Devlin's Angle

July 2009

Trisecting Devlin's Angle

THIS COLUMN HAS BEEN EDITED FIRST BY KATHERINE SOCHA, THEN BY JANET BEERY, AND NOW FINALLY BY MONICA NEAGOY. SCROLL DOWN OR TELEPORT TO SEE BEERY'S VERSION SCROLL DOWN OR TELEPORT FURTHER TO SEE SOCHA'S VERSION, AND SCROLL DOWN EVEN FURTHER OR TELEPORT TO SEE DEVLIN'S ORIGINAL. READ ON TO FIND OUT WHY THIS MONTH'S COLUMN HAS BEEN EDITED.

Know your audience. Find your voice. Have a clear message. Read your prose out loud. Listen to your editor. These were some of the points emphasized at the MAA PREP workshop on expository mathematical writing, held at the MAA Carriage House from June 29 to July 2. Directed by four well-known mathematics writers, Ivars Peterson (workshop organizer), Paul Zorn, Underwood Dudley, and Keith Devlin, fifteen participants explored mathematical writing for a wide range of audiences and publications. Drawing on years of experience, the workshop leaders made presentations on the writing, editing, and publication processes, from the overall structure of an article or book down to the details of copy editing and punctuation.

To you, our diligent readers returning for the final iteration of Devlin's Angle trisection, writing and editing must be a matter of import. Perhaps because you too wish to expand your reach beyond your students. Or because you are convinced that writing is one of the finest activities known to mankind. Or simply because you are beguiled by this live, online writing/editing process. Whatever the case, here are some gems that our wise and skilled coaches shared with us.

  • Use few adjectives and no adverbs. Mark Twain would concur. Was it not he who said "substitute 'damn' everywhere you're inclined to write 'very;' your editor will delete it and your writing will be just as it should be"?
  • Avoid cliches like the plague. Search and destroy those language fossils! Here's one you find everywhere: "Algebra is a gateway course." Quite apropos. Such metaphors or expressions have become trite through their overuse and are but a testimony of mental sloth or putrefaction.
  • Write a lot and pare a lot. Write, rewrite, and rewrite again. And only then, after you've rewritten to your own liking and approval might you be ready to really write.
  • Don't say "We shall introduce ..." or "I will give an example of ..." Just do it! Similarly, don't say "it is clear that ..." or "it is easy to see that..." Just make it so. And don't ever write "notice that..."! If it's not noticeable then what are you writing?
  • Put every word under a microscope. Be discerning. Appreciate the difference between "I hit only him in the eye" and "I hit him only in the eye" or "I hit him in the only eye." If you put the expression "to write something down" under a microscope, you realize the descent of thought the phrase suggests - from mind to body (hand/fingers). But don't our ideas come from our consciousness, which resides in every cell of our body? Lakoff and Johnson's Metaphors We Live By might elucidate.
  • It's not about you. Be transparent so the reader can read through you to the material. The mathematics is important. Not yourself. The words that followed this admonition jetted out with the insistence of a stream from a spout: "Mathematics is the most glorious creation of the human intellect so we should treat it with respect and deference." Agreed.
  • Persevere! It is said that Richard Bach received 140 rejections of Jonathan Livingston Seagull before it was ultimately published in 1970. By 1972, over a million copies were in print. It soon topped the New York Times Best Seller list where it remained for 38 weeks. If that isn't perseverance, I don't know what is.
  • Behind every good writer is a good editor. If you are hurt by your editor's remarks, then writing is not for you. If you are obdurate about your work, unwilling to make changes, you may be sacrificing the success of your article or book. Embrace the suggested changes and enjoy the constraints. Remember, your editor sees more clearly; you are too close to your work.

    A perfect segue to the most valuable part of the workshop: the intensive group editing sessions. In groups of three or four, coached by one workshop leader, we edited our drafts. The writings ranged from journal articles to children's books. The Devlin group for example consisted of three mathematicians interested in writing for general audiences. Katherine Socha, of St. Mary's College of Maryland, focused on a co-authored book on fractions for parents, teachers, and children. Janet Beery, from the University of Redlands in California, worked on an article about the history of mathematics for high school teachers. And I, Monica Neagoy, an independent scholar and author from the Washington DC area, concentrated on an algebra book for all who teach algebra. Keith Devlin both guided and participated in the editing process.

    As the four of us edited one another's work, we quickly developed a wonderful rapport that was both positive and productive. We all had strong opinions yet we were open to the other group members' suggestions. Probably because we were true to the role of an editor. Good editors make keen suggestions, open your eyes, offer a different perspective, but leave the writing to you. Our experience validated our guest speaker's words - "The fruit of real collaboration is greater than the sum of its parts" - but contradicted Hemingway's words - "To talk about your work is ... to weaken it, to take away its magic and strength." Au contraire.

