Mathematical writing

Applicable in Film theory;

The last words in the scroll. An opportunity to make an impression. Before the reader’s eyes are jarred by the sudden ending of the page.

The first words are like a tab with the name of the content on it. A person who starts to read pulls on the tab and scrolls out the sentences.

Like the title

  • Text not scanning: Reader had to reread something more than once.

  • “Symbols in different formulas must be separated by words.” (to avoid text not scanning);

  • “There is a definite rhythm in sentences. Read what you have written, and change the wording if it does not flow smoothly. There are many ways to say “therefore”, but often only one has the correct rhythm.”

  • Give the reader “a moment to recuperate from a concentrated sequence of ideas.”

  • Keep apart words that “stick in a reader’s mind longer than others”

    • “words like “this” or “also” in consecutive sentences; as well as unusual or polysyllabic utterances;”

    • “For example, I’d better not say “utterances” any more in the rest of these notes.”

  • “Motivate the reader for what follows.”

  • “Give reasons why the things seem interesting or remarkable.” Let the results speak for themselves if possible.

  • “Many readers will skim over formulas on first reading. So sentences should flow smoothly when all but the simplest formulas are replaced by “blah” or some other grunting noise.”

  • “Don’t use commas, which aren’t necessary.”

  • “The opening paragraph should be your best paragraph, and its first sentence should be your best sentence. If a paper starts badly, the reader will wince and be resigned to a difficult job of fighting with your prose. Conversely, if the beginning flows smoothly, the reader will be hooked and won’t notice occasional lapses in the later parts.

  • Probably the worst way to start is with a sentence of the form “An x is y.” For example,

    • Bad: An important method for internal sorting is quicksort.

    • Good: Quicksort is an important method for internal sorting, because…

    • Bad: A commonly used data structure is the priority queue.

    • Good: Priority queues are significant components of the data structures needed for many different applications.”

  • “Humor is best used in technical writing when readers can understand the joke only when they also understand a technical point that is being made. Here is another example from Linderholm:

    • “… ∅D = ∅ and N ∅ = N , which we may express by saying that ∅ is absorbing on the left and neutral on the right, like British toilet paper.” Try to restrict yourself to jokes that will not seem silly on second or third reading. And don’t overuse exclamation points!”

  • “Should the first word after a colon be capitalized? Yes, if the phrase following the colon is a full sentence. No, if it is a sentence fragment. (This is not “yet” a standard rule, but Don has been trying it for several years and he likes it.) While too many commas will interfere with the smooth flow of a sentence, too few can make a sentence difficult to read. As examples, a sentence beginning with ‘Therefore, ’ does not need the comma following ‘therefore’. But ‘Observe that if 〈symbol〉 is 〈formula〉 then so is 〈symbol〉 because 〈reasoning〉’ at least needs a comma before ‘because’.”

  • “Try to make it clear where new paragraphs begin. When using displayed formulas, this can become confusing unless you are careful.”

  • “Try to make sentences easily comprehensible from left to right. For example, “We prove that 〈grunt〉 and 〈snort〉 implies 〈blah〉.” It would be better to write “We prove that the two conditions 〈grunt〉 and 〈snort〉 imply 〈blah〉.” Otherwise it seems at first that 〈grunt〉 and 〈snort〉 are being proved.”

  • “Don opened class by saying that up until now he has been criticizing our writing; now he will show us what he does to his own. Perhaps apropos showing us his own writing he quoted Dijkstra: “A good teacher will teach his students the importance of style and how to develop their own style—not how to mimic his.””

  • “Upon receiving a question from the audience concerning how many times he actually rewrites something, Don told us (part of) his usual rewrite sequence: His first copy is written in pencil. Some people compose at a terminal, but Don says, “The speed at which I write by hand is almost perfectly synchronized with the speed at which I think. I type faster than I think so I have to stop, and that interrupts the flow.””

  • “He exhorted writers to try to put themselves in their readers’ shoes: “Ask yourself what the reader knows and expects to see next at some point in the text.” Ideally, the finished version reads so simply and smoothly that one would never suspect that it had been rewritten at all.”

  • “Be clear about the contrast you are drawing. The reader should immediately understand what you are referring to.”

  • “While editing for flow, sentences can be broken up by changing semicolons to periods; or if you want the sentences to join into a quickly moving blur, you can change periods to semicolons. Breaking existing paragraphs into smaller paragraphs can also be helpful here. While making such changes make sure to preserve clarity. For example, make sure that any sentences you create that begin with conjunctions are constructed clearly, and that words like ‘it’ have clear antecedents. (Sentences that begin with the word ‘And’ are not always evil.)”

  • Sentence length;

  • “Don says that a computer program is a piece of literature.”

  • “We saw several programs by one student who had developed a very distinctive and (Don thought) colourful style. His prose is littered with phrases like “Oooops! How can we fix this?” and “Now to get down to the nitty-gritty.” This stream-of-consciousness style really does seem to motivate reading, and helps infect the reader with the author’s obvious enthusiasm.”

  • “Don’s secret delight, he confessed today, is to “play a library as if it were a musical instrument.” Using the resources of a great library to solve a specific problem—now that, to him, is real living. One of his favourite ways to spend an afternoon is amongst the labyrinthine archives, pursuing obscure cross-references, tracking down ancient and neglected volumes, all in the hope of finding the perfect quotation with which to open or conclude a chapter. Don takes great pleasure in finding a really good aphorism with which to preface a piece of writing. So many people have written so many neat things down the ages, he said, that it behooves us to take every opportunity to pass them on. Don has been known to take such a liking to a phrase that he has written an article to publish along with it.”

