Peer Gibberish

Well, this is an embarrassing thing to see: according to Nature, the Springer publishing and the Institute of Electrical and Electronic Engineers (IEEE) have had to withdraw at least 120 papers from their subscription services, because the papers were gibberish produced by a program, SCIgen, that strings together words and phrases into computer science-ish texts. SCIgen and this sort of thing are meant for fun (Nature also linked to arXiv vs snarXiv, which lets you try to figure out whether titles are actual preprints on the arXiv server or gibberish), but such nonsense papers have been accepted for conferences or published in, typically, poorly-reviewed forums, to general amusement and embarrassment when it’s noticed.

I’m sympathetic to the people who were supposed to review these papers. It’s hard reading any kind of academic paper, for one. They tend to be written with the goal of presenting novel findings efficiently; whether they’re pleasant to read isn’t a factor. (I wouldn’t be surprised if authors had no idea how to write so as to be enjoyable to read, either. I didn’t get any training in writing-to-be-read and I don’t remember seeing courses in that.) It’s also very hard to read something outside your specialty: the terminology and vocabulary and writing styles can be ferociously localized. Just today I was reading a WordPress post which started from the equations Euler used to describe the flow of viscosity-free fluids, which was at the heart of my thesis, and before eight paragraphs it had got into symbols I barely recognized and into points I’ll need to re-read and re-think before I can grasp them. And reviewing papers is really unappreciated; the best you can really hope for is to dig deep into the paper and understand it so thoroughly you can write a better version of it than the authors did, and so be thanked for making perceptive criticisms when the revised version of the paper comes out. The system makes it too easy to conclude something like “well, I don’t really have the time to understand all of this, but I on skimming it I don’t see anything plainly offensive to all persons, so, it probably makes sense to people who are looking for this kind of paper” and go on to a more pressing deadline, and I admit I don’t have a better system in mind.

I’m also reminded of a bit of folklore from my grad school days, in a class on dynamical systems. That’s the study of physics-type problems, with the attention being not so much on actually saying what something will do from this starting point — for example, if you push this swing this hard, how long will it take to stop swinging — and more on what the different kinds of behavior are — can you make the swing just rock around a little bit, or loop around once and then rock to a stop, or loop around twice, or loop around four hundred times, or so on — and what it takes to change that behavior mode. The instructor referred us to a paper that was an important result but warned us to not bother trying to read it because nobody had ever understood it from the paper. Instead, it was understood — going back to the paper’s introduction — by people having the salient points explained by other people who’d had it taught to them in conversations, all the way back to the first understanders, who got it from the original authors, possibly in talking mathematics over while at the bar. I’m embarrassed to say I don’t remember which paper it was (it was a while ago and there are a lot of key results in the field), so I haven’t even been able to figure how to search for the paper or the lore around it.

The Intermediacy That Was Overused

However I may sulk, Chiaroscuro did show off a use of the Intermediate Value Theorem that I wanted to talk about because normally the Intermediate Value Theorem occupies a little spot around Chapter 2, Section 6 of the Intro Calculus textbook and it gets a little attention just before the class moves on to this theorem about there being some point where the slope of the derivative equals the slope of a secant line which is very testable and leaves the entire class confused.

The theorem is pretty easy to state, and looks obviously true, which is a danger sign. One bit of mathematics folklore is that the only things one should never try to prove are the false and the obvious. But it’s not hard to prove, at least based on my dim memories of the last time I went through the proof. One incarnation of the theorem, one making it look quite obvious, starts off with a function that takes as its input a real number — since we need a label for it we’ll use the traditional variable name x — and returns as output a real number, possibly a different number. And we have to also suppose that the function is continuous, which means just about what you’d expect from the meaning of “continuous” in ordinary human language. It’s a bit tricky to describe exactly, in mathematical terms, and is where students get hopelessly lost either early in Chapter 2 or early in Chapter 3 of the Intro Calculus textbook. We’ll worry about that later if at all. For us it’s enough to imagine it means you can draw a curve representing the function without having to lift your pen from the paper.