    Our experience was so positive that Devlin, the talented multi-tasker, hit upon the idea of using our collaboration as a public exemplar of this important lesson: behind every good writer is a good editor (or team of editors in this case). He suggested that we illustrate the editing process by jointly editing the July edition of Devlin's Angle. And so, the Angle Trisection process was born. We decided to edit serially and "live." Each of us agreed to edit both Devlin's workshop description and mathematical essay, according to specific rules. As all who write for public venues learn, a crucial requirement for success is the willingness of the writer to accept exposure to the criticisms and critiques of others.

    The rules for trisection

    On July 6, Devlin posted his column as well as a draft of an op-ed piece on algebra written for a newspaper. On each subsequent Monday, one of the three trisectors will (1) re-write this column, turning it into a co-authored by Devlin et al., and (2) edit the op-ed piece. Co-authoring the column may range from straightforward editing to wholesale re-writing. The only constraint is that the column must describe the MAA PREP expository writing workshop and the Trisecting Devlin's Angle project. The Trisectors' work on the algebra piece however is limited strictly to editing. This part of the exercise aims to illustrate careful editing of an article that is subject to typical newspaper constraints. The title is fixed and the word limit is 400. The goals are to get past the editor, to engage the readers, and to leave editors and readers with a good sense of what algebra and algebraic thinking are. In this exercise, the task is to improve Devlin's original article. That presents the additional challenge of maintaining the style and voice of the original author while improving on the work itself. The revised pieces will be published on successive Mondays, Socha on July 13, Beery on July 20, and Neagoy on July 27.

    You will find the first version (Devlin's) of the sample op-ed piece here.

    Socha's edited version is here.

    Beery's edited version is here.

    Neagoy's edited version is here.



    BEERY'S VERSION

    Mystery writer Margery Allingham once described a minor character in the novel Dancers in Mourning as a member of the audience who had gotten into the play and who was unabashedly enjoying herself. Fifteen mathematicians "got into the play" at the MAA PREP workshop on expository mathematical writing, held at the MAA Carriage House from June 29 to July 2. Directed by four well-known mathematics writers, Ivars Peterson (workshop organizer), Paul Zorn, Underwood Dudley, and Keith Devlin, participants explored mathematical writing for a wide range of audiences and publications, from MAA journals to local newspapers.

    Drawing on their many years of experience in mathematical writing and editing, the four workshop leaders gave a number of presentations on the writing, editing, and publication process, from the overall structure of an article or book down to the fine details of copy editing and punctuation. As useful as these sessions were, everyone agreed that the most valuable part of the workshop was the time allotted to intensive group editing sessions, where the participants broke into groups of three or four, each with one of the leaders, to edit drafts of articles or books they were working on.

    Participants' writing projects ranged from journal articles to children's books. For instance, the Devlin group consisted of three mathematicians interested in writing for general audiences, but each had a different focus. Katherine Socha, of St. Mary's College of Maryland, worked on a co-authored book on fractions for parents, teachers, and children. Janet Beery, from the University of Redlands in California, was working on an article about the history of mathematics for high school teachers. Monica Neagoy, an independent scholar and author from the Washington DC area, worked on an algebra book for parents and teachers. Neagoy also gets major ninja props (translation: emphatic kudos) for the great title of this month's column. Keith Devlin's job was to both guide and participate in the editing process.

    As the four of us edited each other's work, we quickly developed a wonderful rapport that was both positive and productive. It didn't take long to convince us of the truth of one of the main messages of the workshop, that any piece of writing, no matter how good, can benefit from being looked at by another pair of eyes or, in this case, three other pairs of eyes. As one of us said at the end of the workshop, "I thought I knew what 'knowing your audience' and 'putting yourself in your readers' shoes' meant, but the group editing activity really brought home to me that even the most empathetic writers can benefit from good editing."

    Our experience was so positive that Devlin, always on the lookout for ways to share interesting mathematics and good mathematical practice, hit upon the idea of using our work together as a public example of one of the workshop's take-home lessons: behind every good writer is a good editor (or team of editors). When he suggested that we illustrate the editing process by jointly editing the July edition of his Devlin's Angle column, the Angle Trisectors were born. Since the workshop was nearly over and we soon would scatter to our homes around the country, we decided to edit and collaborate serially and "live" online, with one of us submitting edits and rewrites to both the column and a sample piece of mathematical writing, an op-ed piece on school algebra that Devlin had written and never published, each week. With this added challenge, these three workshop participants really have joined in the play!

