Dorky Poll: Favorite Elision

So what's your favorite lazy-author trick?

Aaaahh, I'll tell you later...

I write training documentation for our engineering database. My favorite shortcut when seriously pressed for time is to refer to the primary document I had been planning to draw from as a "for further information refer to." Since on occasion the referred-to primary document does not exist in a final form yet, this can give rise to some interesting cross-references.

This is a philosophy thing rather than a hard-science or math thing, but my old favorite was "it is intuitively obvious that..." as a shortcut for "it is my controversial claim that...".

I think I spent a significant portion of my elementary analysis class trying to find the most innocuous place in a proof to put my "and now it is obvious that..." moment. At the time, I was just trying to finish problem sets in a very difficult class. I feel a bit differently about it now, in that I took a math class from a guy who won the Fields medal a couple years later.

My favorite tricks of that sort have come directly from professors' mouths, rather than in a textbook.

The very best was the professor of a first-year-grad-level quantum mechanics class saying, "As we all learned in kindergarten..." before pulling out some Lie Group mumbo jumbo.

I hated that class.

In one of my graduate classes, the professor assigned a calculation from one of his papers that used the "with a few lines of algebra it can be shown that ..." formulation. IIRC the problem involved five coupled ordinary differential equations and required some power series expansions as well as the diagonalization of a 5x5 matrix. (To be fair, the 5x5 matrix was in block form as a 3x3 and a 2x2; of course, finding the eigenvalues of an general 3x3 matrix is no fun, since it requires solving a cubic equation.) After (literally, I counted) 25 pages of algebra I wasn't finished but had the end in sight (i.e. I could see exactly what I needed to do to get the final answer), so I just turned in what I had for partial credit. I probably still have it around somewhere in a box in my basement.

I sometimes tell my students about that problem when they complain that their homeworks are too long.

My girlfriend and I had a nice dinner, a few drinks, yada yada yada, I'm really tired today.

My favorite lines come from a published paper.
"It is trivial to show that:"
"and it is even more trivial to show that:"

Once or twice I tried to use the line "the omitted steps are left as an excercize for the grader" when I wasn't sure how to get to the right answer on a test. While my professors were amused, points were deducted liberally.

While taking a senior level optics course the professor (and the book, since he wrote it) would often stop a few steps into a derivation and include " -> algebra -> " to arrive at the final answer.

Reminds me of the cartoon I saw years ago (what was it?) where an instructor points to something on a board, then retires to his office for a long, long time, then returns and says something like, "Just as I thought, it is obvious ... "

I had a math professor who was an ancient, but very nice, guy who had a tendency to ramble. On a few occassions during the course he stopped mid-proof where he claimed a point to be obvious. He then reminded us of his thesis advisor's 'functional definition' of obvious (that which is difficult or impossible to prove), give a chuckle and then move on :)

I'm not sure if this is exactly an elision, but in one of Andre Weil's papers he has to do a difficult estimate for an elliptic differential equation. He says, "then we call on our friend the elliptical engineer, who assures us that..."

I vote that the next such thread be favourite jokes in texts. Back when I was an undergraduate, our classical mechanics prof asserted that there were exactly two jokes in the famously dry and pedantic Goldstein. One of them was in a discussion where the usual Hamiltonian H was replaced with another quantity K. In a footnote he wrote something like "it has been suggested, in a jocular sense, to refer to K as the 'Kamiltonian'".

I never did find the second joke.

Some logic textbook used the expression, "It is straightforward but tedious to show that...", instead of the old "it's obvious" standby. I like that way of putting it because I think it's actually accurate, much of the time--more often than "obvious", anyway. It doesn't imply the author thinks the proof is going to be easy to produce, just not difficult in the way that makes it relevant or interesting given the subject matter of the text. But still difficult enough to be tedious; hence the author's decision to leave it out.

I've been known to use "straightforward but tedious" in research papers to elide some of the details of a calculation that is in fact S but T. When I'm lecturing and want to do something similar, I usually say "At this point math happens, and what we get is ...".

I don't do this often in class, but it does come in handy from time to time.

My favorite, hands down, is from Porteous' Topological Geometry: "The reader will enjoy showing that. . ."

But the one I seem to have acquired (in the sense of acquired characteristic) from my mentors is "by random nonsense". (This is after fighting off the von Neumann-esque "it is obvious that. . .")

I once had a professor who would work through the first steps of a problem with us in class and then say, "and so it's monkeys and typewriters from here..." and leave it for us to bang away at until somebody got it.

Oh, I like that last one. It's not only "proof my delegation" (the general result is left as an exercise to the reader), but there's even an inducement! It's FUN!

Anyone who has taken Giancarlo Rota's introductory probability and statistics course remembers his famous "Italian proof" which consisted of that invocation and the waving of hands.

How about the Sidney Harris cartoon ("And then a miracle happens...")?

Speaking of odd textbooks engaging with the reader, I found this elsewhere on the blogosphere:

The award for best use of the word "potty" in a graduate physics textbook goes to Binney et al., The Theory of Critical Phenomena, page 260:

"'Well, come on,' you will be saying. 'Who are you trying to fool? This argument is clearly potty. For surely, if lambda-hat diverges near the critical point and g-hat does not, there is no way it can be legitimate to make the substitution (lambda-hat goes to g-hat) in the vicinity of T_c? The expansion is divergent, and no amount of shuffling of variables is going to change this.'"

I've always enjoyed the sublime understatement at the end of Watson and Crick's beautifully concise 1953 paper A structure for Deoxyribose Nucleic Acid.

It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material.

How's that for a momentous elision?

I hesitate to say this, because it involves two books I like by an author I like.

In Griffiths's particle physics book, written in 1987, he skips a derivation of Fermi's Golden Rule, saying on p. 195 "A derviation ... will be found in any quantum mechanics text." That might have been true at the time. But in 1995 Griffiths wrote a quantum mechanics text, and it has no dervation of Fermi's Golden Rule.

This is more like the opposite of an elision, and in fact it's a reasonable application of the material, but the phrasing is too good not to share. From B. Lautrup's Physics of Continuous Matter (IoP, 2005) pp189 my emphasis:

"...we arrive at a complete set of equations of motion for the mass density and velocity fields. In this chapter we shall only apply them to the whole universe..."