Simple solution: in a program source, create a very clear comment header that won't be missed, that explains the meanings of the variables. Also, even though physicists can use any names or lengths they like in their papers, they seem to prefer concision: f = G M1 M2 / r^2 If the reader understands the math, short variable names aid comprehension, not the reverse.
This actually bothered the hell out of me. For anything more complicated that highschool physics, this is terrible. You start to run out of letters and start using capitals and noncapitals, and even worse is that there are some "globals" that are not really variables but well-known constants. So you're trying to distinguish between uppercase / lowercase / variable / constant and keep all that in your head. There real…
Fair enough, but don't forget the Greek alphabet, both upper and lowercase. There are plenty of math notation issues, but a shortage of symbols isn't on the list. I don't think anyone in physics thinks multiple-character variables solves any real problems. Practitioners are more likely to craft a new symbol, like h-bar (ℏ) for the reduced Planck's Constant, at the point where ordinary h wasn't adequate:
ℏ = h / 2 π
> There really is no logical reason to do this, other than established practice.
I can think of one logical reason -- it works for people who don't think very much about the symbols because they're thinking about the math.
> Don't even get me started on the mathematician way of explaining things, where instead of explaining the concept and filling in the gaps, you take a 20 variable equation and start by describing all the variables one by one.
I won't try to excuse every example of this, but in physics, explaining each variable and constant is a very good way to approach an understanding of the equation as a whole.
> By the time you reach the end, you can't remember what the beginning did, so you have to go back and forth all the time.
That's temporary, it only lasts until real familiarity sets in, until the relationships become instinctive. It's like the old joke about prisoners who tell jokes by number.