One of the many problems with the essay discussed in yesterday's post is that it was poorly written. Finnis and George seemed to go out of their way to be as unclear as possible, frequently choosing tortured, ambiguous phrasings when clearer options were readily at hand. This is something of an occupational hazard among academics, especially in the social sciences. Too many practitioners seem to think obscurity equals profundity. If you express yourself clearly it is too easy for your critics to spot the shallowness of your ideas.

I recently read a book called Learn to Write Badly: How to Succeed in the Social Sciences by Michael Billig. The title is meant as cynical advice for graduate students in the social sciences. As an example he provides an e-mail he received advertising a special issue of a journal in qualitative psychology:

This combining of ontologies and epistemologies gives rise to both benefits and creative tensions and provides a focus for inquiry into enhancing awareness of researcher impact. The aim of this Special Issue is to provide an international forum within which the disparate array of questions that are arising about a pluralistic approach to qualitative research in psychology can be posed and debated. Recognising the potential that this approach offers for accessing the different layers and dimensions of a complex and constructed social reality brings with it both curiosity and questions about its ontology, epistemological tenets, theoretical frameworks and practical applications.

Billig now provides a lengthy analysis, which includes passages like this:

We can note what makes the extract especially clunky. It is stuffed with big nouns and noun phrases, such as `ontologies' and `epistemologies', as well as phrases like `enhancing awareness of researcher impact'. We can also note that no people appear in this extract: no one is identified as doing anything. If anything is to be done--any action is to be performed--then it will be an abstract concept that does it. The combining of epistemologies and ontologies gives rise to something--with the combiner left in the shadows. People are not identified as recognizing the potential of this combining, but the recognizing itself does something: it brings with itself `curiosity' and `questions'. And both these latter two things--curiosity and questions--seem to exist independently from any identifiable people who might be curious and who might be asking questions.

Aficionados of the evolution/creation dispute are accustomed to wading through this kind of prose. Creationists and ID folks often try to accomplish through opacity what they cannot accomplish through strong arguments. If you are familiar with the writings of David Berlinski then you know what I'm talking about. For example, his manifesto, “The Deniable Darwin” contains one paragraph after another like this:

In its most familiar, textbook form, Darwin's theory subordinates itself to a haunting and fantastic image, one in which life on earth is represented as a tree. So graphic has this image become that some biologists have persuaded themselves they can see the flowering tree standing on a dusty plain, the mammalian twig obliterating itself by anastomosis into a reptilian branch and so backward to the amphibia and then the fish, the sturdy chordate line - our line, cosa nostra - moving by slithering stages into the still more primitive trunk of life and so downward to the single irresistible cell that from within its folded chromosomes foretold the living future.

This is not how you write when you have something to say. This is how you write when you are trying to impress people with how well you write. You can picture Berlinski muttering, “Damn, I'm good!” as he pecked out those two ridiculous sentences.

Poor writing is also ubiquitous in mathematical culture. In research journals, if, after the paper's introduction, you include two consecutive sentences of exposition, you will be accused of excessive wordiness. Likewise if, in proving a theorem, you unwisely choose to throw in a few words whose purpose is not to advance the proof, but merely to make it easier to follow.

This is bad enough in research journals, which are, at least, only read by other specialists, but it becomes positively scandalous in textbooks. I came to that conclusion in college, where I found that nearly all of my textbooks were written in the style of reference books. They were just a relentless pile of definitions, lemmas, theorems and proofs, carefully written to be devoid of passion or voice or anything else that might risk arousing some interest in the reader. As I spent college and graduate school wading through one miserable turd tome after another, I thought to myself that a person must truly hate mathematics to present it so poorly.

The trouble is that over the years I have found that when I raise these objections to my colleagues, they frequently disagree. They think the jargon-filled, notation-dense, just the facts ma'am approach is exactly the way it should be. If you look at the classic textbooks, the ones that are held up by mathematicians as exemplars of what a textbook ought to be, they are always of the stilted, boring sort.

You can imagine, then, how good it felt when, in graduate school, I came across Morris Kline's book Why The Professor Can't Teach, published in 1977 but still relevant today. It includes a chapter entitled, “Follies of the Marketplace: A Tirade on Texts.” This chapter so perfectly expressed my own thoughts about textbooks that I was practically in tears. I recently had occasion to go back and reread it, so let me share a few especially excellent passages.

Explanations of mathematical steps are usually inadequate--in fact, enigmatic. Because mathematicians do not take the trouble to find out what students know at any particular level, they do not know how much explanation is called for. But the decision is readily made. It is easier to say less. This decision is reinforced by the mathematician's preference for sparse writing. If challenged he replies, “Are the facts there?” This is all one should ask. Correctness is the only criterion and any request for more explanation is met by a supercilious stare. Surely one must be stupid to require more explanation. Though brevity proves to be the soul of obscurity, it seems that the one precept about writing that mathematicians take seriously is that brevity is preferable above everything, even comprehensibility. The professor may understand what he writes but to the student he seems to be saying, “I have learned this material and I defy you to learn it.”

That's just about perfect. As is this:

There are textbook writers who believe that a mathematical presentation that is logically sound explains itself to the reader who faithfully follows the author step by step. Presumably the meaning need not be stated by the author explicitly but can be grasped by the reader from the details he ploughs through. The authors do not see the need to take the readers into their confidence, to explain where the road is going, why this one is better than another, and what is really achieved. They give no inkling of how the proof was arrived at, why anyone sought the result to begin with, or why anyone should want it now. In effect, the texts are challenges to clairvoyance.

And this:

A glaring deficiency of mathematics texts is the absence of motivation. The authors plunge into their subjects as though pursued by hungry lions. A typical introduction to a book or chapter might read, “We shall now study linear vector spaces. A linear vector space is one which satisfies the following conditions...” The conditions are then stated and are followed almost immediately by theorems. Why anyone should study linear vector spaces and where the conditions come from are not discussed. The student, hurled into this strange space, is lost and cannot find his way. Some introductions are not quite so abrupt. One finds the enlightening statement, “It might be well at this point to discuss...” Perhaps it is well enough for the author, but the student doesn't usually feel well about the ensuing discussion. A common variation of this opening states, “It is natural to ask...,” and this is followed by a question that even the most curious person would not think to ask.

Folks, we're only a few pages in to a lengthy chapter. Reading this as a graduate student was certainly a boost to my confidence, since it was nice to see that someone with credibility felt as I did.

I'll close with a story. In college I took a full-year course in real analysis. In the first semester we discussed the standard topics of real analysis, while in the second we moved on to more high-brow fare like measure theory, Lebesgue integration, differential forms, and analysis on manifolds. The professor wrote the textbook himself, meaning we got the chapters, hot off the press, for free.

Sadly, the chapters were worth what we paid for them. The book was a textbook on how not to write a textbook. It was guilty of everything Kline described, and of several other things he didn't. I honestly felt embarrassed for the professor, that he would write so poorly about a subject he obviously cared about deeply. I liked both the professor and the class, but his book was appalling.

The book was later published by Springer. It subsequently won an award for mathematical exposition.