Chapter 9 EXTRA: Paul explains the Hangman's paradox

...... Paul looked intently at Wolfgang. "Imagine," he said, "that it's Monday and a guy is in a prison cell. He's going to be hanged and the jailer says that exactly at noon on some day during the week, they'll come in and take him out and hang him. But the jailer says the guy will never be able to figure out which day they'll come to take him. It'll always be a surprise." He glanced at the others. "Okay, so far?"
...... "Yeah," said Wolfgang.
...... "Fine," said Kip.
...... Alex didn't say anything.
...... Paul continued. "So the guy figures that if he's alive Saturday afternoon, then, since the following day, Sunday, is the last day, then they'll like have to take him out and hang him on noon Sunday. Still okay?"
...... "Yeah," said Kip.
...... Alex and Wolfgang nodded.
...... "Well, they can't take him on Sunday," said Paul, "because it wouldn't be a surprise."
...... "I think I see where this is going," said Wolfgang.
...... "So," Paul went on, "the guy figures that since they can't take him on Sunday, then if he's alive on Friday afternoon, they'll have to take him on Saturday. Okay?"
...... "I get the idea," said Kip. "And they can't take him Saturday, because it wouldn't be a surprise."
...... Paul nodded. "And he uses the same logic to prove they couldn't take him on Friday, or Thursday, or--"
...... "I get it," said Kip. "He's proved they can't ever hang him."
...... "Yeah," said Paul. "So they come in on, I don't know, like Tuesday and take him away. He is surprised--after he proved that he couldn't be surprised. And that's the paradox."
...... "It doesn't feel super, ultra-convincing," said Wolfgang after a few seconds where nobody said anything. "There might be something wrong with how you define surprise, or something like that."
...... "Yeah, I know," said Paul. "But it does like worry me a little."

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