What on Earth does typesetting have to do with vector calculus, you ask? I’m glad you asked. Let me explain! First, (some) history of Linotype typesetting. Actually, there’s a video. The video is from this bunch of people who are going to make a movie about the history (and joy) of the Linotype typesetting machine.
The Wikipedia article about Linotype is quite informative as well. Linotype, for the first time, let people get on with the job of typing and did the job of putting together the characters automatically. The Linotype is one of two basic types of hot-metal typesetting: Monotype, single-character typesetting, and Linotype, single-line typesetting, both developed in the 19th century.
Keep in mind also that Donald Knuth, the
inventor god of TeX, only started work on TeX in 1977, after a book he sent off to be typeset came out badly done. He wanted a way of typesetting his documents himself. ‘You know what, I know you’re the ‘professional’ typesetters, but I can do this better… There. I’ve written a computer program to replace you.’
This brings me to the connection between typesetting methods and the Laplacian in cylindrical coordinates. You see, I was reading a paper by B.R.Morton. That name, by the way, is among the more recognisable names in fluid mechanics. The paper is from Physics of Fluids, October 1967. The paper deals with entrainment models for laminar jets and plumes, which may not be of concern to the reader here (or perhaps they are, but never mind that), and therefore uses the Navier-Stokes equations.
Here’s one component of the momentum equation that the paper presents:
There’s only one problem with that equation: it’s wrong. The radial component of the Laplacian, to be specific, is wrong. Here’s what that bit should actually say:
How do I know that the mistake was generated in typesetting, and not made by the author? Well, for one, this equation is referred to in the paper at fifteen different places. I find it hard to believe that the author referred to an equation that often and didn’t look at it even once. The paper is from before the age of TeX, before the age of digital typography. Which means that somebody who probably didn’t know vector calculus was given the job of typesetting the article.
If you’ve read the Linotype or the hot-metal typesetting articles on wiki, you know enough to see what I think happened with the equation. The (1/r) and the (r) got pulled to the right one spot each. And because this was the age of mechanical typesetting, the error couldn’t be corrected without a lot of expense, and was left as it was. I don’t know if an erratum was published in the journal along with the article; I wouldn’t be too surprised if that were the case.[hr]
Yes, I realise that this was probably too Sheldon-Cooperish for most people’s liking (who’s seen the game that Drs. Cooper and Farah-Fowler have invented? It’s called ‘Counterfactuals’…).
Hat-tip: Srinivas, for the video.
[End. Fini. Kaputski. Linotype. Laplacian!]