December 2023: Mermin on writing physics
Boojums, spoons and dog turds
This month I’ve been reading Boojums All The Way Through, a collection of essays by the physicist N. David Mermin. I’d read some of it before as a PhD student (my second supervisor recommended the book for his advice on writing equations, which I’ll get to later) and was reminded of it last month when I came across his talk Writing Physics.
I always enjoy reading Mermin. He’s interested in the same conceptual topics at the heart of quantum physics and relativity that fascinate me, and also he’s always insightful about writing. Also, importantly, he’s funny. In this newsletter I’ll pull out a few highlights from Writing Physics and Boojums.
Boojums
I should probably start by explaining what the boojums are about. “Boojum” is a word Mermin introduced to describe a geometric pattern in a phase of superfluid helium which… well, tbh I know nothing about this topic and you can read Wikipedia just as well as I can, so here it is. The term comes from the last lines of Lewis Carroll’s poem The Hunting of the Snark:
He had softly and suddenly vanished away—
For the Snark was a Boojum, you see.
The idea is that the boojum pattern is what remains after a more symmetric pattern has softly and suddenly vanished away.
After coming up with the term, Mermin had to persuade people to use it. E pluribus boojum is about his campaign to make “boojum” the accepted scientific term, by first getting it in print in some conference proceedings, then getting other people to use it in similar venues, and then finally bootstrapping his way to a mention in Physical Review Letters after a protracted argument with the editors. At this point he had an authoritative source and his term could become the canonical one.
Spoons
My favourite section from Writing Physics is about reflections in spoons. I’ve quoted the whole section because it’s such a clear explanation:
If you are a scientist outreach can strike at any time. It hit me in the following form: "Why is it that when I look at one side of a spoon I see my reflection right side up, and when I turn the spoon over I see my reflection upside down?'' Please answer by Wednesday in 250 words suitable for a ten-year old. This turned into an all-day challenge. It helped not knowing any conventional optics, because I first had to figure out for myself that the spoon behaved as advertised. Then I looked in a spoon to make sure. It did. Then I had to decide what I could take for granted. In this case, how flat mirrors behave. Then I had to find a concise way to express the simulation of a curved mirror by a collection of flat ones. Then I had to find a way to say this in a language of spoons, not mirrors, anticipating and thwarting every imaginable misreading. Here's the result:
“To make it easier to picture, think of an enormous spoon, about as big as your head, not counting the handle. You can understand how a curved mirror behaves by thinking of it as built up out of lots of little flat mirrors. So suppose the enormous spoon is a wooden one, made to reflect by gluing a lot of little flat mirrors to both its surfaces, like mosaic tiles on the inside and outside of a dome.
“Now imagine holding the spoon vertically some distance from your face, and looking directly into the bowl part of the spoon, with the middle of the bowl at the level of your eyes. As you lower your eyes toward the lower part of the bowl, the little mirrors that you see will tilt upwards, so you see in them the reflection of the upper part of your face. But as you raise your eyes toward the upper part of the bowl, the little mirrors that you see will tilt downwards, so you see in them the reflection of the lower part of your face. In other words you see yourself upside down.
“On the other hand, if you turn the spoon so you're looking at the outside of its bowl, then as you lower your eyes the little mirrors that you see tilt downwards and you see a reflection of the lower part of your face, and as you raise your eyes the mirrors that you see tilt upwards and you see a reflection of the upper part. So reflected in that side, you look right-side up.''
You may not think so, but that is serious writing. The agony of producing it was similar to what I endured trying to produce the disquisitions on relativistic and quantum physics in the earlier parts of this lecture.
I definitely believe him about the difficulty of producing this explanation. This sort of conceptual distillation is hard. I’m a technical writer, and most of the time I write fairly formulaic things like tutorials and reference material, where there’s an standard structure and you just have to follow it. Sometimes, though, I get to write conceptual documentation, and that is a much harder task (also a more satisfying one when it works). You have to find a structure that makes sense of the material, rather than shoving it into the standard one. Normally you discover subtleties that you didn’t even realise were there when you started.
Mermin calls the formulaic type of writing “writing up physics”, to distinguish it from the sort of “writing physics” that transforms its subject:
… While there has to be something there before the writing begins, that something only acquires its character and shape through writing. My transformation of the spoon into a dome with mosaics is clearly not writing up physics. I like to think it is writing physics. The distinction between the two might shed some light on current debates in the "science wars'' between physicists and social constructivists. The physicists believe that there is a clean distinction between objective truth and mere social convention. They view physics as a process of discovering and writing up objective truths. Social constructivists — at least the ones I find interesting — maintain that objective truth and social convention are so deeply entangled that it's impossible to separate the two. For them physics is not writing up. Physics is writing.
(He says this “writing”/“writing up” distinction came from Jonathan Culler in an earlier talk in the series – unfortunately I can’t find a transcript of that one.)
