Really good point. That always annoys me with most formulas. I have to dig back several paragraphs (with no scope/indexing tool) to figure out what the individual variables mean.
And a lot of papers do not even bother to explain some variable but just assume the reader already knows it.
One of the earlier commenters made this mistake very prominently enthusing over Maxwell's equations.
Yes of course the formula looks better shorter when you already know what it means. But that completely misses the point that it was written down to explain it to someone who doesn't already know what it means. If you already do you're the wrong target audience.
Longer variable names would help. Or for online paper just have a tooltip that opens the paragraph that explains what the variable mans when you hover over it would also help a lot.
Or maybe some color coding to easily find it (there was a recent link here recent explaining FFT which used this trick very successfully)
But I guess most Mathematicians don't bother because they only write for a small circle of colleagues anyways.
Maxwell's equations were not "written down to explain it to someone who doesn't already know what it means". They, quite simply were written down to express relationships between the motion of charge, and the behavior of electric and magnetic fields as a consequence.
You have to understand the physics behind the equations (what's charge? what's an electric field) as well as the mathematical structure (what's a vector space? what's a line integral?) in order to make use of them. They are equations used to answer questions like "What happens to the strength of this magnetic field if I increase the velocity of this charged particle responsible for generating it"? They aren't meant to be explanatory (but have the beautiful side-effect of explaining how light propagates in a vacuum.)
I agree with you. A book that aims to TEACH should provide the most common form of the equation and provide detailed annotations of what everything is. (Wikipedia should be like this as well since I know no one is using it as a reference).
For a REFERENCE, you can just list the equations in their most commonly used form.
And a lot of papers do not even bother to explain some variable but just assume the reader already knows it. One of the earlier commenters made this mistake very prominently enthusing over Maxwell's equations.
Yes of course the formula looks better shorter when you already know what it means. But that completely misses the point that it was written down to explain it to someone who doesn't already know what it means. If you already do you're the wrong target audience.
Longer variable names would help. Or for online paper just have a tooltip that opens the paragraph that explains what the variable mans when you hover over it would also help a lot.
Or maybe some color coding to easily find it (there was a recent link here recent explaining FFT which used this trick very successfully)
But I guess most Mathematicians don't bother because they only write for a small circle of colleagues anyways.