    • “So how are we to find that wonderfully apposite quotation with which to preface our term paper? Serendipity, said Don. Live a full and varied life, read widely, keep your eyes and ears open, live long and prosper. You will stumble across great quotations. For example, Webster defines ‘bit’ as “a boring tool”—Don was able to use this when introducing a computer science talk.””

    • “Don has found another quote that so well expresses his philosophy on the subject of error that he is having it carved in slate by English stonecutters, to occupy pride of place in his garden: The road to wisdom? Well it’s plain and simple to express: err and err and err again but less and less and less.”

  • “Feynman discussed his disappointment with his experience of serving on the Challenger Disaster Panel; he complained that instead of discussing ideas, the panel spent all their time “word- smithing” (deciding how to reword or re-punctuate sentences in the committee’s report).

    • Feynman’s dismay at the amount of time he spent dealing with commas, wicked-whiches, and typographic presentation is not unique. Don said, “Word-smithing is a much greater percentage of what I am supposed to be doing in my life than I would have ever thought. That’s one of the main reasons I am teaching this course.””

  • When writing Surreal Numbers: “Don rented a hotel room (“near where Ibsen wrote”) and spent his week writing, taking long walks (“to get my head clear”), eavesdropping on his fellow hotel guests at breakfast (“so I could hear what dialog really sounds like”), and pretending that Jill’s visits were clandestine (“we had always read about people having affairs in hotels . . . ”).

    • Don said he wrote “with a muse on my shoulder.” Every night’s sleep was filled with ideas and solutions; before dozing off he would have to get up and write down the first letter of every word of the ideas he had (and he would spend the morning decoding these cryptic scribbles). He told us that he was more perceptive during this week—his description of the King’s Garden during an evening walk was worthy of Timothy Leary.”

  • “Jeff never saw a book with too many examples. Use lots. Even a very simple example will get three-quarters of an idea across. A page or two later you can refine it with a complex example that illustrates all the “grubbies.” But finding good examples— examples that illustrate all and only the points you are concerned with—is not easy; Jeff has no recipe. You must be prepared to spend a lot of time on it.”

    • “examples are welcome additions to most papers. Leslie said, “It is better to have one solid example than to have a dry, abstract, academic paper.” He also said that it is never a mistake to have too simple an example (“at least not for a lecture”). Demonstrating that “examples keep you honest,” Leslie told us about a major revision of one of his published theories upon discovering that his original draft of the theory was not powerful enough to deal with the example that he wanted to use in his paper.”

  • Nils Nilsson: “Indeed, real communication happens only when writing is charged with artistic passion.”

  • “Nils once took a course in photography from a teacher who declared that: Composition = Organisation + Simplification. “

  • “Lie, if it helps. You can add the correct details later on, but it is essential to present the reader with something straightforward to start off with. So don’t be afraid to bend the facts initially where this leads to a useful simplification and then pay back the debt to truth later by gradual elaborations.”;

    • “Another noteworthy characteristic of this manual is that it doesn’t always tell the truth.” -— Don Knuth, The TEXbook (page vii)

  • “[Mary-Claire van Leunen] suggests that we try “Ben Franklin’s exercise,” rewriting a passage of someone else’s from memory and limited written hints—but that we try it with Don’s writing. When we have finished, what do we like better about Don’s version? What do we like better about our own?”

    • She read us a passage from The Autobiography of Benjamin Franklin where Franklin mentions it:

    • “A question was once, somehow or other, started between Collins and me, of the propriety of educating the female sex in learning, and their abilities for study. He was of opinion that it was improper, and that they were naturally unequal to it. I took the contrary side, perhaps a little for dispute’s sake. He was naturally more eloquent, had a ready plenty of words; and sometimes, as I thought, bore me down more by his fluency than by the strength of his reasons. As we parted without settling the point, and were not to see one another again for some time, I sat down to put my arguments in writing, which I copied fair and sent to him. He answered, and I replied. Three or four letters of a side had passed, when my father happened to find my papers and read them. Without entering into the discussion, he took occasion to talk to me about the manner of my writing; observed that, though I had the advantage of my antagonist in correct spelling and pointing (which I ow’d to the printing-house), I fell far short in elegance of expression, in method and in perspicuity, of which he convinced me by several instances. I saw the justice of his remarks, and thence grew more attentive to the manner in writing, and determined to endeavor an improvement.

    • About this time I met with an odd volume of the Spectator. It was the third. I had never before seen any of them. I bought it, read it over and over, and was much delighted with it. I thought the writing excellent, and wished, if possible, to imitate it. With this view I took some of the papers, and, making short hints of the sentiment in each sentence, laid them by a few days, and then, without looking at the book, try’d to compleat the papers again, by expressing each hinted sentiment at length, and as fully as it had been expressed before, in any suitable words that should come to hand. Then I compared my Spectator with the original, discovered some of my faults, and corrected them. But I found I wanted a stock of words, or a readiness in recollecting and using them, which I thought I should have acquired before that time if I had gone on making verses; since the continual occasion for words of the same import, but of different length, to suit the measure, or of different sound for rhyme, would have laid me under a constant necessity of searching for variety, and also have tended to fix that variety in my mind, and make me master of it. Therefore I took some of the tales and turned them into verse; and, after a time, when I had pretty well forgotten the prose, turned them back again. I also sometimes jumbled my collections of hints into confusion, and after some weeks endeavored to reduce them into the best order, before I began to form the full sentences and compleat the paper. This was to teach me method in the arrangement of thoughts. By comparing my work afterwards with the original, I discovered many faults and amended them; but I sometimes had the pleasure of fancying that, in certain particulars of small import, I had been lucky enough to improve the method or the language, and this encouraged me to think I might possibly in time come to be a tolerable English writer, of which I was extreamly ambitious.”

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