There’s a great bit at the end on the collaboration between Landau and Lifshitz, authors of a famous textbook series:
It is also said that even Landau's profound technical papers were actually written by Lifshitz. Many physicists look down on Lifshitz: Landau did the physics, Lifshitz wrote it up. I don't believe that for a minute. If Evgenii Lifshitz really wrote the amazing papers of Landau, he was doing physics of the highest order. Landau was not so much a coauthor, as a natural phenomenon — an important component of the remarkable coherence of the physical world that Lifshitz wrote about so powerfully in the papers of Landau.
Dog turds
Finally, here’s What’s wrong with these equations?, where Mermin gives advice on how to add equations to writing. This is one of these topics where most scientists eventually end up learning something implicitly through reading and writing papers, but there isn’t much explicit written advice, other than this essay:
Nothing in freshman composition courses prepares us for the literary problems raised by the use of displayed equations. Our knowledge is acquired implicitly by reading textbooks and articles most of whose authors have also given the problem no thought. When I was a graduate teaching assistant in a physics course for non-scientists, I was struck by the exceptional clumsiness with which extremely literate students, who lacked even the exposure to such dubious examples, treated mathematics in their term papers. The equations stood out like dog turds upon a well manicured lawn. They were invariably introduced by the word “equations” as in “Pondering the problem of motion, Newton came to the realization that the key lay in the equation
F = ma.”
To these innocents equations were objects, gingerly to be pointed at or poked, not inseparably integrated into the surrounding prose.
(The PDF I linked above is the version that got published in Physics Today, rather than the version in the book. Sadly Physics Today changed all the dog turds into “droppings”. I guess that’s one fight with the editors that Mermin lost.)
Mermin has three rules, which boil down to 1. punctuate your equations and include them in the flow of text; 2. number all the equations, not just the ones you think someone might want to refer back to; and 3. if you refer back to an equation, describe it with some helpful short handle:
No compassionate and helpful person would herald the arrival of Eq. (7.38) by saying "inserting (2.47) and (3.51) into (5.13)..." when it is possible to say "inserting the form (2.47) of the electric field E and the Lindhard form (3.51) of the dielectric function e into the constitutive equation (5.13)”. To be sure, it's longer this way. To be sure, it's longer this way. Consistent use of the Good Samaritan rule might well increase the length of your paper by a few percent. But admit it. Your paper is probably already too long by at least 30% because you were in such a rush to get it out that you didn't really take enough care putting it all together.
That last rule also has a useful corollary. If you find yourself referring back to some equation that you can’t think of a good handle for, that’s a sign you have more work to do:
… is the equation itself essential? Or is it the kind of nasty and fundamentally uninteresting intermediate step that readers would either skip over or, if seriously interested, work out for themselves, in neither case needing to have it appear in your text? If so, drop it. You will then have to revise the argument that referred back to it, but the chances are good that clarity will benefit from not having at the heart of the argument an uncharacterizable monster of an equation.
This has got to be one of the most useful essays I’ve read. I’ve used the three rules over and over since submitting the dog-turd-strewn piece of text that prompted my second supervisor to get me to read this as a first year PhD student.
Other things this month
I’ve been slowly reading a couple of books with unusual ways of explaining special relativity: Bondi’s Relativity and Common Sense and Epstein’s Relativity Visualized. Might write a newsletter on this if I ever manage to digest them properly.
I went down a wikipedia hole about British public schools and ended up reading Thomas Hughes’s Tom Brown’s School Days as part of it. It’s the classic “school story” that set the conventions for the genre, based on the author’s own schooling at Rugby in the 1830s. I was surprised how much I enjoyed it! The stories of the messes he gets into are entertaining, and even the second half, where Hughes pivots into Improving Literature and has Tom stop cheating and poaching and start reading the Bible, is interesting from a historical point of view. Hughes was writing for boys who are going to go to public school themselves and who presumably have a lot of shared context about how they work that I’m missing, so it’s fun to try to fill in the gaps. (Why is there something called “School House” and separately something called “School”? OK, so “School” seems to be all the other houses put together, but why do they play an enormous rugby match against each other, and why are the sides so unbalanced? And why is Tom Brown automatically in School House with no explanation? I never really got to the bottom of this one.)
After that I had to reread Orwell’s Boys’ weeklies essay, which goes very well with it. The first chunk of the essay is about formulaic school stories in 1930s magazines, which still recycle the tropes from Tom Brown. (So does Harry Potter, for that matter. They just work.)
I liked Venkatesh Rao’s Charnel Vision a lot:
> This blog, of course, has been wandering about in a half-alive funerary haze through the last few years, trying to discover renewed purpose in the digital charnel ground that is the old blogosphere, and public social media generally.
I’ve been appreciating all his attempts to orient to the current mess and figure out how and what to write. They feel refreshing in a world where a lot of writers are either struggling to write anything or still derping their old derp in increasingly stale ways (I’ve been doing about 80:20 of each). Most of the ones I like are paid posts on his newsletter, so I don’t know how useful these links are going to be if you’re not a subscriber, but heres’s a couple: Fluid Fogs and Fixed Flows and Blithe Spirits and Heavy Souls.
Next month
I’m going to think about physics some more. No plans more specific than that.
Also right after sending this I’m going to log in to Twitter, after several months off, and soak in the digital charnel ground vibes.