's readers. (And I don't only mean the Fowler-type prescriptivist readers, though I suppose there's no reason to be jarring them needlessly either.) An excellent point of evidence is the fact that Pullum had to ask the author directly which meaning he had intended in the ivory-billed sentence; had he used a "which", no clarification would have been needed.
In the particular case of the sentence quoted above, there is no concomitant advantage to using "that" over "which" that would compensate for the negative effect of jarring or confusing the reader. Thus, its use should be prescriptively deprecated. (This issue of compensation allows me to avoid proscriptions against splitting infinitives or dangling prepositions, the slavish following of which leads to circumlocutions and semantic errors. Avoiding these negative effects clearly compensates for the oh so very slight jarring effect on some small fraction of true-believing Fowlerians.) By a similar argument, the use of "which" for restrictive relatives should be deprecated as well in formal writing.
What I am arguing is that even though the language does not enforce the distinction between nonrestrictive and restrictive in terms of "which" versus "that" (and commas versus none), respectively, there is still a good reason to write as if it did. There was nothing wrong in the quoted sentence even under the intended interpretation, just something infelicitous.
Am I trying to have my cake and eat it too? To be able to rail prescriptively while keeping my linguistic descriptivist moral stance? Yes.
Different people have different styles for overall organization of a technical paper. There is the "continental" style, in which one states the solution with as little introduction or motivation as possible, sometimes not even saying what the problem was. Papers in this style tend to start like this: "Consider a seven-dimensional manifold Q, and define its hyper-diagonal as the ...." This style is designed to convince the reader that the author is very smart; how else could he or she have come up with the answer out of the blue? Readers will have no clue as to whether you are right or not without incredible efforts in close reading of the paper, but at least they'll think you're a genius.
Of course, the author didn't come up with the solution out of the blue. There was a whole history of false starts, wrong attempts, near misses, redefinitions of the problem. The "historical" style involves recapitulating all of this history in chronological order. "First I tried this. That didn't work because of this, so I tried this other way. That turned out to be stupid. Then I tried this other way...." This is much better, because a careful reader can probably follow the line of reasoning that the author went through, and use this as motivation. But the reader will probably think you are a bit addle-headed. Why would you even think of trying half the stuff you talked about?
The ideal style is the "rational reconstruction" style. In this style, you don't present the actual history that you went through, but rather an idealized history that perfectly motivates each step in the solution. "We consider the problem of XXX. The obvious thing to try is X. But such-and-such a pithy example shows that that fails miserably. Nonetheless, the example points the way naturally to solution Y. This works better, except for such-and-such an obscure case. We patch solution Y to handle this case, forming solution Z. Voila." Of course, the author doesn't tell you that he came up with solution Y before solution X, which only occurred to him after he came up with solution Z, and he skips solutions A, B, and C because, in retrospect, they are nowhere on the natural path to Z, even though at the time he was completely convinced they were on the right track. The goal in pursuing the rational reconstruction style is not to convince the reader that you are brilliant (or addle-headed for that matter) but that your solution is trivial. It takes a certain strength of character to take that as one's goal. But the advantage of the reader thinking your solution is trivial or obvious is that it necessarily comes along with the notion that you are correct.
I've just discovered James Pryor's "Guidelines on Writing a Philosophy Paper". Despite the ostensible limited goal of the guidelines, they are much more broadly applicable than just to philosophy papers. I especially like the characterization of readers as "lazy, stupid, and mean".
People seem to fall prey to adverbials like "however" and "rather" seducing them into running on sentences.
This type of approach has been used in previous models, however, the presented algorithm adopts a different foundation.But these words are not conjunctions, subordinating or otherwise. They are adverbs, like "on the other hand" or "unfortunately". The following is, presumably, clearly infelicitous.
This type of approach has been used in previous models, unfortunately, the presented algorithm adopts a different foundation.By the same token, so is the sentence with "however". It is easily corrected:
This type of approach has been used in previous models; however, the presented algorithm adopts a different foundation.or
This type of approach has been used in previous models. The presented algorithm, however, adopts a different foundation.
Email messages should be treated as personal letters. You wouldn't write a handwritten letter with misspellings, would you? Or a typewritten letter in which you didn't bother to use the shift key? Then you shouldn't do that in an email. Doing so implies to many readers that you don't respect them enough to bother with such "niceties".
On a related topic, by convention, words in all caps in email messages are to be read as if the author were shouting them. This is typically not the intended interpretation. According to RFC 1855:
Use symbols for emphasis. That *is* what I meant. Use underscores for underlining. _War and Peace_ is my favorite book.
To recurse is to curse again, not an activity that an academic, or an algorithm for that matter, should engage in. When a process is repeated or is subject to recursion, it is said to recur.
The use of the pronoun "he" as a bound pronoun of neutral gender is problematic on two grounds. First, its use is blatantly sexist (although the sexism is of a historical nature, so that those who continue to use "he" in this way have a defensible position). Second, and more importantly, many readers confronted with such a use of "he", including myself, tend to find that it causes a jarring effect as they stop to wonder whether or not the writer intended to imply that the referent of the pronoun is male. Anything that causes a jarring effect like this on a substantial portion of your readers should be avoided, as it serves only to distract them from the important substance of your writing.
Now, I turn to a more recent variant of the same problem. The use of the pronoun "she" as a bound pronoun of neutral gender is problematic on two grounds. First, its use is blatantly sexist (although the sexism is of an anti-historical nature, so that those who continue to use "she" in this way have a defensible position). Second, and more importantly, many readers confronted with such a use of "she", including myself, tend to find that it causes a jarring effect as they stop to wonder whether or not the writer intended to imply that the referent of the pronoun is female. Anything that causes a jarring effect like this on a substantial portion of your readers should be avoided, as it serves only to distract them from the important substance of your writing.
But what alternatives are there? In everyday speech, "they" or "them" is used for this purpose, but this disturbs the sensibilities of prescriptivists, who, I should remind you, are a substantial portion of your readers. And anything that causes a jarring effect like this on a substantial portion of your readers....
Rewriting the sentence is the only practicable alternative. Do it and be done with it.
Pat Winston in his lecture on How to Speak notes that covering up parts of overhead transparencies and revealing them slowly like a strip-tease artist is a technique that drives 10 per cent of your audience nuts. I am in that 10 per cent. The desire to use this technique means only one thing: There is too much information on the slide. Split it into multiple slides. Winston recommends using overlays instead, but overlays are really a different and specialized overhead technique, and are not typically necessary for remedying this problem.
By the way, if you make slides using computerized means and want to use an overlay, consider "implicit" overlays instead. An implicit overlay is a series of separate slides each of which includes the contents of a different prefix of the overlay slides. Implicit overlays have the advantage that no Scotch taping of slide material is required, and no fumbling with the overlay pieces is needed. One just continues placing single sheets on the projector as usual, but each one in the overlay series has some additional material added to the previous one.
A citation is not a first-class participant in a sentence; it cannot serve as a noun phrase. Rather it is a parenthetical -- that is why it appears in parentheses -- and like all parentheticals should be removable without changing the well-formedness of the sentence in which it appears. Thus, the following sentences are ill-formed. (Try reading them without the material in parentheses.)