Here is a 3-paragraph summary of the blog post "Sleeping Beauty and ChatGPT":
The Sleeping Beauty problem is a classic probability puzzle that goes like this: Sleeping Beauty is put to sleep on Sunday while a fair coin is flipped. If the coin lands heads, she wakes up only on Monday. If it lands tails, she wakes up on both Monday and Tuesday. Each time she wakes up, she has no memory of any previous awakening, and she is asked: what is the probability that the coin landed heads?
This deceptively simple question has divided mathematicians and philosophers for years, producing two main camps. "Halfers" argue the probability is 1/2, since the coin is fair and no new information has been gained upon waking. "Thirders" argue the probability is 1/3, reasoning that there are three equally likely scenarios in which Sleeping Beauty could find herself awake, and only one of them corresponds to heads. The blog post explores this debate and puts it to the test in a creative way, by asking ChatGPT to weigh in on the problem.
The experiment with ChatGPT adds a fun and modern twist to this long-standing puzzle, raising interesting questions about how AI systems reason through philosophical and probabilistic dilemmas. Whether ChatGPT sides with the halfers or thirders, the exercise highlights just how tricky questions about self-locating belief and probability can be, even for sophisticated language models. The Sleeping Beauty problem remains a wonderful example of how mathematics and philosophy intersect in surprising and thought-provoking ways.