Why the ‘Sleeping Beauty Problem’ Is Keeping Mathematicians Awake

Usually, there are clear answers in mathematics—especially if the tasks are not too complicated. But when it comes to the Sleeping Beauty problem, which became popular in 2000, there is still no universal consensus. Experts in philosophy and mathematics split into two camps and ceaselessly cite—often quite convincingly—arguments for their respective side.

Put yourself in the position of Sleeping Beauty: You wake up, you don’t know what day it is, and you don’t know if you have been woken up before. You only know the theoretical course of the experiment. What are the probabilities for each event? You can investigate this both mathematically and empirically. Suppose you flip a coin 100 times and get tails 52 times and heads 48 times. Put another way, the Monday/heads scenario occurs 48 times, and Monday/tails and Tuesday/tails occur 52 times each.

According to the calculus of conditional probabilities, it follows that in the general case , the three values are equal: P=P=P. Because all three probabilities must add up to 1, each individual value is ⅓. In other words, because Sleeping Beauty is awakened twice as often in the case of tails as in the case of heads, she should answer with ⅓, from Elga’s point of view.

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