The Orthography of Equations

Posted by jns on 21 July 2010

Every now and then this little image appears on my Facebook page, as a sponsored ad, with the headline “Become a Physics Teacher”. The sponsors claim that they will help me get a master’s degree online in education so that I can become a physics teacher.

Now tell me, if you were considering paying someone to help you get certified in, say, programming C++, how would you respond if the image in their add had this programming fragment:

i = i + 1;

I don’t know that the above is a very clear analogy to any of you, but the point is this: if the ad in question displays a lack of knowledge of the idioms of the discipline, should you trust the advertiser to provide what’s on offer in a reliable way?

Why do I object to this little image? May I see a show of hands from the physical scientists who know the answer please?

Yes, that’s right. In this most famous equation from physics, a result of Einstein’s Special Theory of Relativity, the letters ‘m’, representing mass, and ‘c’, representing the speed of light in vacuum, are never, ever written as upper-case letters; they are always, invariably written in lower case. I should, perhaps, be more grateful that the ’2′ is at least written as a superscript.

A tiny detail, a nit that I’m picking? Would you trust a brain surgeon with dirty fingernails? A car mechanic who’s not aware of what a “spark plug” is called?

Long ago I started to draft a blog entry called “On the Orthography of Equations”, but I never got around to it. It was going to relate a story and draw some interesting conclusions.

The events of the story happened, now, some 20 years ago. I was talking to a secretary in our University department who was typing (yes, on a typewriter) a paper for another faculty member. She asked for some advice on how to type an equation. While I was answering her question I mentioned that if she put some space between two symbols and moved another to a slightly different place that the equation would be significantly easier to read.

“Easier to read?” she exclaimed. Clearly the idea that equations were somehow “read” rather than merely looked at surprised her. And that was when I realized that, to this secretary and likely to most people with relatively little mathematical training, the symbols in equation were mostly decorative and they did not realize that how the symbols are deployed affect the meaning and readability of the equations.

I was nearly as surprised as she to discover this, although it’s an observation I’ve never yet figured out what to do with. Neither am I sure that this was the blog post that I was going to write, but there you go–it’s the one you got.