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Monday, February 3, 2014

Re-visiting Sleeping Beauty

(via Rachel CALMUSA/WikimediaCommons)

In chapter 11 ("Is Time an Illusion") of Max Tegmark's new book "The Mathematical Universe" the author, while discussing the nature of time and human consciousness, touches upon the "Sleeping Beauty" puzzle/paradox, which I mentioned here almost two years ago:

http://math-frolic.blogspot.com/2012/03/sleeping-beautynot-your-childhood-fairy.html

This is one of the most interesting and delicious (perhaps even complicated, in some ways) puzzles around, as people argue vociferously for either of two different answers (1/2 or 1/3), because of the conditional probabilities involved.
[Here is one statement of the puzzle: Sleeping Beauty undergoes the following experiment, being told all these details ahead of time. On Sunday she will be put to sleep. A fair coin will then be tossed to determine which experimental procedure is undertaken. If the coin comes up heads, Beauty is awakened and interviewed on Monday, and the experiment ends. If the coin comes up tails, she is awakened and interviewed on Monday AND Tuesday. But when she is put to sleep again on Monday, she is given an amnesia-causing drug which ensures she cannot remember the prior awakening. In this case, the experiment ends after she is interviewed on Tuesday.  Whenever Sleeping Beauty is awakened and interviewed, she is asked, "What do you believe is the probability that the tossed coin landed on  heads?" -- What is her answer?]
In re-visiting the links I provided in my original blog post I discovered that the "Tanya Khovanova" link has since added further lo-o-ong discussion of the issues by two commenters back-and-forth, which is probably worth checking out if you are especially interested in probability in general, or this problem in particular (if these areas don't interest you, don't visit it, lest you fall into a deep, deep coma, or alternatively, your head explode ;-)

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