On 3/17/2013 9:21 AM, Kaba wrote: > 17.3.2013 14:25, email@example.com wrote: >> Maths texts and lectures often refer to observations as being "easy to >> check", >> "trivial" or "obvious." > > I find two extreme situations for why someone uses such weasel words. > > 1) The writer is an expert, and is bored of going around the same > argument for himself for the thousandth time. The claim is probably > correct. > > 2) The writer is a novice, and does not have the energy to go into > details which detract him from the main point he is trying to make. > There is a high risk of the claim being incorrect, or of that the claim > is correct, but has a tedious proof. > > I'll concentrate on the type 1 writers; the type 2 writers hopefully > improve on their writing as time passes. > > Speaking of books in particular, whose main purpose is to teach, one > quality metric for me is to count the density of weasel words in the > text. An unfortunate example is Lang's Algebra, where everything is > obvious, easy and trivial. This is almost always contradictory. If it > really is trivial, then why not write it down; it should take about the > same space as stating it trivial. If it takes more than a few sentences, > then it is not trivial. I find the advice in Strunk & White (Elements of > Style) relevant: "Do no inject opinion." > > A contrasting example is to take any book from John Lee (Introduction to > Topological Manifolds, Introduction to Smooth Manifolds, Riemannian > Manifolds). These are masterpieces to learn from. No weasel-words, > precise, and minimum amount of errors of any kind. It shows that the > author is interested on transmitting knowledge as efficiently as > possible, and also knows how to do that. > > To me, the use of weasel words reflect a lack of effort; that the writer > isn't interested on giving the reader the best learning experience he > can. They make a book confusing to read, and indeed, I have sometimes > missed important points this way. You can afford to be careless when > writing to experts, but not when you are writing to students (readers of > the book). > > In my opinion, weasel words do not undermine the readers confidence. To > the contrary: they contaminate the reader with a false sense of > security, opinions of what is easy and what is not. What actually > happens to me is that, if the claim is not immediately obvious, I skip > checking that claim to get back to the flow of the text. > > Related, there is this effect which I call the Stockholm Syndrome for > Mathematicians :) This happens when people read a book which leave large > gaps in their proofs, and force the reader to fill them. From the > helplessness of the start of not understanding, because information is > missing, the reader works through the proofs, and increasingly builds > confidence in himself. After having mastered the book this way, his > emotions have gone through a rollercoaster of frustration to a feeling > of control. And suddenly those positive feelings are projected to the > book; since I know this well, the book must be great. But it's not the > book; it's the massive work that was done to recover the details and > essential techniques. I hope future writers avoid writing their books > this way; it's abuse in disguise. >
Although both quasi and David Ullrich have made wonderfully insightful statements in response to yours, I appreciate the criticisms you give here.
Not everyone has a social circle where they can get answers to questions or help for clarification. That usually turns into looking for another book with a slightly different presentation.
When you do that enough, you start to realize that there is often a significant amount of "cut and paste" happening.
You also realize that there are a great many texts being written with the intent to condense material for a specific program of study or specific time frame for instruction. That also truncates presentations in unfortunate ways.
Along the same lines, there are books produced specifically for the purpose of providing an encyclopedic reference without a priority for explanations.
One aspect that can improve the situation generally, however, is if author's were to be more explicit for a certain amount of time before reverting to abbreviated forms and "weasel" words as you have characterized them.
At least that would give readers a little more to work with notation before the presentation becomes overly terse.
The same holds for redirecting the reader to the notation borrowed from other sources. At least, it should be explained properly in an appendix.
In spite of any criticisms, one should realize that most of the mathematics that is done is done in journals or other forms that are not so easily accessible. The authors who produce books, no matter how badly in the opinion of their readers, have made those materials available to a wider audience.
That last statement may not apply to widely available elementary topics. But, it is still relevant for those with interests in more complex subject matter.