Yet another weird SF fan

I'm a mathematician, a libertarian, and a science-fiction fan. Common sense? What's that?

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Yet another weird SF fan

Saturday, December 18, 2010

The Unexpected Hanging and Reality

There's a well-known paradox (explained here) about unexpected execution:

Once upon a time, on a Sunday evening, a prisoner was found guilty. The judge declared the prisoner would go to prison and be executed sometime in the coming week (Monday through Friday), but that the exact day would be a surprise for the prisoner. Now, the prisoner reasoned as follows: “I can’t be executed on Friday; because, in that case, it wouldn’t be a surprise. After Thursday, by process of elimination I’d know the exact day. So, Friday isn’t the day. But then, Thursday can’t be the day either. If I’m not executed by Wednesday, then I’ll know the day is Thursday, since I’ve just ruled out Friday. So, it’s not Thursday either. Similarly, it’s not Wednesday, Tuesday, or Monday. Hallelujah, I’m saved!”
This has had a real-world analog:

When the hangman failed to summon him from his cell by late December, Toshihiko Hasegawa, a convicted murderer, reckoned that, by the practices of Japan's penal system, he had at least one more year to live.

After weeks of intense foreboding over the approach of death, Mr. Hasegawa wrote his adoptive mother to tell her that he could at last breathe freely again for one more year, when he expected that his execution watch would resume.


Two days later, though, without any advance notice to him or his family, the 51-year-old prisoner was led from his cell and hanged.

In both cases, what appeared to be logical reasoning didn't quite work.


Anonymous Vader said...

The problem, of course, is that as soon as the prisoner is convinced that he can't be hanged on Friday, because it would then not be a surprise, it becomes possible for it to be a surprise.

An interesting variation on the Liar's Paradox, I think.

11:36 AM  

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