And how is not this the most reprehensible ignorance, to think that one knows what one does not know? But I, O Athenians! in this, perhaps, differ from most men; and if I should say that I am in any thing wiser than another, it would be in this, that not having a competent knowledge of the things in Hades, I also think that I have not such knowledge.
Shtetl-Optimized’s Mistake of the Week series finally resumes today, with what’s arguably the #1 mistake of all time. This one’s been noted by everyone from Defense Secretary Donald Rumsfeld, to some toga-wearing ancient dude, to the authors of the paper Unskilled and Unaware of It: How Difficulties In Recognizing One’s Own Incompetence Lead to Inflated Self-Assessments.
Rather than give examples of this mistake — where would I start? where would I stop? how often have I made it myself? — I figured it’d be easier to give an example where someone didn’t make it. Today I received an email from a graduate student who had proved a quantum oracle separation, and wanted to know whether or not his result was too trivial to publish. I get fan mail, I get hate mail, I get crank mail, I get referee requests, but this is something I almost never see. After telling the student why his result was, indeed, too trivial to publish, I wrote:
There’s no shame in proving things that are already known, or that follow easily from what is. Everyone does it, the more so when they’re just starting out … The very fact that you cared enough to ask me if your result is trivial bodes well for your proving something nontrivial.