Why do academics feel the need to stuff their papers with “nontrivial” results? After all, if a paper is remembered decades after it was written, it’s almost always for a simple core idea — not for the extensions and applications that fill 90% of the paper’s bulk.
The nontriviality virus can infect even the greats: think of Leonid Levin’s famous paper on universal search. According to legend, the reason Levin was scooped by Cook and Karp is that he spent a year trying to prove Graph Isomorphism was NP-complete! You see, that would’ve been a deep, publication-worthy result, unlike the “obvious” fact that there exist natural NP-complete problems.
Here’s a more recent example. In my opinion, this 43-pager by Barak et al. is one of the sweetest computer science papers of the past decade. But what makes it so sweet is a two-sentence insight (my wording):
There’s no generic, foolproof way to “obfuscate” a computer program. For even if a program looked hopelessly unreadable, you could always feed it its own code as input, which is one thing you couldn’t do if all you had was a “black box” with the same input/output behavior as the program in question.
So why did the authors go on for 43 more pages?
One possibility was suggested to me by Robin Hanson, an economist at George Mason who spews interesting ideas out of his nose and ears. Depending on your prejudices, you might see Robin as either a visionary futurist or a walking reductio ad absurdum of mainstream economic theory. Either way, his web page will surprise and provoke you.
When I talked with Robin in August, he speculated that nontrivial results function mainly as “certificates of smartness”: that is, expensive, difficult-to-fake evidence that the author(s) of a paper are smart enough that their simple core idea is likely to be worth taking seriously. Without these certificates, the theory goes, we academics would be deluged by too many promising ideas to entertain them all — since even if the ideas are simple, it usually isn’t simple to ascertain their worth.
Note that this theory differs from a more standard complaint, that academics fill their papers with nontrivial results for the sole purpose of getting them published. On Robin’s account, nontrivial results actually are useful to readers, just not in the way the paper advertises. Think of the author as a groom, the reader as a bride, and the nontrivial result as a wedding ring. The bride doesn’t care about the actual ring, but she does care that the groom was rich and devoted enough to buy one.
One prediction of Robin’s theory would be that, once you’ve established your smartness within the community, you should be able to get papers published even if they contain only simple observations. Another prediction would be that, if you’re very smart but emotionally attached to a simple idea, you should be able to buy exposure for your idea by encrusting it with nontrivialities. (As Robin remarked to me, everything in social science is either obvious or false; the only question is which.)
I don’t have anything deeper to say about Robin’s theory, but I’m enjoying the freedom to blog about it anyway.