Sunday, September 10, 2006

Tony Blair: The Unexpected Hanging

Tony Blair's current position - he has said he will go within a year but doesn't want people to know when he will go - reminds me of "The Paradox of The Unexpected Hanging". In this a prisoner is sentenced to death and the judge tells he will be hanged one day in the next week, and that the execution will be a surprise to him - he won't know the day of the hanging. The prisoner thinks about this and decides he can't possibly be hanged on Friday; if he got through Thursday without being hanged, he would know that the hanging would have to be on Friday, so it would not then be a surprise. He applies similar reasoning to the rest of the week and decides that it is impossible to satisfy the judge's conditions, and so the sentence cannot be carried out. Thursday comes along and he is hanged, to his surprise, and the judge's conditions have been satisfied.

I first came across the unexpected hanging in Martin Gardner's "Unexpected hanging and Other Mathematical Diversions". I've done a brief search and it seems that the analysis of this paradox has moved on from the one given in Gardner. The (current) article in Wikipedia is intresting. I find the shortened version of the paradox particularly revealing. In this the prisoner is told he will be hanged the next day and that it will be a surprise.

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