Your g is my e – Has time come for a physics notation standard?

Standards make sure the nuts fit the bolts.
[Image Source: nutsandbolts.mit.edu]

The German Institute for Standardization, the “Deutsches Institut für Normung” (DIN), has standardized German life since 1917. DIN 18065 sets the standard for the height of staircase railings, DIN 18065 the surface of school bags to be covered with reflective stripes, and DIN 8270-2 the length of the hands of a clock. The Germans have a standard for pretty much everything from toilets to sleeping bags to funeral service.

Many of the German standards are now identical to European Standards, EN, and/or International Standards, ISO. According to DIN ISO 8610 for example the International Standard Day begins on Monday and the week has seven days. DIN EN 1400-1 certifies that a pacifier has two holes so that baby can still breathe if it manages to suck the pacifier into its mouth (it happens). The international standard DIN EN ISO 20126 assures that every bristle of your toothbrush can withhold a pull of at least 15 Newton (“Büschelauszugskraftprüfung” bristle-pull-off-force-test as the Germans call it). A lot of standards are dedicated to hardware supply and electronic appliances; they make sure that the nuts fit the bolts, the plugs fit the outlets, and the fuses blow when they should.

DIN EN 45020 is the European Standard for standards.

Where standards are lacking, life becomes cumbersome. Imagine every time you bought envelopes or folders you’d have to check they will actually fit to the paper you have. The Swedes have a different standard for paper punching than the Germans, neither of which is identical to the US American one. Filing cross-country taxes is painful for many reasons, but the punch issue is the straw that makes my camel go nuts. And let me not even get started about certain nations who don’t even use the ISO paper sizes because international is just the rest of the world.

Standards are important for consumer safety and convenience, but they have another important role which is to benefit the economic infrastructure by making reuse and adaptation dramatically easier. The mechanical engineers have figured that out a century ago, why haven’t the physicists?

During the summer I read a textbook on in-medium electrodynamics, a topic I was honestly hoping I’d never again have anything to do with, but unfortunately it was relevant for my recent paper. I went and flipped over the first 6 chapters or so because they covered the basics that I thought I know, just to then find that the later chapters didn’t make any sense. They gradually started making sense after I figured out that q wasn’t the charge and η not the viscosity.

Anybody who often works with physics textbooks will have encountered this problem before. Even after adjusting for unit and sign conventions, each author has their own notation.

Needless to say this isn’t a problem of textbooks only. I quite frequently read papers that are not directly in my research area, and it is terribly annoying having to waste time trying to decode the nomenclature. In one instance I recall being very confused about an astrophysics paper until it occurred to me that M probably wasn’t the mass of the galaxy. Yeah, haha, how funny.

I’m one of these terrible referees who will insist that every variable, constant, and parameter is introduced in the text. If you write p, I expect you to explain that it’s the momentum. (Or is it a pressure?) If you write g, I expect you to explain it’s the metric determinant. (Or is it a coupling constant? And what again is your sign convention?) If you write S, I expect you to explain it’s the action. (Or is it the entropy?)

I’m doing this mostly because if you read papers dating back to the turn of the last century it is very apparent that what was common notation then isn’t common notation any more. If somebody in a hundred years downloads today’s papers, I still want them to be able to figure out what the papers are about. Another reason I insist on this is that not explaining the notation can add substantial interpretational fog. One of my pet peeves is to ask whether x denotes a position operator or a coordinate. You can build whole theories of mixing these up.

You may wnat to dsicard this as some German maknig am eelphnat out of a muose, but think twice. You almots certainly have seen tihs adn smiliar memes that supposedly show how amazingly well the human brain is at sense-making and error correction. If we can do this, certainly we are able to sort out the nomenclature used in scientific papers. Yes, we are able to do this like you are able to decipher my garbled up English. But would you want to raed a whoel essay liek this?

The extra effort it takes to figure out somebody else’s nomenclature, even if it isn’t all that big a hurdle, creates friction that makes interdisciplinary work, even collaboration within one discipline, harder and thus discourages it. Researchers within one area often settle on a common or at least similar nomenclature, but this happens typically within groups that are already very specialized, and the nomenclature hurdle further supports this overspecialization. Imagine how much easier it would be to learn about a new subject if each paper used a standard notation or at least had a list of used notation added at the end, or in a supplement.

There aren’t all that many letters in the alphabets we commonly use, and we’d run out of letters quickly would we try to keep them all different. But they don’t need to be all different – more practical would be palettes for certain disciplines. And of course one doesn’t really have to fix each and every twiddle or index if it is explained in the text. Just the most important variables, constants, and observables would already be a great improvement. Say, that T that you are using there, does or doesn’t that include complex conjugation? And the D, is that the number of spatial coordinates only, or does it include the time-coordinate? Oh, and N isn’t a normalization but an integer, how stupid of me.

In fact, I think that the benefit, especially for students who haven’t yet seen all that many papers, would be so large that we will almost certainly sooner or later see such a nomenclature standard. And all it really takes is for somebody to set up a wiki and collect entries, then for authors to add a note that they used a certain notation standard. This might be a good starting point.

Of course a physics notation standard will only work if sufficient people come to see the benefit. I don’t think we’re quite there yet, but I am pretty sure that the day will come when some nation expects a certain standard for lecture notes and textbooks, and that day isn’t too far into the future.