    How can you "get into the play" of expository mathematical writing? Mystery writer Margery Allingham also wrote that "light reading is not light writing," and expository writing may indeed take more effort and practice than technical writing. So, write early, write often, write widely, write articles, write reviews, write referee's reports, write doggerel, write as much as you can. Write, write, write. And then ... find a good editor.

    Read on for the rules the "trisectors" have agreed to follow as they edit and rewrite Devlin's column and his op-ed piece on school algebra.

    The rules for trisection

    Here are the rules Devlin and his Angle Trisectors will follow for their demonstration of the power of editing and collaboration. On July 6, Devlin posted his column as well as a draft of an op-ed piece written for a local or national newspaper. Each week for the rest of the month, one of the three trisectors will (1) re-write this column, turning it into a co-authored work by her, Devlin, and, if she wishes, any trisectors who have gone before, and (2) edit the associated draft op-ed piece by Devlin.

    Co-authoring the column may range from straightforward editing to wholesale re-writing. The only constraint is that the column must describe the MAA PREP expository mathematical writing workshop and the subsequent Trisecting Devlin's Angle project. The outcomes are unpredictable because we are working serially and onstage (and generally at the last minute) for all the world to see.

    Unlike our co-authoring work, the Trisectors' work on the draft article about algebra is limited strictly to editing. This part of the exercise aims to illustrate careful editing of an article that is subject to typical newspaper constraints. The op-ed piece must explain to parents what algebra is and why children may find it difficult to master. The title is fixed and the body of the work has a strict upper limit of 400 words. The goals are to get past the editor, to grab and keep the attention of the readers, and to leave editors and readers with as good an understanding of algebra and algebraic thinking as is possible in just 400 words. In this exercise, the task is to improve Devlin's original article. That presents the additional challenge of maintaining the style and voice of the original author while improving on the work itself.

    The revised pieces will be published on successive Mondays, Socha on July 13, Beery on July 20, and Neagoy on July 27.

    You will find the first version (Devlin's) of the sample op-ed piece here.

    Socha's edited version is here.

    Beery's edited version is here.

    Neagoy's edited version is here.



    SOCHA'S VERSION

    Mystery writer Margery Allingham once described a minor character in the novel Dancers in Mourning as a member of the audience who had gotten into the play and who was unabashedly enjoying herself. Fifteen mathematicians "got into the play" at the Summer 2009 MAA PREP workshop on mathematical writing, led (or, more accurately, coached) by four well-known mathematics writers: Ivars Peterson - director extraordinaire; Paul Zorn - MAA President-elect-elect (sic: his term as President-elect does not begin until January!); Underwood Dudley - veteran editor, writer, and guide; and Keith Devlin - NPR's Math Guy.

    With a range of writing styles from Proustian to Seussian, participants and leaders together spent nearly four days on the writing, editing, and publishing processes, from developing the overall structure of an article or a book to relishing the finer details of copy editing. The workshop included blocks of time dedicated to intensive group editing sessions, organized loosely by type of writing (journal articles, children's books, writing for general audiences, and textbooks). One workshop leader mentored each group. During these sessions, we all (leaders, too) brought drafts of articles or book chapters for the slightly terrifying prospect of editing our own writing in public.

    The Devlin group consisted of three mathematicians interested in writing for general audiences, and each of us had a different focus. Janet Beery, from the University of Redlands in California, was working on an article about the history of mathematics. Monica Neagoy, working on an algebra textbook for both students and parents, is an independent scholar and author from the Washington DC area. (Monica gets major ninja props for the great title of this month's column.) Katherine Socha, of St. Mary's College of Maryland, worked on a co-authored book on fractions for parents, teachers, and children. And Keith Devlin's job was to gauge the state of each project, guide both group and individual progress, and goad the group to finer editing and writing.

    As the four of us edited each other's work, we quickly developed a wonderful rapport that was both positive and productive. Devlin, that talented multi-tasker, hit upon the brilliant idea of using our work together as a public exemplar of the workshop's take-home lesson: behind every good writer is a good editor (or team of editors). He suggested to the group that we jointly edit the July edition of this column, Devlin's Angle; but unfortunately, given our limited time, we could not complete the project before scattering to our homes around the country. On the "make lemonade" principle, Devlin convinced us to illustrate the editing and co-writing process serially and online. With the added challenge of editing and co-writing "live" on MAA Online, these three participants really have joined in the play. As all who write for public venues learn over and over, a crucial requirement for success is the willingness of the writer to accept exposure to the criticisms and critiques of others. One deep breath, and here we go!

