The Clairvoyant Penny

http://commons.wikimedia.org/wiki/File:United_States_penny,_obverse,_2002.jpg

Mathematician Thomas Storer offers a foolproof way to foretell the future: Flip a penny and ask it a yes-or-no question. Heads means yes, tails means no.

How can you be sure the answer is accurate? Simple: Flip it again and ask, “Will your present answer have the same truth value as your previous answer?”

  • Suppose the answer is yes. This is either true or false. If it’s true, then the original response was true. If it’s false, then the truth value of the original response is not false, i.e., it’s true.
  • If the answer to the second question is no, this too is either true or false. If it’s true, then the original response was true. If it’s false, then the original response was not false, i.e., true.

Since all the outcomes agree, the penny’s original response is guaranteed to be correct.

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One Solution

The Professor brightened up again. ‘The Emperor started the thing,’ he said. ‘He wanted to make everybody in Outland twice as rich as he was before — just to make the new Government popular. Only there wasn’t nearly enough money in the Treasury to do it. So I suggested that he might do it by doubling the value of every coin and bank-note in Outland. It’s the simplest thing possible. I wonder nobody ever thought of it before! And you never saw such universal joy. The shops are full from morning to night. Everybody’s buying everything!’

— Lewis Carroll, Sylvie and Bruno

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