66: The Diminishing Returns of Double-Checking: A Phenomenological and Mathematical Sketch
(Epistemic status: Morally correct; based on lived experience and some hand-wavy probability theory that holds up shockingly well.) Picture this: You're working on something with reasonably high stakes - coding a function on a deadline, writing up a proof, filling out a form or application, or taking a test. You check it once, and it looks good. But a nagging feeling remains - should you check again? And again, after that? And at what point do you actually stop? I'm particularly bad about this. My natural inclination is to check things twice, three times, sometimes four or more times before I throw up my hands and call it good. And I've noticed something curious about the phenomenology of each successive check - they feel different in a way that maps surprisingly well onto the actual mathematics of error detection. On the first check, you're sharp, with focused attention. You're tacitly assuming that you've made an error, but just one error, and one that you can...