    The rules for trisection

    Here are the rules Devlin and his Angle Trisectors will follow for this demonstration of the power of co-authoring and the power of editing. Devlin is providing his column as well as a draft of an op-ed article written for a local or national newspaper. Each week for the rest of the month, one of the three will (1) re-write this column, turning it into a co-authored work by Devlin and X, and (2) edit the associated draft op-ed article by Devlin.

    Co-authoring the column may range from straightforward editing to wholesale re-writing. In this case, the column - describing the PREP workshop and the subsequent Trisecting Devlin's Angle project - may evolve to a true co-authorship: the by-line likely will read Beery, Devlin, Neagoy, and Socha. Or three separate columns may be created, with bylines Devlin and Beery, Devlin and Neagoy, and Devlin and Socha. Or two columns may be created, with bylines Devlin and two Trisectors, and Devlin and the third Trisector. The outcomes are unpredictable because we are working serially and onstage for all the world to see.

    Unlike our co-authoring work, the Trisectors' work on the draft article about algebra is limited strictly to editing. This part of the exercise aims to illustrate careful editing of an article that is subject to typical newspaper constraints. The op-ed piece must explain to parents what algebra is and why children may find it difficult to master. The title is fixed and the body of the work has a strict upper limit of 400 words. The goals are to get past the editor, to grab and keep the attention of the readers, and to leave editors and readers with as good an understanding of algebra and algebraic thinking as is possible in just 400 words. In this exercise, the task is to improve Devlin's original article. That presents the additional challenge of maintaining the style and voice of the original author while improving on the work itself.

    The revised pieces will be published on successive Mondays. As we progress, successive Trisector editors will edit the original version of both the column and the op-ed article, though each may take into account the work of the previous editors. In this case, it's not plagiarism, it's collaborative writing and editing over the Internet.

    How can you get into the play? Write early, write often, write widely, write reviews, write articles, write doggerel, write as much as you can. Write, write, write. And then ... find a good editor.

    You will find the first version (Devlin's) of the sample op-ed piece here.

    Socha's edited version is here.

    Beery's edited version is here.

    Neagoy's edited version is here.



    DEVLIN'S ORIGINAL VERSION

    Behind every good writer is a good editor. That point was emphasized time and again by the four instructors (coaches would be a more accurate term) at the MAA PREP workshop on mathematical writing held at the MAA's Carriage House from June 29 through July 2. Those instructors were Ivars Peterson (who organized the workshop), Paul Zorn, Underwood Dudley, and myself. It was the second year the four of us have given such a workshop, which focused on mathematical writing and editing for a wide variety of audiences and publications, from research journals to national and local newspapers.

    Drawing on our many years of experience in mathematical writing, the four of us gave a number of presentations on various aspects of the writing, editing, and publication process, from overall structure of an article or book down to the fine details of copy editing and punctuation. But I think all present would agree that of most value were the intensive group editing sessions, where the participants broke into groups of three or four, each with one of the instructors, to edit drafts of articles they were working on.

    My group consisted of three mathematicians interested in writing for general audiences, but each had a different focus. By good fortune, the four of us rapidly developed a wonderful group dynamic, and as we worked through the different drafts articles, I felt that there could be valuable lessons to be learned by people not at the workshop if we could create a public record of our process. The ideal would have been a video of our activities, but that would have required considerable advance planning. So I hit upon the idea of taking the July edition of Devlin's Angle and letting the group edit it. Since we would all be back at our home locations, joint editing was not really possible, so each group member would have to edit it individually. That would lose much of the dynamic of group editing, but it would, I hoped, illustrate how a piece of writing can benefit by being looked at by another pair of eyes.

    The "safe" way would be to go through the whole process and then post the final results online. But being aware of the popular success of TV reality shows such as Survivor, I felt it might be more fun to have the added danger of doing this "live", without knowing in advance just how it would turn out. One thing this would demonstrate was that a crucial requirement for any editing process to be successful is the willingness of the writer to expose him or herself to the critiques of others - to listen to what they say and be prepared to accept advice. To most of us, this does not come easy, though in my experience, the more times you go through it the easier it gets - primarily because you come to realize just how much better the finished product is as a result. It would be false modesty for me to pretend I do not have a reputation as a "good writer". But that reputation is built on the largely invisible shoulders of the many excellent editors who have worked with me over the years to turn my initial submitted drafts into the polished pieces everyone gets to see. To be sure, I always go through several iterations of my draft before I let an editor see it. Indeed, what I send in is invariably something that I cannot see how to improve any more. But I know from experience that there is usually a lot more that can be done to improve it.

