Ineffective Theory

Expository content is underrated

I am increasingly of the view that expository (dare I say pedagogical? no) content is severely underrated. When I say that, I mean two things:

  1. The writers (or more generally, creators) of quality exposition do not receive as much prestige as they should.

  2. Potential expository writers underestimate the amount of credit they would receive, even taking the first point into account.

Both are true at many levels, but particularly so at the “top”, or at any frontier of knowledge. My direct experience is mostly in physics research, but I’ve begun to see the same pattern elsewhere, enough to suspect that it’s a general phenomenon, particularly occurring anywhere novelty is valued. (More on that connection at the end.)

It’s pretty remarkable for both to be true. If true, the consequences are pretty clear. Everybody should spend more time both producing (fixing point 2) and recommending (1) expository articles. (Presumably funding agencies should tweak their behavior, as well as hiring committees, and so on.)

That leaves us with: why should anyone believe the two claims above are true? Certainly research papers outnumber expository papers by an order of magnitude or two. The average expository paper is read more (that’s the point!), while being somewhat less likely to be cited, at least per read.

Perhaps relatedly, the median research paper is of far lower quality than the median expository work. I expect that a world where more people are producing exposition will have a lower quality median and a higher quality maximum. Since it’s usually fairly cheap to select high-quality papers, there’s no major cost to lowering the median, and of course there’s a large benefit to improving the maximum.

Finally, it’s notable that the best way to learn something at the frontier is, by a large margin, to find the inventor and talk. This isn’t true for more mundane things like calculus, where the inventors are dead and would do a terrible job explaining anyway. For these lower-level topics, enough time and effort has been put into constructing high-quality explanations that it’s pretty feasible to learn from a nice video or set of lecture notes (or both).

Leaving academia and moving to software, let’s consider Rust libraries. There is certainly no shortage of Rust GUI libraries. But tutorials for using these libraries are scarce. To take a particular example, consider iced: one year ago, there were none. A similar situation exists across the other most commonly used libraries.

Or, libraries for parser combinators. There are a few options, so again, no shortage of actual libraries. But explanations of how to use these are surprisingly scarce. Such articles are, in some sense, redundant. Expository work always is. If you want to know how to use combine, just learn about parsec. But that’s more work — vastly more for anybody not familiar with functional programming. Reducing time-to-learn is valuable.

I don’t think I’m alone in noting that expository content is underrated: see for instance Grant Sanderson. But I want to emphasize here the value of expository content being produced at or near the frontier; in other words, for researchers. I badly wish there was more of it.

Finally, a note about novelty. It is completely reasonable to read the above and object:

But this is little more than a call to devalue novel contributions relative to educational work! The purpose of research is novel work, the purpose of education is pedagogical work, and the desire to confuse the two is just a manifestation of a deeper desire to redirect funding to people who, to be frank, find the former out of reach.

Such requests have been made before, and amount to mere value judgements about what type of contribution (or, perhaps, what type of contributor?) is more important. Such judgements are not my intention here.

(There’s an easy reply, along the lines of “oh, you’re overestimating how novel most research really is”. This is simultaneously true, irrelevant — suppressing a distribution also suppresses the tail — and an incredibly lazy jab at an entire area of human endeavor.)

No, I claim that our hypothetical objector is underestimating the novelty of high-quality expository work. Finding efficient explanations is difficult. Exposing information to new audiences is difficult. Drawing connections between old results and new trends is difficult. And these aren’t difficult in the sense of “boring work that takes a lot of time” — these are tasks that have a lot of intellectual content.

Knowledge isn’t just a list of propositions that are true, or a list of programs that have been written. The meat of knowledge is just as much in the connections between the facts, and that’s the stuff that good explanations are meant to reveal. The alchemists, measured by man-hours, spend nearly all of their time on those explanations, not the ostensible frontier.