Writing On The Pareto Frontier
I have a personal rule: don’t write something which someone else has already written better.
This is easier than it sounds. For instance, suppose I’m writing an intro to systems biology. I don’t need it to be the most comprehensive intro ever written, or the most accessible intro. I just need it to be good enough on each of these axes that no other work is better on both at once.
In other words, I try to always write things which are the Pareto Best In The World.
Of course this generalizes to more dimensions as well: I might also care about writing something rigorous, or communicating intuitions, or making the piece enjoyable to read, or including good visualizations, or …. I don’t need to write the best piece in the world along any particular dimension. I just need to write a piece good enough on enough dimensions that nothing else beats it on every dimension which I care about.
Ways To Be On The Pareto Frontier
One natural way to be on the Pareto frontier is to write about a new idea, or at least an idea unusual enough that few people have written about it.
As with writing, new ideas are not necessarily that difficult to find. The trick is to combine things: finding a novel and interesting idea in complexity theory is a lot harder than finding a novel and interesting application of complexity theory to caricature art. On the LessWrong frontpage right now, there’s an interesting post about applying the idea of film study (i.e. athletes watching films of their games) to become better at research. I’ve been writing a whole series of posts intended to practice applying frames from math in unusual ways, and some interesting novel ideas have already come out of them—e.g. optimizing multiple imperfect filters.
Research goes through a pipeline. First, researchers write papers, packed with jargon and assuming lots of background context. As results come together, they get boiled down into overview papers. Then come textbooks and programming libraries. Eventually, there might even be courses.
At each of those steps, work is done to distill the results—to explain them, draw analogies, add visuals, suggest exercises and applications, etc. In general, there’s a Pareto frontier with new cutting-edge results along one axis, and well-distilled results along the other. Pushing that Pareto frontier outward means finding some result which hasn’t been explained very well yet, understanding it oneself, and writing that explanation.
Note that Pareto optimality is again relevant to choosing examples/explanations: different examples will make sense to different people. Just offering very different examples from what others have written before is a good way to reach the Pareto frontier.
<Topic> For <Audience>
Probably the most successful statistics book in the first half of the twentieth century was Fisher’s Statistical Methods for Research Workers, which was essentially a repackaging of statistics for biologists. Glancing at my bookshelf, I see Basic Category Theory For Computer Scientists. COVID posts aimed at the rationality community have been a hot topic over the past year-and-a-half.
In general, a natural way to find a Pareto frontier is to pick a topic, pick an audience which doesn’t usually specialize in that topic, and write an intro to the topic for the audience.
Of course, this requires some background knowledge on both the topic and the audience—e.g. writing “Statistics for Biologists” requires background in both statistics and biology. So, it overlaps nicely with Being The Pareto Best In The World. The writing aspect also adds another dimension: it’s not just statistics and biology skills which are relevant, but writing skills as well. That means there’s three axes along which our skill could be Pareto optimal—and the more axes, the more “elbow room” we have on the Pareto frontier.
Context & Background
One question I get all the time about my work is “Why is <particular result> interesting?”; I sometimes write posts which give more context, but often I just write up results.
Some writing optimizes for communicating an idea clearly. Other writing optimizes for explaining why the idea is interesting/useful, or where it came from, rather than explaining the idea itself. These are both useful, so they’re both axes relevant to Pareto optimality of writing.
Another example: if you want to know why high-school calculus is interesting, then a physics class or a history book (like History Of √-1) will give more context than studying calculus itself. (In fact, this was how I first picked up calculus in high school—the actual calculus course came a few months later.)
Finally, obviously, writing can be optimized to be fun to read. Embedding interesting ideas in fiction, for instance, is one cool way to reach a Pareto frontier. Just writing fun-to-read nonfiction is also great—whether it’s James Mickens’ rants on computer security, or visual proofs from Euclid’s elements, or drawings of the internals of everyday objects with cartoon mammoths.
All of these different dimensions—novel ideas, distillation, targeting, context/background, fun writing, and plenty of others which I didn’t get to here—are different things one might want from a piece of writing. They are all different ways to be on the Pareto frontier, and any combination of them is also a way to be on the Pareto frontier.
To achieve Pareto optimality, a piece of writing does not need to have completely novel ideas or amazing distillation or be super fun to read or …. It just needs to be good enough on enough of those axes that no other piece of writing is better on all of them.