Is Your Theory of Everything Pure Enough?
by Giulio Chiribella
Feb 19, 2015
4 minutes
Let’s play a game. You get a box with two compartments and one ball. The ball could be in either compartment with equal probability, and my job is to guess which one. Ok, it’s not the most exciting game, but at least it’s fair. My odds are 50/50.
But suppose I know that your box was produced in a factory where a conveyor belt brought boxes to a cannon, which shot balls into one compartment or another depending on a coin toss. The coin toss was done once a day, and all the boxes produced on the same day have the ball in the same compartment. If I managed
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