Sunday, 30 December 2012

Making maths easier to follow in sociology

One issue I have when I read a maths-heavy social science paper is that it's difficult to skim through them. Some people might think this is because they are denser and more complex. This is certainly true in some cases but I don't think that's actually the main issue. The key requirement for skimming is that you can start reading the text at any point. If I'm familiar with a topic I can usually jump into an interesting looking patch of text in a paper and go from there. It's good to have the additional definitions and background at the start of the piece for those who are new to the area but it can be safely skipped by anyone already aware of the issues.

Unfortunately this is rarely possible with maths as the symbols used are defined throughout the piece, so any skimming soon requires flicking back through the article to find the definition of each symbol. Some notation is used consistently enough for its meaning to be inferred from context but its pretty rare and the point of using mathematical notation is not to create a system of hieroglyphs that each cover a unique concept. What this inevitably means is that I have to start at the very beginning of a paper and work through in order to make sure I don't miss any definitions. I've read econometrics textbooks that use notation they defined three chapters earlier!

I think there might be a better way to do this.

What if every mathematical symbol in a paper could have its definition brought up by rolling the mouse over it or clicking on it.

I envision a latex package for it working something like the following:

\definemathsymbols{i}{An individual survey respondent.}
\definemathsymbols{\epsilon_{uik}}{The uniform component of measurement error.}

Any subsequent use of the symbol would insert the mouseover text on the right so that a reader who is skimming can easily find out what your idiosyncratic notation means.

Then if you wanted to redefine a symbol you would just use the command again:

\definemathsymbols{i}{The currently selected ego in the simulation.}

These definitions are not designed to give a complete understanding of what's being done in the paper but they should allow a casual reader to skim a few equations and work out whether it's worth diving deeper into.

Not sure of the technical difficulties in implementing this but I think it could make a reader's job much easier.

If anyone wants to collaborate on writing a package or pointing in the direction of an existing one I'd be interested to hear from you.

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