23 December 2006

Alice in Puzzle-Land

“How do I know for sure that I'm awake?” asked Alice. “Why can't it be that I'm now asleep and dreaming all this?”

“Ah, that's an interesting question and one quite difficult to answer!” replied the King. “I once had a long philosophical discussion with Humpty Dumpty about this. Do you know him?”

“Oh, yes!” replied Alice.

“Well, Humpty Dumpty is one of the keenest arguers I know—he can convince just about anyone of just about anything when he puts his mind to it! Anyway, he almost had me convinced that I had no valid reason to be sure that I was awake, but I outsmarted him! It took me about three hours, but I finally convinced him that I must be awake, and so he conceded that I had won the argument. And then—”

The King did not finish his sentence but stood lost in thought.

“And then what?” asked Alice.

“And then I woke up!” said the King, a bit sheepishly.

—Raymond Smullyan, Alice in Puzzle-Land. This is a fun book of logic puzzles ranging from cute to outrageously intricate. A fine gift for the mathematician on your list (though I hear The Annotated Alice is even better).

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