What’s the story behind the unexpected hanging paradox?
This is one of my all-time favorite paradoxes. A man receives a death sentence. The judge says to him, "You will be put to death sometime next week—Monday through Friday—but the day will be a surprise." In his cell, the prisoner starts thinking it out. He concludes: "If I'm alive at the end of Thursday, then the execution has to be on Friday. But if I know this by Thursday evening, it won't be a surprise—so Friday is out." Which leads him to think: "If Friday is eliminated, then Thursday can't be either. But if I'm still alive by Wednesday evening, I'll know it will have to be on Thursday—and that means Thursday can't be a surprise either." Through this reverse reasoning, he continues to cross out days one at a time until he finally convinces himself that an execution next week is out of the question. And still—on Wednesday at noon—the executioner shows up, totally unexpectedly. The judge's threat was kept: the execution did occur, and it was indeed surprising. As with many paradoxes, this one toys with language and expectation. The inmate believed he was clever enough to outwit the system by thinking things through. But no amount of manipulatively twisting logic or rationalizing he was in the clear—he was wrong. The shock still occurred. It's similar to thinking you can win a game of sheer chance because you think hard enough.
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