On technical writing

SolitaryRoad.com

Website owner:  James Miller

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It is my basic nature to analyze, try to reduce the complicated to the simple, to simplify, to try to reduce things to their essence, to try to get to the bottom of things, to their basic components. That is just the way my mind works. In my technical writing, when I write about topics in mathematics, physics, or chemistry it is my basic nature to try to present ideas in the best possible way; in an organized, thoughtful way; as clearly as possible. I always want to do a good, careful, thorough job. I really want my reader to understand me. I am just very particular about how I do things. I put thought into every word and every phrase. I have to satisfy myself and I am not easily satisfied. I am always trying to think of a way to say a thing better, a way to better present an idea. Are there some examples that would help? Is there a sketch or diagram that would clarify something or help me in conveying my meaning better? If it takes time, that doesn’t matter. I am willing to put a lot of effort and time into doing the job I am trying to do. Concepts in mathematics, physics and chemistry are often somewhat obtuse and difficult to understand. My object is to make them simple and easy to understand. And I feel that if my reader does not understand me, then I have not done my job. It is my fault and not his if he doesn’t understand me. The purpose of writing is communication and if I didn’t communicate, I failed. My standards are high. I word and then I reword. I want a good job, one that satisfies me. My object is to say a thing in such a way that my reader will understand what I am saying with little effort. I don’t want to say more than I need to say. I don’t to use unnecessary words. I wish to be as brief as possible. And I don’t want to say less than is needed either. How to present ideas and concepts is very much a matter of judgement and sense. You wish to keep things as concise as possible but also accurate and complete. I have been writing for years and all these things have always characterized my writing. Years later when I read something I wrote sometime in the past I usually feel good about the job I did. I think, “I did a very good job on this!” Sometimes when I read something I have written I am not completely happy with the way I said something or presented something and I rewrite it and get it so that it makes me happy. Why do I say all this? I say it because not everyone really cares about trying to do a good job. Not everyone is willing to take real pains and effort. Not everyone has really high standards. Not everyone is particular and thoughtful about what they say and how they say it. Not everyone tries to reduce things to their essence, to simplify. Some people have a natural inclination instead to dress things up, to add flourishes, to complicate. I am talking about writers of textbooks in mathematics, physics and other technical fields. There are many people who have a natural inclination towards complicating. The more complicated and elaborate and fancy their work, the better they feel about it. (Just like some people like to dress in fancy clothes of the latest fashion to make a big impression.) Or their idea of a great job in mathematical exposition is to use as few words as possible, to use all kinds of terse short-cut notations and symbols, to write in such a cursive way as to put in two mind-squashing sentences a concept I would treat with several paragraphs. How a person writes reveals a great deal about himself, about his basic nature, his character, his mentality, his mind. I have a very bad opinion of most writing in the fields of mathematics, physics, and most technical fields. I have been struggling with mathematics textbooks all my life. There are a few good, well-written ones. You can see that the authors are conscientious, thorough, understand the subject well, and have made a real effort to do a good job of presenting the ideas. I know what books they are and I have a high regard for the authors. However, they are the exceptions. I think the good textbooks are about one out of twenty. Maybe less than that. Almost everything that I know about mathematics I have had to dig out of poorly written books. I long ago learned the importance of having a few books on any particular subject that I am studying. That way, if all the books are poor, I may find one author that explains a particular idea in a way I can understand. This frustration with mathematical writing goes all the way back to my high school and college days. I have seen a whole lot of terrible mathematics textbooks. Most of those that were used in my college were atrocious. Thankfully, in most cases I was able to find other textbooks to study from. One of my big frustrations back then was the phenomenon of getting “hung up” — hung up on one statement or another in a text book. I would be carefully following the steps in an author’s proof and then he would say , “It is obvious that .... ” or “obviously” (this or that is true.); I don’t know how many times I have gotten hung up when an author said “It is obvious that ...” It wasn’t at all obvious to me. Usually when I did figure out the reason supporting that statement, I didn’t think it was at all obvious. That is where he should have spent some time explaining. I have long felt that the main reason so many ideas in mathematics are so difficult to understand is not that the ideas themselves are really so very difficult. But rather it is the obtuse, poor explanations. That author who passes so quickly, glibly, superficially over some obscure subject may know very well what he is talking about — but I don’t know what he is talking about. He has left me far behind. So if you can’t understand the book, perhaps you might think you might understand the presentation of the professor. I personally will generally choose books over professors. One of the best sets of books on mathematics that I have was written by Russians. They exhibit a depth, clarity and breadth of understanding of the subject matter that one rarely finds in American authors. Perhaps the reason they are so good has something to do with the minds and characters of the authors.

I used to wonder why so much mathematical exposition was so obtuse and poor. I suspected the authors of deliberately being obtuse. I think now that there are a lot of reasons. It all has to do with human nature and the way people are. Desire to impress, laziness, indifference, lack of real understanding of the subject, lack of thoughtfulness, lack of methodicalness, etc. It takes thought, effort, and a certain kind of mind to present a thing well.

Feb 2018