    Devlin's Angle is a bit different from most other academic writing, in that it is an opinion column. It is meant to have a conversational tone. I deliberately leave it with some rough edges. As I write it, I always imagine myself speaking the words to a friend sitting across from me in a bar. (Ivars told the group he reads all his writing aloud to see how it sounds.) Moreover, it is not edited by anyone else. This month's issue is different - each Monday for the remainder of July, you will see a freshly edited version.

    The Angle trisectors and the rules for trisection

    Let me introduce our three Angle trisectors. Katherine Socha is at St. Mary's College of Maryland. Her main focus at the workshop was writing a book on fractions suitable for students, teachers, and parents. Janet Beery, from the University of Redlands in California, was working on an article about the history of mathematics. And Monica Neagoy is an independent scholar and author from the Washington D.C. area, who is writing an algebra textbook for both students and their parents. (Monica is the person who gets the credit for the great title of this month's column.) At the workshop, over several intensive meetings, all three proved themselves to be talented writers with well developed styles, as well as natural and creative editors. (If they had not, this month's experimental column format would not have been possible.) Each contributed in different ways, demonstrating why the mythical lone writer of popular culture - generally locked away and starving in a tiny garret - is really up against it when pitted against the collective talents of a group. We quickly developed the respect and trust required for editing to be successful. We also had a lot of fun working together. I'm looking forward to seeing what they produce.

    Here are the rules we agreed to for this exercise. Each week for the remainder of the month, one of them will edit this column, along with a sample draft article by me (see momentarily), with the new versions being published on successive Mondays. They will edit the original version (of both the column and the sample), though of course, as we progress, successive editors can take into account, and incorporate if they wish, changes made by previous editors. Their editing of the main body of the column can range from changes in punctuation to the complete rewriting or even nixing of entire paragraphs. The only constraint is that they tell the same overall story about the workshop and how and why we came to embark on this exercise. (They each get to determine for themselves exactly what this amounts to.) They are all free to take entire passages from the others - it's not plagiarism in this case, rather collaborative writing over the Internet. (In a for-real case, the final version would have my name at the top, and the editor would get at most a footnote acknowledgement. This is why authors should really value and look forward to the editing process: those editors make you look smart!)

    All versions will remain on the website for comparison.

    Since most readers who find this month's topic of interest will likely be motivated by a desire to improve their skills in writing about mathematics (rather than about a workshop), in addition to editing the column, I supplied a short piece I had written about algebra. Here the constraints are a bit different. The intention is to write a short op-ed piece for a local or national newspaper that will explain to parents what algebra is and why their children may be finding it difficult. The title is fixed and the piece has a strict upper limit of 400 words, excluding the title. It has to get past the editor, grab and keep the attention of the readers, and leave them with as good an understanding of algebra and algebra-learning as is possible in just 400 words. In this case, the goal is to improve my article - unlike editing the workshop description, where they can make major changes of they wish. That presents an additional challenge of maintaining the style and voice of the original author. If an editor feels that a passage, or even the entire piece, needs to be re-written, then their response will be to suggest an alternative, which in a for-real case I would then have to recast in my voice. (We won't do that last step in this exercise. The goal is to demonstrate the process, not the result.) Of course, editors are not obliged to change anything. Part of good editing is knowing when something is fine just as it is. If one of our three editors makes very few changes, that can still indicate good editing. In our group edits, there were plenty of passages in the various drafts the group provided that none of us thought required any changes. Professional editors are generally paid by the overall length of the article, not the number of change they make! Consequently, I always start out assuming an editor is right and I am wrong, and then think about the point. Over the years, I have found that I end up accepting around 90% of an editor's suggestions, either verbatim or by finding a way of my own to address the issue that elicited the suggested change.

    For the record, the sample passage is taken from a slightly longer op-ed piece I wrote a year ago that did not get past the editor (though it did lead to the newspaper writing a substantial article of its own on the topic, in which I was quoted extensively). As a result, I worked on it quite a lot to get it into the best shape I could. It is not a first draft by any means. But it has never been edited by anyone else. Until now.

    Tune in next week for episode 2. You will find the first version (Devlin's) of the sample op-ed piece here.

    Socha's edited version is here.

    Beery's edited version is here.

    Neagoy's edited version is here.


    Devlin's Angle is updated at the beginning of each month. Devlin's most recent book for a general reader is The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern, published by Basic Books.
    Mathematician Keith Devlin (email: devlin@stanford.edu) is the Executive Director of the Human-Sciences and Technologies Advanced Research Institute (H-STAR) at Stanford University and The Math Guy on NPR's Weekend Edition.