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Saturday, December 4, 2010

Gardner Strikes Again

For today's amusement, a paradox quoted directly from Martin Gardner's "The Jinn From Hyperspace":

"Now for a final paradox. There is a certain event that I guarantee will or will not take place during the next ten minutes. You are absolutely incapable of predicting correctly whether it will or won't occur. I don't mean that it's unlikely you can predict it. I mean it is logically impossible to predict it!
"You don't believe it? Then do the following. If you think the event will occur write "Yes" inside the blank rectangle below. If you think it won't happen, write "No" inside the rectangle.
"If you predicted correctly, I'll send you a million dollars.
The event is: You will write "No" inside the rectangle."


As Gardner might say, "Gotcha!"

This is just one of many paradoxes entangled with self-reference and classic problems of causation/prediction when dealing with human language and logic.

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