Date: Mon, 14 Jan 2008 13:51:52 -0500 From: "William J. Rapaport" Subject: The Surprise Fire Drill (a paradox?) ------------------------------------------------------------------------ Subject: The Surprise Fire Drill (a paradox?) ------------------------------------------------------------------------ Today in class I told you that I had been told that there was going to be a fire drill. But there wasn't, which surprised me. That makes what (didn't) happen an interesting example, more or less, of a paradox called the "Surprise Hanging" (also known as the "Unexpected Hanging" or the "Surprise Examination"). One version of the story goes like this: A defendant is found guilty and sentenced to be hanged(*) within the week on the condition that the hanging will be a surprise. The defendant is distraught, but his lawyer is ecstatic. The lawyer explains that the sentence cannot be carried out: He cannot be hanged on Friday (the last day of the week), because if he hasn't been hanged by then, he'll know that he has to be hanged on Friday; but then it won't be a surprise. He cannot be hanged on Thursday, because (1) we just ruled out Friday, and (2) by the same reasoning as before, if he wasn't hanged before Thursday, then being hanged on Thursday won't be a surprise. Similar reasoning rules out all the other days of the week. However, the defendant is hanged on Wednesday; it came as a complete surprise! There are many attempts to resolve the paradox. In my opinion, the most interesting is by my CSE colleague, Prof. Stuart C. Shapiro: Stuart C. Shapiro, A Procedural Solution to the Unexpected Hanging and Sorites Paradoxes, Mind 107, 428 (October 1998) 751-761. preprint version: http://www.cse.buffalo.edu/~shapiro/Papers/hangman.pdf archival version (may only be accessible from buffalo.edu computers): http://www3.oup.co.uk/jnls/list/mind/hdb/Volume_107/Issue_428/pdf/1070751.pdf ------------------------------------------------------------------------ (*) Yes, "hanged". If you hang a picture on the wall, it has been HUNG up. But if you hang a human, he or she has been HANGED. English is strange. Date: Mon, 14 Jan 2008 14:59:41 -0500 From: Saleh Sayad Subject: Re: The Surprise Fire Drill (a paradox?) actually there was a Fire Drill It happened minutes before you came to class Date: Mon, 14 Jan 2008 15:09:36 -0500 From: "William J. Rapaport" Subject: Re: The Surprise Fire Drill (a paradox?) Aha! thanks for the update! I had been told it would be during the 9:00 a.m. hour. Date: Mon, 14 Jan 2008 15:38:56 -0500 From: "William J. Rapaport" Subject: Re: The Surprise Fire Drill (a paradox?) | Date: Mon, 14 Jan 2008 15:21:10 -0500 | From: Chandah Agrawal | Subject: Re: The Surprise Fire Drill (a paradox?) | | Sir but what about the day tuesday! It would come as a surprise too. | Monday wont be a surprise because the defendant would already be | thinking about first day of the week when he is about to be | hanged. So will tuesday also do the job Yes--the guilty person can be hanged on any day; it will always be a surprise, despite the fact that the lawyer has reasoned apparently logically that he cannot be hanged on any day! Date: Mon, 14 Jan 2008 16:00:22 -0500 From: Devanshu Pandey Subject: Re: The Surprise Fire Drill (a paradox?) Hello Professor, Well the solution by Dr. Shapiro was quite long so I didnt read all of it. But may be hanging the criminal on Wednesday came as a surprise because he could be hanged two days before or two days after Wednesday. So he wouldn't know what to think. -Devanshu Pandey Date: Tue, 15 Jan 2008 09:44:49 -0500 From: "William J. Rapaport" Subject: Re: The Surprise Fire Drill (a paradox?) For more background on the Unexpected Hanging paradox (a bit less technical than Prof. Shapiro's article :-), take a look at: Gardner, Martin (1969), The Unexpected Hanging and Other Mathematical Diversions (New York: Simon & Schuster), Ch. 1: "The Paradox of the Unexpected Hanging", pp. 11-23, 245-246. http://www.amazon.com/gp/reader/0226282562/ref=sib_dp_pt/104-8529091-2424706#reader-link Also see: http://mathworld.wolfram.com/UnexpectedHangingParadox.html Date: Tue, 15 Jan 2008 13:21:24 -0500 From: Dan Padgett Of course, now that you told everyone that the TAs can give surprise quizzes, they can only be given on Wednesdays. William J. Rapaport wrote: > Sorry folks--I hit "send" too soon--the message about recitations was > intended for the TAs, not for you. Date: Tue, 15 Jan 2008 13:28:25 -0500 From: "William J. Rapaport" | Of course, now that you told everyone that the TAs can give surprise | quizzes, they can only be given on Wednesdays. ... and won't you be surprised if they're not! :-)